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```Department of Mathematics
The Ohio State University
2016-2017 Mathematics Courses
Course
Number
1050
1075
1116
1118
1125
1126
1130
1131
1135
1136
1148
1149
1150
1151
1152
1156
1157
1161.01
1161.02
1165
1166
1172
1181H
1187H
1295
2137
2138
2153
2162.01
2162.02
2167
2168
2173
Course Title
Precollege Mathematics I
Precollege Mathematics II
Excursions in Mathematics
Mathematics for Architects
Mathematics for Elementary Teachers I
Mathematics for Elementary Teachers II
Number and Operations for Teachers
Measurement & Geometry for Teachers
College Algebra
Trigonometry (Autumn 2016)
Trigonometry (Spring 2017)
Pre-Calculus
Calculus I
Calculus II
Calculus for the Biological Sciences
Mathematical Modeling for the Biological Sciences
Accelerated Calculus I
Accelerated Calculus I for Honors Engineers
Math for Middle School Teachers I
Math for Middle School Teachers II
Engineering Mathematics A
Honors Calculus I
Honors Problem Solving
Introductory Seminar
Algebra and Coordinate Geometry for Teachers
Calculus and its History for Teachers
Calculus III
Accelerated Calculus II
Accelerated Calculus II for Honors Engineers
Calculus for Middle School Teachers
History of Mathematics for Middle School Teachers
Engineering Mathematics B
Course
Number
2174
2177
2182H
2255
2366
2415
2568
3345
3350
3532
3588
3589
3607
3618
4181H
4182H
4350
4504
4507
4512
4530
4545
4547
4548
4551
4552
4556
4557
4568
4573
4575
4578
4580
4581
5520H
5522H
5529H
5530H
5540H
5576H
Course Title
Linear Algebra & Differential Equations for Engineers
Mathematical Topics for Engineers
Honors Calculus II
Differential Equations and Their Applications
Introduction to Discrete Mathematics
Ordinary and Partial Differential Equations
Linear Algebra
Foundations of Higher Mathematics
Introduction to Mathematical Biology
Mathematical Foundations of Actuarial Science
Practicum in Actuarial Science
Introduction to Financial Mathematics
Beginning Scientific Computing
Theory of Interest
Honors Analysis I
Honors Analysis II
Quantitative Neuroscience
History of Mathematics
Geometry
Partial Differential Equations for Science & Engineering
Probability
Analysis Overview
Introductory Analysis I
Introductory Analysis II
Vector Analysis
Complex Analysis
Dynamical Systems
Partial Differential Equations
Linear Algebra for Engineering Graduate Students
Elementary Number Theory
Combinatorial Mathematics
Discrete Mathematical Models
Abstract Algebra I
Abstract Algebra II
Honors Linear Algebra and Differential Equations
Honors Complex Analysis
Honors Combinatorics
Honors Probability
Honors Differential Geometry
Honors Number Theory
Course
Number
5590H
5591H
5630
5631
5632
5633
5634
5756
5757
Course Title
Honors Abstract Algebra I
Honors Abstract Algebra II
Life Contingencies I
Life Contingencies II
Financial Economics for Actuaries
Loss Models I
Loss Models II
Mathematical Methods in Relativity Theory I
Mathematical Methods in Relativity Theory II
Mathematics 1050
Precollege Mathematics I
Autumn, Spring
5 credits
Catalog Description:
Fractions and decimals, basic algebra, graphing lines, factoring, systems of equations. Credit for
this course will not count toward graduation in any degree program.
Prerequisite:
Math Placement Level T; or Math 1040 or 40 or 50; or permission of department.
Exclusions:
Not open to students with credit for any Math course above 1050 (050).
Purpose of Course:
Mathematics 1050 is designed to meet the needs of the students entering The Ohio State
University at the lowest placement, course code T. This course will prepare students for Math
1075.
Follow-up Course:
Math 1075
Sequencing Chart:
Page 1
2016-2017
Math 1050
Mathematics 1050
Precollege Mathematics I
Autumn, Spring
5 credits
Text:
Beginning Algebra, 8th edition, by Aufmann & Lockwood, Cengage, ISBN: 9781305942653
Topics List:
1. Review: real numbers, number line, integral exponents, scientiﬁc notation, negative
numbers, fractions, order of operations, basic geometry.
2. Linear equations and inequalities in one variable. Applications: word problems.
3. Graphical representations, straight lines as graphs, slope, intercepts, slope-intercept form,
and point-slope form. Linear inequalities in two variables.
4. Systems of two linear equations in two unknowns.
5. Polynomials: addition, subtraction, multiplication, factoring, division.
6. Solving quadratic equations by factoring. Applications.
7. Introduction to function notation.
Page 2
2016-2017
Math 1050
Mathematics 1075
Precollege Mathematics II
Autumn, Spring
4 credits
Catalog Description:
value; inequalities; and applications.
Prerequisite:
Math Placement Level S, a grade of C– or better in Math 1050, or credit for Math 75 or 1074.
Exclusions:
Not open to students with credit for any higher numbered math class, or for any quarter math class
numbered higher than 75.
Text:
Intermediate Algebra: Math 1075, OSU Custom Edition, Miller, O'Neill & Hyde, McGraw-Hill,
ISBN 9781269577980
Follow-up Courses:
 Math 1116 for students in liberal arts or students in the precertification programs on
regional campuses.
 Math 1125 for students intending to pursue a M.Ed. in early or middle childhood.
 Math 1130 College Algebra for Business
 Math 1148 Traditional College Algebra
Sequencing Chart:
Page 1
2016-2017
Math 1075
Mathematics 1075
Precollege Mathematics II
Autumn, Spring
4 credits
Topics List:
Ch. 4 Linear Inequalities
4.1
Solving linear inequalities using addition & subtraction
4.2
Solving linear inequalities using multiplication & division
4.3
Solving compound inequalities
4.4
Solving absolute value equations & inequalities
4.5
Graphing systems of inequalities in two variables
Ch. 6 Factoring Polynomials
6.1
Introduction to factoring polynomials
6.2
Factoring trinomials of the form x 2  bx  c
6.3
Factoring trinomials of the form ax 2  bx  c
6.4
Factoring special binomials
6.5
Factoring by grouping; General strategies for factoring
6.6
Solving equations by factoring
Ch. 9 Rational Functions
9.1
Graphs of rational functions
9.2
Reducing rational expressions; Multiplying and dividing rational expressions
9.3
9.4
Combining operations; Complex rational expressions
9.5
Solving equations containing rational expressions
9.6
Inverse and joint variation; Other applications yielding equations with fractions
7.1
Extraction of roots and properties of square roots
7.2
Solving quadratic equations by completing the square
7.3
7.4
7.5
Complex numbers; Solving quadratic equations with complex solutions
Ch. 8 Functions: Linear, Absolute Value, and Quadratic
8.1
Functions and representations of functions
8.2
Linear Functions
8.3
Absolute value functions
8.4
Ch. 10 Square Root & Cube Root Functions and Rational Exponents
10.3 Multiplying & dividing radical expressions
10.4 Solving equations containing radical expressions
Page 2
2016-2017
Math 1075
Mathematics 1116
Excursions in Mathematics
Autumn, Spring
3 credits
Catalog Description:
Critical thinking and problem solving, with relevant topics met in everyday life. Appropriate for
non-science majors.
Prerequisite:
Math Placement Level R or higher; or credit for 1075, 75, 104, 1073 or 1074;
or ACT math score ≥ 22 or SAT math score ≥ 520 (scores must be less than 2 years old).
Exclusions:
Not open to students with credit for Math 1152 or higher, or for quarter math class numbered 153
or higher.
Purpose of Course:
The emphasis in this course is on intuitive understanding and developing some facility for
applying mathematical ideas to problem solving.
Follow-up Courses:
None. Math 1116 is a terminal course.
Text:
Excursions in Modern Mathematics, 8th edition, by Tannenbaum, Pearson,
ISBN 9780321825735
Topics List:
1. Graph theory: graphs, Euler and Hamilton circuits, algorithms for Traveling Salesman
Problem, spanning trees, etc.
2. Voting & apportionment: preference ballots; apportionment paradoxes; Congressional
apportionment; methods of Jeﬀerson, Adams, and Webster.
3. Patterns & growth: Fibonacci and recursive sequences, golden ratio, population growth
models: linear, exponential, and logistic.
4. Symmetry: Rigid motions, rosettes, friezes, rudiments of group theory.
5. Counting & probability: counting principles, permutations and combinations,
multiplication rule, randomness, probability.
6. Fractals: recursive deﬁnitions, standard examples (Koch snowﬂake, Sierpinski gasket
etc.), self-similarity, fractional dimension.
7. Linear programming: mixture problems, examples in low dimension, corner point
principle, algorithms.
Page 1
2016-2017
Math 1116
Mathematics 1118
Mathematics for Architects
Autumn, Spring
3 credits
Catalog Description:
Topics in geometry for architecture majors.
Prerequisite:
Enrollment in the School of Architecture and: Math Placement Level L or M; C- or better in
1148 or 1150; or credit for 148 or 150.
Purpose of Course:
The majority of the audience is made up of Architecture majors for whom the course is a
requirement. The intent of the course is to introduce these students to the mathematics inherent in
2D and 3D design. Moreover, there is an emphasis on similar figures and the issues that arise
when scaling lengths, areas, and volumes.
Follow-up Courses:
There are really no follow-up courses. To start any other mathematics sequence will probably
involve beginning at an appropriate entry level course. Students interested in further course
work in mathematics should consult the Mathematics Advisors in 250 Mathematics Bldg.
Text:
Course Notes, by Snapp
Topics List:
1.
2.
3.
4.
5.
6.
7.
8.
Page 1
Geometric models, transformations, matrices.
Plane tessellations, concepts of symmetry.
Polyhedra: Platonic and Archimedean.
Invariants: area, volume, Euler characteristic.
Mathematics of perspective drawing.
String art: curves deﬁned as envelopes of tangent lines, ruled surfaces.
Discrete curvature: Descartes theorem and beyond.
Higher dimensions: tesseracts and other 4-D polyhedra.
2016-2017
Math 1118
Mathematics 1125
Mathematics for Elementary Teachers I
Autumn, Spring
5 credits
Catalog Description:
Math 1125 involves numbers, operations, geometry, measurement, and mathematical reasoning
for prospective elementary school teachers.
Prerequisite:
A grade of C- or above in 1075; or credit for 1074, 75, or 104; or Math Placement Level R or
above; or ACT math score ≥ 22 or SAT math score ≥ 520 (scores must be less than 2 years old)
and enrollment in Early Childhood or Special Education major, or in Middle Childhood major or
pre-major with area of concentration different than Math.
Exclusions:
Not open to students with credit for 106.
Purpose of Course:
To develop an appreciation of, and basic competency in, the use of analytical thought in the
development of a cohesive body of useful mathematical knowledge, with special emphasis on
topics encountered in elementary and middle school mathematics programs. Math 1125
addresses the meaning of whole numbers, integers, rational numbers, and operations with these,
number theory, and algebraic thinking. Appropriate only for those preparing to become early
childhood educators and for those preparing to teach subjects other than math in middle school.
Follow-up Courses:
Math 1126.
Text:
Mathematics for Elementary Teachers, with Activity Manual, 4rd Edition, by Sybilla Beckmann,
Pearson, ISBN for the package is 9780321836715 (loose-leaf) and Student Packet.
Topics List:
1. Counting and the decimal system.
2. Fractions and integers and their meaning.
3. Addition and subtraction of fractions, decimals, and integers.
4. Multiplication of fractions, decimals, and integers.
5. Division of fractions, decimals, and integers.
6. Ratios and proportional reasoning.
7. Number theory: factors and multiples, LCM, GCF, divisibility tests, prime numbers,
unique factorization, notations for fractions and decimals.
8. Algebraic thinking: writing expressions, solving equations, sequences.
9. Problem solving and justification are themes of the course.
*Currently taught in either lecture/recitation or workshop format.
Page 1
2016-2017
Math 1125
Mathematics 1126
Mathematics for Elementary Teachers II
Autumn, Spring
5 credits
Catalog Description:
Continuation of 1125: Math 1126 involves geometry, measurement, number theory, algebraic
thinking, counting techniques, probability, a mathematical reasoning for prospective elementary
school teachers.
Prerequisite:
A grade of C- or above in 1125; and enrollment in Early Childhood or Special Education major,
or in Middle Childhood major or pre-major with area of concentration different than Math.
Exclusions:
Not open to students with credit for 107.
Purpose of Course:
To develop an appreciation of, and basic competency in, the use of analytical thought in the
development of a cohesive body of useful mathematical knowledge, with special emphasis on
topics encountered in elementary and middle school mathematics programs. Math 1126
addresses basic geometric concepts and measurement, symmetry and rigid motions, congruence,
similarity and scaling, coordinate geometry, algebraic thinking, linear functions, counting
techniques and probability. Appropriate for those preparing to become early childhood
educators and for those preparing to teach subjects other than math in middle school.
Text:
Mathematics for Elementary Teachers, with Activity Manual, 4rd Edition, by Sybilla Beckmann,
Pearson, ISBN for the package is 9780321836715 (loose-leaf) and Student Packet.
Topics List:
1. Spatial visualization and basic geometric concepts: angles, 2- and 3-D shapes and their
properties.
2. Measurement: meaning of length, area, volume, measurement techniques, unit
conversion, actions preserving area/volume, and scaling.
3. Transformations: symmetry, congruence, similarity.
4. Geometric constructions with various tools (compass, paper folding).
5. Algebraic thinking: expressions, measurement formulas, scaling, functions, use of
formulas, graphs, and tables, sequences, and coordinate geometry.
6. Counting: inclusion/exclusion, fundamental counting principle, tree diagrams,
permutations and combinations, Pascal’s triangle.
7. Basic ideas of probability: Law of Large Numbers, sample and event spaces, use of tree
diagrams, simulations, and discussion of common misconceptions.
8. Problem solving and justifications at multiple levels are themes of the course.
*Currently taught in either lecture/recitation or workshop format.
Page 1
2016-2017
Math 1126
Mathematics 1130
Autumn, Spring
4 credits
Catalog Description:
Algebraic, exponential, and logarithmic functions. Matrix algebra. Applications to business.
Prerequisite:
Math Placement Level N; C- or better in 1075; or credit for 104; or ACT math score ≥ 22 or SAT
math score ≥ 520 (scores must be less than 2 years old).
Exclusions:
Not open to students with credit for 1131 or for any math course numbered 1149 or higher, or a
quarter-system math course numbered 150 or higher.
Purpose of Course:
Math 1130 is a pre-calculus course with a finance section slanted toward a business program.
Follow-up Course:
Math 1131
Text:
Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences,
13th Edition; by Haeussler, Paul, and Wood; published by Pearson; ISBN 9781256966096
Topics List:
Review of Algebra:
0.7: Equations, In Particular Linear Equations.
1.2: Linear Inequalities.
1.3: Applications of Inequalities.
1.6: Sequences
Functions:
2.1: Functions.
2.2: Special functions.
2.3: Combinations of functions.
2.4: Inverse Functions.
2.5: Graphs of functions
Page 1
2016-2017
Math 1130
Mathematics 1130
Autumn, Spring
4 credits
3.1: Lines
3.2: Applications and Linear Functions.
3.4: Systems of Linear Equations.
3.6: Applications of Systems of Equations.
4. Exponential and Logarithmic Functions:
4.1: Exponential Functions.
4.2: Logarithmic functions.
4.3: Properties of Logarithms.
4.4: Logarithmic and Exponential Equations.
5. Mathematics of Finance:
5.1: Compound Interest.
5.2: Present Value.
5.3: Interest Compounded Continuously.
5.4: Annuities
5.5: Amortization of Loans.
6. Matrix Algebra:
6.1: Matrices.
6.2: Matrix Addition and Scalar Multiplication.
6.3: Matrix Multiplication.
6.4: Solving Systems by Reducing Matrices.
6.6: Inverses
Page 2
2016-2017
Math 1130
Mathematics 1131
Autumn, Spring
5 credits
Catalog Description:
Survey of calculus of one and several variables; applications to business.
Prerequisite:
Math Placement Level L; C- or better in 1130, 1148, 1144, or 1150; credit for 130 or 148.
Exclusions:
Not open to students with credit for a math course numbered 1151 (151.xx) or higher, or for 132
or 1134.
Text:
Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences,
ISBN-13: 978-1-256-96609-8.
Topics List:
1. Idea of limits, continuity, and derivative. Interpret derivative as a limit, slope, and rate of
change.
2. Calculate derivatives of algebraic, exponential, and logarithmic functions.
3. Monotonicity, concavity, extrema of functions, second derivative tests, applications to
graphing.
4. Applications: marginal analysis in business, optimization.
5. Anti-derivatives, separable ﬁrst-order ODEs.
6. Riemann integral, substitution, Fundamental Theorem, area, applications.
7. Partial derivatives, extrema and second derivative test for two-variable functions,
Page 1
2016-2017
Math 1131
Mathematics 1135
Number and Operations for Teachers
Autumn, Spring
5 credits
Catalog Description:
This course is the first in a two semester sequence for teachers of elementary and middle grade
students. This course focuses on concepts of numbers and arithmetic operations, including modern
and historical perspectives.
Prerequisite:
A grade of C- or above in 1075; or credit for 1074, 75, or 104; or Math Placement Level R or
above; or ACT math subscore of 22 or higher that is less than 2 years old.
Exclusions:
Not open to students with credit for 106.
Text:
Mathematics for Elementary Teachers, with Activity Manual, 4th Edition, by Sybilla Beckmann,
Pearson, ISBN for the package is 9780321836715 (loose-leaf).
Purpose:
This course covers the concepts of whole numbers (positive and negative), place value (base-ten
and alternate bases), decimals, and fractions. Some content on irrational numbers appears at the
end, and this is extended in Algebra and coordinate geometry for teachers (2137). The four
arithmetic operations are covered both conceptually and algorithmically. Attention is given to
ensuring that students can perform the algorithms correctly and explain why they give accurate
answers. Lastly, the course covers the concepts of proportions and how they are related both to
multiplication/division and to fractions. Factors, divisibility, and some elementary number theory
complete the course.
Topics List:
1. Counting numbers, decimals
2. Meaning of fractions
3. Meaning of addition and subtraction
4. Meaning of multiplication
5. Multiplying fractions, decimals, integers
6. Meaning of division
7. Dividing fractions, decimals, integers
8. Meaning of ratios, rates, proportions
9. Greatest common divisor, least common multiple
10. Rational and irrational numbers
Page 1
2016-2017
Math 1135
Mathematics 1136
Measurement & Geometry for Teachers
Autumn, Spring
5 credits
Catalog Description:
This course is the second in a two semester sequence for teachers of elementary and middle
grade students. This course focuses on concepts of measurement and geometry, including
modern and historical perspectives.
Prerequisite:
A grade of C- or above in “Number and Operations for Teachers” (Math 1135)
Text:
Mathematics for Elementary Teachers, with Activity Manual, 4th Edition, by Sybilla Beckmann,
Pearson, ISBN for the package is 9780321836715 (loose-leaf).
Recommended Supplemental Texts:
 Geometric Structures: An Inquiry-Based Approach for Prospective Elementary and
Middle School Teachers, by Douglas Aichele and John Wolfe, Pearson, ISBN
9780131483927
 Elementary Geometry for Teachers, by Thomas Parker and Scott Baldridge, Sefton-Ash
Publishing, ISBN 9780974814056
Purpose:
The course consists of fundamental topics in Euclidean geometry starting with measurement.
This includes the concepts of length, area, volume, angles, units of measurement, precision and
error.
The basic properties of two and three dimensional geometric shapes and their relationships are a
central part of the course. Special emphasis is put on geometric reasoning through problem
solving, including unknown angle, length, area, and volume. The course also covers topics on
transformations in the plane, symmetries, congruence, and similarity. Some geometric
constructions and basic geometric proofs are included.
Additional topics include an introduction to functions and equations, primarily in the linear case,
and a brief introduction to probability.
Topics List:
1. Measurement
2. Planar shapes
3. Polyhedra
4. Plane geometry
5. Transformations in the plane, congruence, symmetry
6. Linear equations and graphs
7. Algebra and linear equations
8. Probability
Page 1
2016-2017
Math 1136
Mathematics 1148
College Algebra
Autumn, Spring, Summer
4 credits
Catalog Description:
Functions: polynomial, rational, radical, exponential, and logarithmic. Introduction to rightangle trigonometry. Applications.
Prerequisite:
Math Placement Level N; C- or better in 1075; or credit for 104 or 148; or ACT math score ≥ 22
or SAT math score ≥ 520 (scores must be less than 2 years old).
Exclusions:
Not open to students with credit for 1144 or 1150 or higher, or for a quarter-system math course
numbered 150 or higher.
Purpose:
College Algebra provides students a college level academic experience that emphasizes the use
of algebra and functions in problem solving and modeling, where solutions to problems in realworld situations are formulated, validated, and analyzed using mental, paper-and-pencil,
algebraic and technology-based techniques as appropriate using a variety of mathematical
notation. Students should develop a framework of problem-solving techniques (e.g., read the
problem at least twice; define variables; sketch and label a diagram; list what is given; restate the
question asked; identify variables and parameters; use analytical, numerical and graphical
solution methods as appropriate; determine the plausibility of and interpret solutions). – Adapted
from the MAA/CUPM CRAFTY 2007 College Algebra Guidelines. This course is intended to
satisfy the requirements of the Ohio Board of Regents TMM001 College Algebra course with
learning outcomes specified in: http://regents.ohio.gov/transfer/otm/otm-learning-outcomes.php
Text:
College Algebra & Trigonometry, 1st Edition, by Miller and Gerken, published by McGraw-Hill.
ISBN: 9781259976612
Technology: All students are required to have a graphing calculator, TI-83 or TI-84.
Note: Any calculators (including TI-89 and TI-92) that use a Computer Algebra System
(CAS) are not permitted.
Page 1
2016-2017
Math 1148
Mathematics 1148
College Algebra
Autumn, Spring, Summer
4 credits
Sequencing Chart:
Topics List:
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Week 13
Week 14
Page 2
Section 1.7 – Inequalities
Section 2.3 – Functions and Relations
Section 2.4 – Linear Equations in Two Variables
Section 2.5 – Applications of Linear Equations
Section 9.1 – Systems of Linear Equations in Two Variables
Section 9.2 – Systems of Linear Equations in Three Variables
Section 2.6 – Transformations of Graphs
Section 2.7 – Analyzing Graphs of Functions
Test 1
Section 2.8 – Algebra of Functions and Composition
Section 3.1 – Quadratic Functions and Applications
Section 3.2 – Polynomial Functions
Section 3.3 – Division of Polynomials
Section 3.5 – Rational Functions
Section 3.5 – Rational Functions
Section 3.6 – Polynomial and Rational Inequalities
Test 2
Section 4.1 – Inverse Functions
Section 4.2 – Exponential Functions
Section 4.2 – Exponential Functions
Section 4.3 – Logarithmic Functions
Section 4.3 – Logarithmic Functions
Section 4.4 – Properties of Logarithms
Section 4.4 – Properties of Logarithms
Section 4.5 – Exponential and Logarithmic Equations
Section 4.6 – Modeling with Exponential and Logarithmic Functions
Comprehensive review, Final Exam
2016-2017
Math 1148
Mathematics 1149
Trigonometry
Autumn, Spring, Summer
3 credits
Catalog Description:
Trigonometric functions and their properties. Vectors, polar coordinates and complex numbers.
Prerequisite:
C- or better in 1148, or permission of department.
Exclusions:
Not open to students with credit for 1144, or for any math course numbered 1150 or higher.
Text:
Precalculus: Mathematics for Calculus, 6th Edition, by J. Stewart, L. Redlin, and S. Watson,
Technology:
A graphing calculator is a required component in this course. It is recommended that you use a TI83, TI-83 plus, or a TI-84. Note that the TI-89, TI-92, and calculators that use a
Computer Algebra System are not permitted.
Topics List:
6.1
6.2
6.3
5.1
5.2
5.3
5.4
5.5
Angle Measure
Trigonometry of Right Triangles
Trigonometric Functions of Angles
The Unit Circle
Trigonometric Functions of Real Numbers
Trigonometric Graphs
More Trigonometric Graphs
Inverse Trigonometric Functions and Their Graphs
Midterm 1
Page 1
Autumn 2016
Math 1149
Mathematics 1149
Trigonometry
Autumn, Spring, Summer
3 credits
6.4
6.5
6.6
7.1
7.2
7.3
7.4
7.5
8.3
Right Triangles
The Law of Sines
The Law of Cosines
Trig. Identities
Double/Half Angle and Product‐Sum Formulas
Trig. Equations
More Trig. Equations
Polar Forms of Complex Numbers; De Moivre’s Theorem
Midterm 2
9.1
9.2
11.1
11.2
11.3
Page 2
Vectors in Two Dimensions
The Dot Product
Parabolas
Ellipses
Hyperbolas
Autumn 2016
Math 1149
Mathematics 1149
Trigonometry
Autumn, Spring, Summer
3 credits
Catalog Description:
Trigonometric functions and their properties. Vectors, polar coordinates and complex numbers.
Prerequisite:
C- or better in 1148, or permission of department.
Exclusions:
Not open to students with credit for 1144, or for any math course numbered 1150 or higher.
Text:
College Algebra & Trigonometry Mathematics 1e, by Miller and Gerken, ISBN 9781259976612.
This textbook is packaged with an access code to Connect Math for a period of 720 days. It may
be purchased at the bookstore or online via Carmen/Canvas.
Technology:
A graphing calculator is a required component in this course. It is recommended that you use a TI83, TI-83 plus, or a TI-84. Note that the TI-89, TI-92, and calculators that use a
Computer Algebra System are not permitted.
Topics List:
5.1
5.2
5.3
5.4
5.5
5.6
Angles and Their Measure
Right Triangle Trigonometry
Trigonometric Functions of any Angle
Trigonometric Functions and the Unit Circle
Graphs of Sine and Cosine Functions. Omit sinusoidal behavior.
Graphs of Other Trigonometric Functions.
Midterm 1
5.7
6.1
6.2
6.3
6.5
7.2
7.3
Inverse Trigonometric Functions. Omit inverse cot(t), sec(t), and csc(t).\
Fundamental Trigonometric Identities
Sum and Difference Formulas
Double-Angle and Half-Angle Formulas
Trigonometric Functions. Solving graphically is optional.
The Law of Sines
The Law of Cosines
Midterm 2
Page 1
Spring 2017
Math 1149
Mathematics 1149
Trigonometry
Autumn, Spring, Summer
3 credits
8.3
8.4
8.5
11.1
11.2
11.3
Page 2
Complex Numbers in Polar Form. Omit nth roots of complex numbers.
Vectors
Dot Product
The Ellipse. Applications is optional.
The Hyperbola. Applications is optional.
The Parabola. Applications is optional.
Spring 2017
Math 1149
Mathematics 1150
Precalculus
Autumn, Spring
5 credits
Catalog Description:
Functions: polynomial, rational, radical, exponential, logarithmic, trigonometric, and inverse
trigonometric. Applications.
Prerequisite:
Math Placement Level M.
Exclusions:
Not open to students with credit for 1144, 1148, 1149, for any higher numbered math course, or
for any quarter-system math course 150 or higher.
Text:
College Algebra & Trigonometry Mathematics 1e, by
Miller and Gerken, ISBN
9781259976612. This textbook is packaged with an access code to Connect Math for a period of
720 days. It may be purchased at the bookstore or online via Carmen/Canvas.
Technology:
Every student is required to have a graphing calculator comparable in capability to a TI-83 or
TI-84. However, calculators with symbolic algebra capabilities are not allowed during exams or
quizzes.
Topics List:
2.3
2.4
2.6
2.7
2.8
3.1
3.2
3.3
Functions and Relations.
Linear Functions. Cover the average rate of change only.
Transformations of Graphs.
Analyzing Graphs of Functions. Omit step functions.
Algebra and Composition of Functions.
Quadratic Functions. Omit models using regression.
Introduction to Polynomial Functions.
Division of Polynomials and The Remainder and Factor Theorems.
Omit Synthetic Division.
3.4
Zeros of Polynomials.
Cover only paragraph 2 (“Apply the fundamental theorem of algebra”).
3.5
3.6
4.1
Rational Functions.
Polynomial and Rational Inequalities. Omit applications.
Inverse functions.
Midterm 1
Page 1
2016-2017
Math 1150
Mathematics 1150
Precalculus
Autumn, Spring
5 credits
4.2
4.3
4.4
4.5
4.6
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6.1
Exponential Functions.
Logarithmic Functions.
Properties of Logarithms.
Exponential and Logarithmic Equations.
Modeling with Exponential and Logarithmic Functions.
Omit logistic growth and models using regression.
Angles and Their Measure.
Right Triangle Trigonometry.
Trigonometric Functions of any Angle.
Trigonometric Functions and The Unit Circle.
Graphs of Sine and Cosine Functions. Omit sinusoidal behavior.
Graphs of Other Trigonometric Functions.
Inverse Trigonometric Functions.
Fundamental Trigonometric Identities.
Midterm 2
6.2
6.3
6.5
7.1
7.2
7.3
8.3
8.4
8.5
9.1
9.2
11.1
11.2
11.3
Sum and Difference Formulas.
Double-Angle and Half-Angle Formulas.
Trigonometric Equations. Solving graphically is optional.
Applications of Right Triangles. Omit the bearing of an object.
The Law of Sines.
The Law of Cosines.
Complex Numbers in Polar Form. Omit nth roots of complex numbers.
Vectors.
Dot Product.
Systems of Linear Equations in Two Variables. Cover briefly.
Systems of Linear Equations in Three Variables. Omit modeling.
The Ellipse. Applications is optional.
The Hyperbola. Applications is optional
The Parabola. Applications is optional
Midterm 3
12.1
12.2
12.3
Page 2
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences.
2016-2017
Math 1150
Mathematics 1151
Calculus I
Autumn, Spring, Summer
5 credits
Catalog Description:
Differential and integral calculus of one real variable.
Prerequisite:
Math Placement Level L, or C- or better in: 1150, or in both 1148 & 1149; or in 150 or 1144.
Exclusions:
Not open to students with credit for any higher numbered math class.
Text:
Calculus for Scientists and Engineers: Early Transcendentals 2nd edition, by Briggs, Cochran,
Topics List:
1.1
Review of Functions
1.2
Representing Functions
1.3
Inverse, Exponential, and Logarithmic Functions
1.4
Trigonometric Functions and Their Inverses
2.1
The Idea of Limits
2.2
Definitions of Limits
2.3
Techniques for Computing Limits
2.4
Infinite Limits
2.5
Limits at Infinity
2.6
Continuity
3.1
Introducing the Derivative
Midterm 1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
4.1
4.2
Page 1
Working with Derivatives
Rules of Differentiation
The Product and Quotient Rules
Derivatives of Trigonometric Functions
Derivative as Rates of Change
The Chain Rule
Implicit Differentiation
Derivatives of Logarithmic and Exponential Functions
Derivatives of Inverse Trigonometric Functions
Related Rates
Maxima and Minima
What Derivatives Tell Us
2016-2017
Math 1151
Mathematics 1151
Calculus I
Autumn, Spring, Summer
5 credits
Midterm 2
4.3
4.4
4.5
4.6
4.7
4.9
5.1
5.2
5.3
5.4
Graphing Functions
Optimization Problems
Linear Approximations and Differentials
Mean Value Theorem
L’Hospital’s Rule
Antiderivatives
Approximating Areas under Curves
Definite Integrals
Fundamental Theorem of Calculus
Working with Integrals
Midterm 3
5.5
6.1
Substitution Rule
Velocity and Net Change
Final
Page 2
2016-2017
Math 1151
Mathematics 1152
Calculus II
Autumn, Spring, Summer
5 credits
Catalog Description:
Integral calculus, sequences and series, parametric curves, polar coordinates, vectors.
Prerequisite:
C- or better in 1151, 1156, 152.xx, 161.xx or 161.01H; or 114 or 1114.
Exclusions:
Not open to students with credit for any higher numbered math class or with credit for quartersystem Math courses numbered 153.xx or above.
Text:
Calculus for Scientists and Engineers: Early Transcendentals, 2nd OSU custom edition, by Briggs,
Topics:
7.1
6.2
6.3
6.4
6.5
6.6
6.7
7.2
Basic Approaches to Integration
Regions Between Curves
Volume by Slicing
Volume by Shells
Length of Curves
Surface Area
Physical Applications
Integration by Parts
Midterm 1
7.3
7.4
7.5
7.8
9.1
9.2
9.3
9.4
9.5
9.6
Trigonometric Integrals
Trigonometric Substitution
Partial Fractions
Improper Integrals
Overview of Sequences and Series
Sequences
Series
Divergence and Integral Tests
Ratio, Root, and Comparison Tests
Alternating Series
Page 1
Midterm 2
10.1
10.2
10.3
10.4
8.1
8.2
8.3
11.1
11.2
Approximating Functions with Polyn
Properties of Power Series
Taylor Series
Working with Taylor Series
Basic Ideas of Differential Equations
Direction Fields and Euler’s Method
Separable Differential Equations
Parametric Equations
Polar Equations
Midterm 3
11.3
12.1
12.2
12.3
12.4
12.5
Calculus in Polar Coordinates
Vectors in the Plane
Vectors in Three Dimensions
Dot Products
Cross Products
Lines and Curves in Space
Final
2016-2017
Math 1152
Mathematics 1156
Calculus for Biological Sciences
Autumn
5 credits
Catalog Description:
Limits, continuity, derivatives, mean value theorem, extrema, curve sketching, related rates,
differentiation of the trig, log, and exponential functions, basic integration techniques, with
particular motivations from and application to the Biological Sciences.
Prerequisite:
A grade of C- or above in 1148 and 1149, or a grade of C- or above in 1150, or credit for 150, or
Math Placement Level L. Not open to students with credit for 1151 (151.xx) or above. GE quant
reason math and logical analysis course.
Exclusions:
Not open to students with credit for 1151, or with credit for any higher numbered math class.
Purpose of Course:
To provide students with a solid foundation in one-variable differential calculus, to model and
analyze phenomena in the Biological Sciences.
Follow-up Course:
Math 1157
Text:
Calculus for Biology and Medicine, 3rd Edition, by Claudia Neuhauser, Pearson, ISBN
9780321644688
Topics List:
1.2
1.3/2.1
2.2
3.1-3.4
3.5
4.1
4.2-4.3
4.4
4.5-4.7
5.1-5.3
5.4
5.5
5.8
6.1
6.2
6.3
7.1-7.2
Page 1
Elementary Functions
Graphing/Exponential Growth and Decay
Sequences
Limits and Continuity
Properties of Continuous Functions
Derivatives
Rules of Differentiation, Product and Quotient Rules
Chain Rule and Higher Derivatives
Derivatives of Special Functions and Inverse Functions
Extrema, Mean Value Theorem, Monotonicity, Concavity, Inflection Points
Optimization
L'Hospital's Rule
Antiderivatives
The Definite Integral
The Fundamental Theorem of Calculus
Applications of Integration
Integration Techniques
Also: Small-group Projects
2016-2017
Math 1156
Mathematics 1157
Mathematical Modeling for the Biological Sciences
Spring
5 Credits
5 credits
Catalog Description:
Models in life sciences using multivariable calculus, linear algebra, dynamical systems, and
ordinary differential equations.
Prerequisite:
C- or better in: 1156, 1151, 1161.xx or 1181H; or credit for 152.xx.
Exclusions:
Not open to students with credit for 1152 or with credit for any higher numbered math class.
Purpose of Course:
To provide students with a solid foundation in one-variable calculus, to introduce multi-variable
tools in a biological setting, to model and analyze phenomena in the life sciences.
Text:
Calculus for Biology and Medicine, 3rd Edition, by Claudia Neuhauser, Pearson, ISBN
9780321644688
Topics List:
7.3
7.5
7.6
8.1
8.2
9.1-9.2
9.3
10.3
10.4
11.1-11.2
11.3-11.4
Also:
Page 1
Rational Functions and Partial Fractions
Numerical Integration
Taylor Approximation
Solving Differential Equations
Equilibria and Their Stability
Linear Systems and Matrices
Linear Maps, Eigenvectors, an Eigenvalues
Multivariable functions & Partial Derivatives
Tangent Planes, Differentiability, and Linearization
Linear Systems: Theory and Applications
Nonlinear Autonomous Systems: Theory and Applications
Small-group Projects
2016-2017
Math 1157
Mathematics 1161.01, 1161.02
Accelerated Calculus I
Accelerated Calculus I for Honors Engineer
Autumn
5 Credits
Catalog Description:
Differential and integral calculus of one real variable.
Autumn, Spring
5Credits
%5
5 credits
Prerequisites:
Math Placement Level L and previous calculus experience.
Exclusions:
For 1161.01: Not open to students with credit for any math course numbered 1152 or higher, or
for the quarter-system math courses 151.xx and 152.xx, or for any quarter-system course
numbered 162.xx or higher.
For 1161.02: Intended for students in Freshman Engineering Honors.
Text:
Calculus for Scientists and Engineers: Early Transcendentals, 2nd OSU custom edition, by
Briggs, Cochran, Gillett, Person, ISBN: 9781269753449
Topics:
2.1; 2.2
2.2; 2.3
2.4; 2.5
2.5; 2.6
2.7
3.1
3.2; 3.3
3.4; 3.5
3.5; 3.6
3.7
The Idea of Limits; Definition of Limits
Definition of Limits; Limit Laws
Infinite Limits; Limits at Infinity
Limits at Infinity; Continuity, the Intermediate Value Theorem
Precise Definition of Limits
Introducing the Derivative
Rules of Differentiation; Product and Quotient Rules
Derivatives of Trig Functions; Derivatives as Rate of Change
Derivatives as Rate of Change; The Chain Rule
Implicit Differentiation
Midterm 1
Page 1
2016-2017
Math 1161.01, 1161.02
3.8; 3.9
3.10
4.1
4.2; 4.3
4.4
4.5; 4.6
4.6; 4.7
4.9
5.1
5.2
Mathematics 1161.01, 1161.02
Accelerated Calculus I
Accelerated Calculus I for Honors Engineer
Autumn
5 Credits
Derivatives of Logarithms and Exponential Functions; Derivatives of Inverse
Autumn, Spring
5Credits
Functions
%5
Related Rates
5
credits
Maxima and Minima
What derivatives Tell Us; Graphing
Optimization Problems
Linear Approximations and Differentials; Mean Value Theorem
Mean Value Theorem; L'Hopital's Rule
Antiderivatives
Approximating Areas under Curves, Sigma Notation
Definite Integrals
Midterm 2
5.3
5.4; 5.5
5.5; 6.1
6.2
6.3
6.4
6.5; 6.6 11.5
6.7
6.8; 6.9
7.1; 7.2
Fundamental Theorem of Calculus
Working with Integrals; Substitution Rule
Substitution Rule; Velocity and Net Change
Regions between Curves
Volumes by Slicing
Volumes by Shells
Lengths of Curves; Surface Area
Physical Applications: Density & Mass, Work, Lifting Problems, Force &
Pressure
Log and Exponential Functions Again; Exponential Growth and Decay
Integration: Basic Approaches; Integration by Parts
Midterm 3
7.3
7.4
7.5
7.8
Trig Integrals
Trig Substitutions
Partial Fractions
Improper Integrals
Final
Page 2
2016-2017
Math 1161.01, 1161.02
Mathematics 1165
Math for Middle School Teachers
Autumn
5 Credits
Catalog Description:
Algebra and reasoning for middle school teachers.
Autumn, Spring
5Credits
%5
5 credits
Prerequisite:
A grade of C- or above in 1148 and 1149, or grade of C- or above in 1150, or credit for 150, or
Math Placement Level L; and enrollment in Middle Childhood Education major within either
College of Arts and Sciences or College of Education and Human Ecology with Math as an Area
of Concentration.
Purpose of Course:
The purpose of the course is to prepare teachers of middle school students. In particular, it
intends to deepen and extend the prospective teachers’ content knowledge of the mathematics
they will teach as well as their ability to reason with and communicate that knowledge.
Follow-up Courses:
Math 1166, Math 2167, and Math 2168
Text:
Course Notes, by B. Snapp
Recommended Text:
9780131449282
Topics List:
1. Number systems (whole, integer, rational, real): uses, notations (including place value),
and comparison of size. Addition and Subtraction
2. Division algorithm, Euclidean algorithm, Diophantine equations, counting techniques.
3. Algebra: polynomials, their structure and arithmetic, division algorithm.
4. Solving equations: linear, quadratic, etc., using complex numbers.
5. Introduction to mathematical induction.
6. Applications: modeling real-world topics.
7. Problem solving (a theme throughout the course).
Page 1
2016-2017
Math 1165
Mathematics 1166
Math for Middle School Teachers II
Spring
5 Credits
Catalog Description:
Geometry for middle school teachers.
Autumn, Spring
5Credits
%5
5 credits
Purpose of Course:
The purpose of the course is to prepare teachers of middle school students. In particular, it
intends to deepen and extend the prospective teachers’ content knowledge of the mathematics
they will teach as well as their ability to reason with and communicate that knowledge.
Prerequisite:
C- or better in 1165, and enrollment in Middle Childhood Education major with Math as an Area
of Concentration.
Follow-up Courses:
Math 2167 and Math 2168
Text:
Course Notes.
Topics List:
1. Visual reasoning via “proofs without words.” Measurement (also teaching measurement
in middle school)
2. Geometric constructions, congruence, similarity, and problem solving.
3. Coordinate geometry with emphasis on solving equations.
4. Non-Euclidean geometries.
5. Geometric transformations coordinate geometry, complex numbers.
6. Scaling and relationship between perimeter and area.
7. Measurement issues.
8. Modeling real-world situations.
Page 1
2016-2017
Math 1166
Mathematics 1172
Engineering Mathematics A
Autumn, Spring, Summer
5 Credits
Catalog Description:
Autumn, Spring
Techniques of integration, Taylor series, differential calculus of several variables. 5Credits
%5
5 credits
Prerequisites:
C- or better in 1151, 152.xx, 1156, 1161.xx, 161.01H, 161.xx, 1114 or 114.
Exclusions:
Not open to students in math, pre-actuarial science, or actuarial science. Not open to students
with credit for any higher numbered math class, or for 1152; or for 254.xx or higher numbered
math class.
Text:
Calculus for Scientists and Engineers: Early Transcendentals, 2nd OSU custom edition, by
Topics:
6.2
6.3
6.4
6.5
6.7
7.1
7.2
7.3
Regions between Curves
Volume by Slicing
Volume by Shells
Lengths of Curves
Physical Applications
Basic Approaches to Integration
Integration by Parts
Trigonometric Integrals
Midterm 1
7.4
7.5
7.8
9.1
9.2
9.3
9.4
9.5
10.1
10.2
10.3, 10.4
Trig Substitution
Partial Fractions
Improper Integrals
Overview of Sequences and Series
Sequences
Series (and Idea of Convergence)
Divergence Test (and Properties of Convergent Series only)
Ratio Test (only)
Approx functions with Polynomials
Properties of Power Series
Taylor Series
Midterm 2
Page 1
2016-2017
Math 1172
Mathematics 1172
Engineering Mathematics A
Autumn, Spring, Summer
5 Credits
11.1
11.2
11.3
11.4
12.1, 12.2
12.3, 12.4
12.5
12.6
12.7
12.8
Parametric Equations
Polar Equations
Calculus in Polar Coordinates
Conic Sections (Conic Sections in Polar optional)
Vectors in the Plane and 3-Space
Dot Products, Cross Products
Lines and Curves in Space
Calculus of Vector-Valued Functions
Motion in Space
Lengths of Curves
Autumn, Spring
5Credits
%5
5 credits
Midterm 3
13.1
13.2
13.3
13.4
13.5
13.6
Planes and Surfaces
Graphs and Level Curves
Limits and Continuity
Partial Derivatives
The Chain Rule
Final
Page 2
2016-2017
Math 1172
Mathematics 1181H
Honors Calculus I
Autumn
5 Credits
Catalog Description:
Single variable calculus treated in depth.
Autumn, Spring
5Credits
%5
5 credits
Prerequisites:
1151 or 151.xx, and permission of department.
Exclusions:
Not open to students with credit for any higher numbered math class.
Text:
ISBN: 9780070576424
Topics:
2.1
2.2
2.3
2.4
2.5
A2
3.1
3.2
3.3
3.4
3.5
3.6
12.2
4.1
4.2
4.3
4.4
4.5
2.6
A4
The Problem of Tangents
How to Calculate the Slope of the Tangent
The definition of the Derivative
Velocity and Rate of Change
The Concept of a Limit; Two Trigonometric Limits
Derivatives of Polynomials
The Product and Quotient Rules
Composite Functions and the Chain Rule
Some trig Derivatives;
Implicit Functions and Fractional Exponents
Derivatives of Higher Order
Indeterminate Form 0/0, L'Hopital's Rule
Increasing and Decreasing Functions, Maxima and Minima
Concavity and Points of Inflection
Applied Maxima and Minima Problems
Reflection & Refraction
Related Rates
Continuous Functions
The Mean Value Theorem
Midterm I
5.2
5.3
5.4
6.1
6.2
6.3
6.4
6.5
6.6
Page 1
Differentials and Tangent Line Approx'n
Indefinite Integrals, Integration by Substitution;
Differential Equations, Separation of Variables
Introduction
The Problem of Areas.
The Sigma Notation and Certain Special Sums
Area under a Curve, Definite Integrals, Riemann
The Computation of Areas as Limits;
The Fundamental Theorem of Calculus
2016-2017
Math 1181H
Mathematics 1181H
Honors Calculus I
Autumn
5 Credits
6.7
7.2
7.3
7.4
7.5; 7.6
7.7
8.2
8.3
8.4
8.5
9.1; 9.2
9.3; 9.4
9.5
9.6; 9.7
Algebraic and Geometric Areas
Autumn, Spring
Area between Two Curves;
5Credits
%5
Volumes: The Disk Method
5 credits
Volumes: The Method of Cylindrical Shells
Arc Length; Area of a Surface of Revolution
Work and Energy
Review of Exponents and Logarithms;
The number e and the function y=e^x
The Natural Logarithm Function, Euler
Applications, Population Growth and Radioactive Decay
Review of Trig.; Der've and Integrals of Sin and Cos
Der've of the Other Four Fns
The Inverse Trig Functions
Simple Harmonic Motion; (“Optional”) Hyperbolic Functions
MIDTERM 2
10.1; 10.2
10.3: 10.4
10.5; 10.6
10.7
10.8
12.2; 12.3
12.3; 12.4
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
Basic Formulas; Method of Substitution
Certain Trig Integrals; Trig Substitutions;
Completing the Square
Integration by Parts
Strategy for Dealing with Integrals
Indeterminate Form 0/0, L'Hopital's Rule; Other Indeterminate Forms
Improper Integrals
What is an Infinite Series?;
Convergent Sequences
Convergent and Divergent Series
General Properties of Convergent Series
Series of Non-negative Terms, Compar. Tests
Integral Test, Euler's Constant
Ratio and Root Test
Alternating Series Test, Absolute Convergence
MIDTERM 3
14.2
14.3
14.4
14.5
14.6
14.8
The Interval of Convergence
Differentiation and Integration of Power Series
Taylor' Series and Taylor's Formula
Computations Using Taylor's Formula
Applications to Differential Equations
Operations on Power Series
FINAL
Page 2
2016-2017
Math 1181H
Mathematics 1187H
Problem Solving
Autumn
1-2 Credits each
Prerequisite:
Permission of Department.
Catalog Description:
An advanced enrichment course for interested and capable students.
Purpose of Course:
To offer an experience in problem solving in mathematics for interested and talented students
beyond what they would encounter in a standard program. It is preparation for the National
Putnam Mathematics Exam. This course is repeatable to a maximum of 6 credit hours, and is
graded S/U. This course may not be counted in a major or minor program in Mathematics.
Topics:
Interesting special problems as chosen by the instructor.
Page 1
2016-2017
Math 1187H
Mathematics 1295
Introductory Seminar
1 credit
Catalog Description:
Seminar on mathematical topics for beginning math and actuarial science majors.
Prerequisite:
Enrollment in math or actuarial science major, or permission of department.
Topics List:
1. Overview of the scope of mathematics, its subfields, and its applications.
2. Discussion of the OSU math major and differences among the tracks.
3. Outline of programs and activities that can benefit math majors.
4. Presentation of various different sorts of career opportunities for math majors.
Page 1
2016-2017
Math 1295
Mathematics 2137
Algebra and Coordinate Geometry for Teachers
Autumn, Spring
3 credits
Catalog Description:
This is one of two independent courses which follow Measurement and geome-try for teachers to
provide necessary content for middle grade teachers. This course focuses on algebra, coordinate
geometry, and their connections through equations in one or more unknowns. Modern and
historical perspectives are woven throughout.
Prerequisite:
A grade of C- or above in “Measurement and Geometry for Teachers” (Math 1136). A grade of
C-or above in Math 1149 or 1150, or credit for 150, or math placement level L.
Text:
Basic Mathematics, by Serge Lang, Springer, ISBN 9780387967875
Purpose:
This course integrates the various types of numbers introduced in the previous course to present
them as members of a single (real) number system. The notion that new numbers are discovered
as solutions to equations is promoted, and motivated by connecting various equations with
mathematical models.
Matrices are introduced and used as linear transformations, mainly in the plane. The complex
numbers are introduced as general solutions to quadratic equations and the relationship between
complex arithmetic and transformations in the plane is explored.
The course ﬁnishes with several weeks of geometry content for middle grade teachers, including
more material on proofs, triangle congruence, and non-Euclidean geometry. The main example is
“Taxicab geometry”, based on the l1 norm.
Topics List:
1. Polynomial arithmetic as “base-x” and binomial theorem
2. Real number system
3. Polynomial equations and their roots
4. Exponential and logarithm functions
5. Complex numbers
6. Matrices
7. Complex arithmetic and linear transformations in the plane
8. Geometry proofs
9. Taxicab geometry
Page 1
2016-2017
Math 2137
Mathematics 2138
Calculus and its History for Teachers
Autumn, Spring
3 credits
Catalog Description:
This is one of two independent courses which follow “Measurement and Geometry for Teachers”
(Math 1136) to provide necessary content for middle grade teachers. This course focuses on
functions and calculus, including modern and historical perspectives.
Prerequisite:
A grade of C- or above in “Measurement and Geometry for Teachers” (Math 1136). A grade of
C- or above in Math 1149 or 1150, or credit for 150, or math placement level L.
Text:
Calculus, by Frank Morgan, CreateSpace Independent Publishing Platform, ISBN
9781478356882
Purpose:
This course serves to introduce students to the key ideas of calculus and to important historical
developments in the subject. A thorough introduction to functions as mappings is given, and the
trigonometric functions are used throughout the course as a key example of functions not given
by algebraic expressions.
The essential concepts of limit, derivative, integral, and the fundamental theorem are
emphasized, together with core applications. An introduction to Taylor series, especially the
Taylor expansions for sine and cosine, completes the class.
Topics List:
1. Functions
2. Elementary approach to how functions change
3. Defining rate of change
4. Concept of limit
5. Derivatives
6. Interpretations of first and second derivatives
7. Sine, cosine and logarithm functions
8. Product rule and chain rule
9. Applications of derivatives
10. Antiderivatives
11. Riemann sums
12. Fundamental theorem of calculus
13. Applications of integration
14. Taylor approximations, infinite sequences
15. Series
Page 1
2016-2017
Math 2138
Mathematics 2153
Calculus III
Autumn, Spring, Summer
4 credits
Catalog Description:
Multivariable differential and integral calculus.
Prerequisites:
C- or better in 1152, 1172, 1534, 1544, 1181H, or 4181H; or credit for 153.xx, 154, 162.xx, or
162.01H.
Exclusions:
Not open to students with credit for any higher numbered math class, or for any quarter math
class numbered 254 or higher.
Text:
Calculus for Scientists and Engineers: Early Transcendentals, 2nd OSU custom edition, by
Topics:
CHAPTER 12. Vectors and Vector-Valued Functions
Section 1. Vectors in the Plane
Section 2. Vectors in Three Dimensions
Section 3. Dot Products
Section 4. Cross Products
Section 5. Lines and Curves in Space
Section 6. Calculus of Vector-Valued Functions
Section 7. Motion in Space
Section 8. Length of Curves
Section 9. Curvature and Normal Vectors
CHAPTER 13. Functions of Several Variables
Section 1. Planes and Surfaces, and brief conic section review
via pages 761 to 766 of Section 11.4
Section 2. Graphs and Level Curves
Section 3. Limits and Continuity
Section 4. Partial Derivatives
Section 5. The Chain Rule
Section 6. Directional Derivatives and the Gradient
Section 7. Tangent Planes and Linear Approximation
Section 8. Maximum/Minimum Problems
Section 9. Lagrange Multipliers
CHAPTER 14. Multiple Integration
Page 1
2016-2017
Math 2153
Mathematics 2153
Calculus III
Autumn, Spring, Summer
4 credits
Section 1. Double Integrals over Rectangular Regions
Section 2. Double Integrals over General Regions
Section 3. Double Integrals in Polar Coordinates
Section 4. Triple Integrals
Section 5. Triple Integrals in Cylindrical and Spherical Coordinates
Section 6. Integrals for Mass Calculations
Section 7. Change of Variables in Multiple Integrals
CHAPTER 15. Vector Calculus
Section 1. Vector Fields
Section 2. Line Integrals
Section 3. Conservative Vector Fields
Section 4. Green’s Theorem
Section 5. Divergence and Curl
Section 6. Surface Integrals
Section 7. Stokes’ Theorem
Section 8. Divergence Theorem
Page 2
2016-2017
Math 2153
Catalog Description:
Multivariable calculus; introduction to Taylor series.
Mathematics 2162.01, 2162.02
Accelerated Calculus II
Accelerated Calculus II for Engineers
2162.01(Sp) 2162.02(Au, Sp)
5 credits
5 credits
Prerequisites:
C- or better in 1161.xx or 1181H.
Exclusions:
For 2162.01: Not open to students with credit for any higher numbered math class numbered
2162 or higher.
For 2162.02: Intended for students in Freshman Engineering Honors and not open to students
with credit for any higher numbered math class numbered 2162 or higher.
Text:
Calculus for Scientists and Engineers: Early Transcendentals, 2nd OSU custom edition, by
Topics:
9.1; 9.2
9.2; 9.3
9.4
9.5
9.5; 9.6
10.1; 10.2
10.3; 10.4
An Overview; Sequences
Sequences; Infinite Series
Divergence and Integral Tests
Ratio, root, and Comparison Tests
Ratio, root, and Comparison Tests; Alternating Series;
Approximating Functions with Polynomials; Properties of power Series
Taylor Series; Working with Taylor Series
11.1; 11.2
11.2; 11.3
Parametric Equations; Polar Coordinates
Polar Coordinates; Calculus in Polar Coordinates
Midterm 1
Page 1
2016-2017
Math 2162.01, 2162.02
12.1; 12.2
12.3;12.4
12.5
12.6
12.7; 12.8
12.9
13.1; 13.2
13.3
13.4;13.5
13.6
Mathematics 2162.01, 2162.02
Accelerated Calculus II
Accelerated Calculus II for Engineers
2162.01(Sp) 2162.02(Au, Sp)
5 credits
5 credits
Vectors in the Plane; Vectors in Three Dimensions
Dot Products; Cross Products
Lines and Curves in Space
Calculus of Vector-Valued Functions
Motion in Space; Length of Curves
Curvature and Normal Vectors
Planes and Surfaces; Graphs and Level Curves
Limits and Continuity
Partial Derivatives; Chain Rule
MIDTERM 2
13.7
13.8
13.9
14.1; 14.2
14.2; 14.3
14.4; 14.5
14.5; 14.6
15.1
15.2
15.3
Tangent Plane and Linear Approximation
Maximum/Minimum Problems
Lagrange Multipliers
Double Integral over Rectangular Regions; Double Integrals over General
Regions
Double Integrals over General Regions; Double integrals in Polar Coordinates
Triple Integrals; Triple Integrals in Cylindricals and Sphericals
Triple Integrals in Cylindricals and Sphericals; Integrals for Mass Calculations
Vector Fields
Line Integrals
Conservative Vector Fields
MIDTERM 3
15.4
15.5
15.6
15.7
15.8
Page 2
Green's Theorem
Divergence and Curl
Surface Integrals
Stokes' Theorem
Divergence Theorem
2016-2017
Math 2162.01, 2162.02
Mathematics 2167
Calculus for Middle School Teachers
Autumn
3 credits
Catalog Description:
Concepts of Calculus for Middle School Math teachers.
Prerequisite:
A grade of C- or above in 1165, or credit for 1164 or 110; and enrollment in Middle Childhood
Education major or pre-major with Math as area of concentration.
Exclusions:
Not open to students with credit for 111.
Purpose of Course:
The purpose of the course is to prepare teachers of middle school students. In particular, it
intends to deepen and extend the prospective teachers’ content knowledge of the mathematics
and mathematical reasoning that they will teach as well as their ability to reason with and
communicate that knowledge.
Follow-up Courses:
Math 2168
Text:
Under Consideration.
Optional text: Calculus Connections: Mathematics for Middle School Teachers. By Asma
Supplementary Text: Course Notes
Topics List:
1. Rates described pictorially, in writing, and with symbols.
2. Informal and formal measurement of (instantaneous) rates and their connection to middle
school mathematics.
3. Informal and formal measurement of (accumulated) areas and their connection to middle
school mathematics.
4. The Fundamental Theorem of Calculus.
5. Applications of differential calculus.
6. Applications of integral calculus.
Page 1
2016-2017
Math 2167
Mathematics 2168
History of Mathematics for Middle School Teachers
Spring
3 credits
Catalog Description:
Historical and mathematical discussion of topics in the middle school math curriculum.
Prerequisite:
C- or better in 2167; or credit for 111. Limited to Middle Childhood majors and pre-majors with
Math as an Area of Concentration.
Purpose of Course:
The purpose of the course is to prepare prospective middle school math teachers. In particular, it
intends to deepen and extend prospective teachers’ connections among topics in mathematics
through the study of the history of mathematics, as well as continuing to develop their ability to
reason with and communicate that knowledge.
Follow-up Courses:
None
Text:
Math through the Ages: A Gentle History for Teachers & Others, Expanded Edition, by
Course Packet
Topics List:
1. History of Mathematics, from ancient to modern times.
2. Development of number systems, operations, geometry, trigonometry, algebra, calculus,
statistics, and probability.
3. Applications: modeling real-world topics.
4. Problem solving (a theme throughout the course).
Page 1
2016-2017
Math 2168
Mathematics 2173
Engineering Mathematics B
Autumn, Spring
3 credits
Catalog Description:
Multiple integrals, line integrals, vector fields, second order ordinary differential equations.
Prerequisite:
Math 1172, 1544, or 154.
Exclusions:
Not open to students with credit for 1152, 2153, or for any higher numbered math class, or for
any quarter-system math class numbered 254 or higher.
Text:
Calculus for Scientists and Engineers: Early Transcendentals, 2nd OSU custom edition, by
Topics List:
13.6
13.8
13.9
14.1
14.2
14.3
(Review of) Directional Derivatives and the Gradient Vector
Maximum and Minimum Values
Lagrange Multipliers
Double Integrals over Rectangular Regions
Double Integrals over General Regions
Double Integrals in Polar Coordinates
Midterm 1
14.4
14.5
14.7
15.1
15.2
15.3
Triple Integrals
Triple Integrals in Cylindrical & Spherical Coordinates
Change of Variables in Multiple Integrals
Vector Fields
Line Integrals
Conservative Vector Fields
16.1
Appendix C
16.2
16.3
16.4
Midterm 2
Basic Ideas of Second Order ODE’s
Complex Arithmetic
Linear Homogeneous Equations
Linear Homogeneous Equations
Applications; Complex Forcing Functions
Final
Page 1
2016-2017
Math 2173
Mathematics 2174
Linear Algebra and Differential Equations
Autumn, Spring
3 credits
Catalog Description:
Matrix theory, eigenvectors and eigenvalues, ordinary and partial differential equations.
Prerequisite:
2173 and either major in ENG, Physics, or Chemistry or permission of math department.
Exclusions:
Not open to students with credit for both (i) 2415 (415) or 2255 (255) and (ii) 2568 (568 or 571).
Text:
Part II: Elementary Ordinary & Partial Differential Equations, OSU custom edition, by Boyce,
Introduction to Linear Algebra, 5th edition, by Johnson, Riess and Arnold, published by Pearson,
ISBN: 9780321628217
Topics List:
Part One = Matrix Algebra
Textbook sections from Arnold, Riess, and Johnson’s Introduction to Linear Algebra, 5th edition
Chapter 1: Matrices and Linear Systems of Equations
Chapter 3: The Vector Space ℝn
Chapter 4: The Eigenvalue Problem
1.1
1.2
1.3
1.5
1.6
1.7
1.9
3.1-3.2
3.3
3.4
Introduction and Gaussian Elimination and Systems of Linear Equations
Echelon Form and Gauss-Jordan Elimination
Consistent Systems of Linear Equations
Matrix Operations
Algebraic Properties of Matrix operations
Linear Independence and Nonsingular Matrices
Matrix Inverses and the Properties
Review and Vector Space Properties in ℝn
Examples of Subspaces
Basis for Subspaces; Dimension
Midterm I
Page 1
2016-2017
Math 2174
Mathematics 2174
Linear Algebra and Differential Equations
Autumn, Spring
3 credits
4.1
4.2
4.4
4.5
4.6
4.7
The Eigenvalue Problem for 2x2 Matrices
Determinants and the eigenvalue Problem
Eigenvalues and characteristic Polynomial
Eigenvectors and Eigenspaces
Complex Eigenvalues and Eigenvectors
Similarity Xformations and Diagonalization
Part Two = Systems of Linear Differential Equations
Textbook Sections from Boyce & DiPrima’s Part II: Elementary Ordinary & Partial Differential
Equations
Ch. 7: Systems of First Order Linear Equations (no lectures, but assigned as an
independent class project)
Midterm 2
Part Three = Partial Differential Equations and Fourier Series
Textbook Sections from Boyce & DiPrima’s Part II: Elementary Ordinary & Partial Differential
Equations
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
Page 2
Two point Boundary Value Problem
Fourier Series
The Fourier Convergence Theorem
Even and Odd Functions
Separation of Variables; Heat Conduction Equation
Other Heat Conduction Problems
The Wave Equation; Vibrations of an Elastic String
Laplace's Equation (optional)
2016-2017
Math 2174
Mathematics 2177
Mathematical Topics for Engineers
Autumn, Spring
4 credits
Catalog Description:
Multiple integrals, line integrals; matrix algebra; linear (ordinary and partial) differential
equations.
Prerequisite:
Major, pre-major, or minor in BiomedE, CEEGS, FABEng, MatScEn, CBE, or WeldEn; and:
1172, 2153, 1544 (154), 254.xx, 263.xx, 263.01H, or 264H
Exclusions:
Not open to students with credit for 2174 or 5520H; or with credit for both (i) 2415 (415), 2255
(255) or 4512 (512) and (ii) 2568 (568 or 571).
Text:
Math 2177, Custom Edition for OSU, Pearson, ISBN-13 978-1-256-82676-7 or ISBN-10 1-25682676-6 –OR– the textbooks listed below.
Topics List:
PART ONE: Multivariable Integral Calculus
Textbook Sections from Calculus for Scientists and Engineers: Early Transcendentals,
by Briggs, Cochran, Gillett and Shulz, Chapters 13-15
2177
Custom
1.8
1.9
2.1
2.2
2.3
2.4
2.5
2.7
3.1
3.2
3.3
Original
Text
13.8
13.9
14.1
14.2
14.3
14.4
14.5
14.7
15.1
15.2
15.3
Topic
Maximum/Minimum Problems
Lagrange Multipliers
Double Integrals over Rectangular Regions
Double Integrals over General Regions
Double Integrals in Polar Coordinates
Triple Integrals
Triple Integrals in Cylindrical and Spherical Coordinates
Change of Variables in Multiple Integrals
Vector Fields
Line Integrals
Conservative Vector Field
Midterm 1
Page 1
2016-2017
Math 2177
Mathematics 2177
Mathematical Topics for Engineers
Autumn, Spring
4 credits
PART TWO: Matrices and Linear Systems of Equations
Textbook Sections from Introduction to Linear Algebra, by Johnson, Riess, and Arnold,
5th edition, Chapter 1: Matrices and Systems of Linear Equations
2177
Original
Custom
Text
4.1
1.1
4.2
1.2
4.3
1.3
4.4
4.4
4.5
1.5
4.6
1.6
4.7
1.7
4.8
1.8
Midterm 2
Topic
Introduction to Matrices and Systems of Linear Equations
Echelon Form and Gauss-Jordan Elimination
Consistent Systems of Linear Equations
Applications (optional)
Matrix Operations
Algebraic Properties of Matrix operations
Linear Independence and Nonsingular Matrices
Data Fitting, Numerical Integration and Numerical Differentiation
PART THREE: 2nd Order Constant Coefficient O.D.E.' s
Textbook Sections from Calculus for Scientists and Engineers: Early Transcendentals,
by Briggs, Cochran, Gillett and Shulz, Chapter 16 and Appendix C
2177
Original
Custom
Text
5.1
16.1
Appx C
Appx C
5.2
16.2
5.3
16.3
5.4
16.4
Midterm 3
Topic
Basic Ideas
Complex Numbers
Linear Homogeneous Equations
Linear Nonhomogeneous Equations
Applications
PART FOUR: Fourier Series & Partial Differential Equations
Textbook Sections from Fundamentals of Differential Equations and Boundary Value
Problems, by Nagle, Saff and Snider, 8th Edition, Chapter 10
2177
Custom
6.1
6.2
6.3
6.4
6.5
6.6
Page 2
Original
Text
10.1
10.2
10.3
10.4
10.5
10.6
Topic
Introduction: A Model for Heat Flow
Method of Separation of Variables
Fourier Series
Fourier Cosine and Sine Series
The Heat Equation
The Wave Equation
2016-2017
Math 2177
Mathematics 2182H
Honors Calculus II
Spring
5 credits
Catalog Description:
Multivariable calculus treated in depth.
Prerequisite:
C or better in 1181H or 4181H.
Exclusions:
Not open to students with credit for both 162.01H and 263.01H
Text:
Calculus with Analytic Geometry, 2nd Edition, by George F. Simmons, published by McGrawHill, ISBN: 0070576424
Topics List:
15.1; 15.2
15.3; 15.4
16.1
16.2
16.3
16.3; 16.4
16.5
17.1
17.2
17.3
17.4
17.5
17.6
17.7
Conic sections: Ellipse, Parabola, Hyperbola
Conic sections: Ellipse, Parabola, Hyperbola
Polar coordinate system
Graphs of polar equations
Polar Equations of conics and spirals
Polar Equations of conics and spirals; Arc length and tangent lines
Areas in polar coordinates
Parametric Equations of Curves
Cycloids and other similar Figures
Vector Algebra, the Unit Vectors i and j;
Derivatives of Vector Functions, Velocity and Acceleration
Curvature and the Unit Normal Vector
Tangential and Normal Components of Acceleration
Kepler's Laws and Newton's Law of Universal Gravitation
Midterm 1
Page 1
2016-2017
Math 2182H
Mathematics 2182H
Honors Calculus II
Spring
5 credits
18.1
18.2
18.3
18.4
18.5
18.6
18.7
19.1
19.2
19.3
19.4
19.5
19.6
19.7; 19.8
19.10
Coordinates and Vectors in 3-D Space
The Cross Product of Two Vectors
The Dot Product of Two Vectors
Lines and Planes
Cylinders and Surfaces of Revolution
Cylindrical and Spherical Coordinates
Function of Several Variables
Partial Derivatives
The Plane Tangent to a Surface
Increments and Differentials, the Fundamental Lemma
The Chain Rule for Partial Derivatives
Maximum and Minimum Problems
Implicit Functions
Midterm 2
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
Volumes as Iterated Integrals
Double Integrals and Iterated Integrals
Physical Applications of Double Integrals
Double Integrals in Polar Coordinates
Triple Integrals
Cylindrical Coordinates
Spherical Coordinates, Gravitational Attraction
Area of Curved Surfaces
Midterm 3
21.1
21.2
21.3
21.4
21.5
Page 2
Line Integrals in the Plane
Independence of Path, Conservative Fields
Green's Theorem
Surface Integrals and Gauss' Theorem
Stokes' Theorem
2016-2017
Math 2182H
Mathematics 2255
Differential Equations and Their Applications
Autumn, Spring, Summer
3 credits
Catalog Description:
Ordinary differential equations, their series solutions, numerical methods, Laplace transforms,
physical applications.
Prerequisite:
C- or better in 2153, 2162.xx, 2173, 2182H, or 4182H; or credit for 254.xx, 263.xx, 263.01H, or
264H.
Text:
Ordinary Differential Equations and their Applications, OSU custom edition, by Boyce,
Topics List:
1.3
2.1
INTRODUCTION
Classification of Differential Equations
Linear Equations with Variable Coefficients
2.2
2.4
2.5
2.6
2.7
2.8
2.9
FIRST ORDER DIFFERENTIAL EQUATIONS
Separable Equations
Differences between Linear and Nonlinear Equations
Autonomous Equations and Population Dynamics
Exact Equations and Integrating Factors
Numerical Approximations: Euler’s Method
The Existence and Uniqueness Theorem
First Order Difference Equations
3.1
3.3
3.2
3.4
SECOND ORDER LINEAR EQUATIONS
Homogeneous Equations with Constant Coefficients
Complex Roots of the Characteristic Equation
Solutions of Linear Homogeneous Equations; the Wronkian
Repeated Roots; Reduction of Order
Midterm 1
3.5
3.6
3.7
3.8
Page 1
Nonhomogeneous Equations; Method of Undetermined Coefficients
Variation of Parameters
Mechanical and Electrical Vibrations
Forced Vibrations
2016-2017
Math 2255
Mathematics 2255
Differential Equations and Their Applications
Autumn, Spring, Summer
3 credits
6.1
6.3
6.2
6.4
6.5
6.6
THE LAPLACE TRANSFORM
Definition of the Laplace Transform
Step Functions
Solution of Initial Value Problems
Differential Equations with Discontinuous Forcing Functions
Impulse Functions
The Convolution Integral
Midterm 2
4.1
4.2
4.3
4.4
HIGHER ORDER LINEAR EQUATIONS
General Theory of nth Order Equations
Homogeneous Equations with Constant Coefficients
The Method of Undetermined Coefficients Material
The Method of Variation of Parameters
5.1
5.2
5.3
5.4
SERIES SOLUTIONS OF SECOND ORDER LINEAR EQUATIONS
Review of Power Series
Series Solutions near an Ordinary Point, Part I
Series Solutions near an Ordinary Point, Part II
Euler's Equation; Regular Singular Points
Midterm 3
5.5
5.6
5.7
Page 2
Series Solutions near a Regular Singular Point, Part I
Series Solutions near a Regular Singular Point, Part II
Bessel's Equation
2016-2017
Math 2255
Mathematics 2366
Introduction to Discrete Mathematics
Spring
2 credits
Catalog Description:
Mathematical reasoning, logic, sets, functions, recursive definitions, elementary counting
principles.
Prerequisites:
C- or better in 1131 or 1151; credit for 132 or 152.xx; or permission of department.
Exclusions:
Open only to majors in MIS (Management Information Systems). Not open to students with
credit for 366.
Text:
Discrete Mathematics with Applications, 4th edition, by Epp, published by Cengage, ISBN:
9780495391326, Lecture Notes by G. Baker.
Topics List:
Topics for this discrete math course depend on future discussions with colleagues in
Management Information Systems.
Page 1
2016-2017
Math 2366
Mathematics 2415
Ordinary and Partial Differential Equations
Autumn, Spring, Summer
3 credits
Catalog Description:
Ordinary and partial differential equations: Fourier series, boundary and initial value problems.
Prerequisite:
2153, 2162.xx, 2173, 2182H, 4182H, both (1172 or 1544 or 154) and 2568, 254.xx, 263.xx,
263.01H, or 264H.
Exclusions:
Not open to students with credit for Math 2255, 5520H, 2174, 255, 415.xx, or 521H.
Textbook:
Elementary Differential Equations and Boundary Value Problems, 10th Edition, by W. Boyce
and R. DiPrima, ISBN 978-1-118-15738-1
Topics List:
1.1
Some Basic Mathematical Models & Direction Fields
1.3
Classification of Differential Equations
1.2
Solutions to some Differential Equations
2.2
Separable Equations
2.1
Linear Equations with Variable Coefficients
2.3
Modeling with First Order Differential Equations
2.4
Difference between Linear and Nonlinear Equations
2.5
Autonomous Equations and Population Dynamics
3.1
Homogeneous Equations with Constant Coefficients;
3.3
Complex Roots of the Characteristic Equation
3.4
Repeated Roots
Midterm 1
3.2
3.4
4.5
3.7
3.9
10.1
Solutions of Linear Homogeneous Equations; the Wronskian
Reduction of Order
Non-homogeneous Equations; Method of Undetermined Coefficients
Mechanical and Electrical vibrations
Forced Vibrations
Two-point Boundary Value Problem
Midterm 2
Page 1
2016-2017
Math 2415
Mathematics 2415
Ordinary and Partial Differential Equations
Autumn, Spring, Summer
3 credits
10.2
10.3
10.4
10.5
10.7
7.1
7.3
7.5
7.6
7.4
Page 2
Fourier Series
The Fourier Convergence Theorem
Even and Odd Functions
Separation of Variables; Heat Conduction in a Rod
Wave Equation: Vibrations of an Elastic String
Introduction
Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
Homogeneous Linear Systems with Constant Coefficients
Complex Eigenvalues
Basic Theory of Systems of 1st Order Linear Equations
2016-2017
Math 2415
Mathematics 2568
Linear Algebra
Autumn, Spring, Summer
3 credits
Catalog Description:
Matrix algebra, vector spaces and linear maps, bases and dimension, eigenvalues and
eigenvectors, applications.
Prerequisite:
C- or above in 1172, 1544, 2153, 2162.xx, 2182H, or 4182H; or C- or above in both 1152 and
CSE 2321; or credit for 154, 254.xx, 263.xx, 263.01H, or 264H.
Exclusions:
Not open to students with credit for 4568 (568), 5520H (520H), or 572.
Text:
Introduction to Linear Algebra, 5th edition, by L.W. Johnson, R.D. Riess, and J.T. Arnold,
Topics List:
1.1
1.2
1.3
1.5
1.6
1.7
1.9
Part I
Introduction to Matrices and Systems of linear equations
Echelon Form and Gaussian-Jordan Elimination
Consistent Systems of linear Equations
Matrix Operations
Algebraic Properties of Matrix operations
Linear Independence and Nonsingular Matrices
Matrix Inverses and Their Properties
Midterm 1
2.1
2.2
2.3
3.1
3.2
3.3
3.4
3.5
5.2
5.3
5.4
3.6
3.7
Page 1
Part II
Vectors in The Plane (Review only because it was done in 1152)
Vectors in Space (Review only because it was done in 1152)
The Dot Product and The Cross
Introduction
Vector Space Properties of ℝn
Examples of Subspaces
Bases for Subspaces
Dimension
Vector Spaces
Subspaces
Linear Independence, Bases, and Coordinates
Orthogonal Bases for Subspaces
Linear Transformation from ℝn to ℝm
2016-2017
Math 2568
Mathematics 2568
Linear Algebra
Autumn, Spring, Summer
3 credits
Midterm 2
4.1
4.2
4.4
4.5
4.6
4.7
Part III
The Eigenvalue Problem for 2x2 Matrices
Determinants and the Eigenvalue Problem
Eigenvalues and Characteristic Polynomial
Eigenvectors and Eigenspaces
Complex Eigenvalues and Eigenvectors
Similarity Transformations and Diagonalization
Final
Page 2
2016-2017
Math 2568
Mathematics 3345
Foundations of Higher Mathematics
Autumn, Spring
3 credits
Catalog Description:
Introduction to logic, proof techniques, set theory, number theory, real numbers.
Prerequisite:
Major or minor in Math, CSE, or CIS.
Math: C- or better in 2153, 2162.xx, 2173, or 2182H; or credit for 254.xx, 263.xx or
263.01H.
CIS or CSE:
C- or better in both CSE 2321 and: C- or better in 1152, 1161.xx, 1172, 1181H, 1534, or
1544; or credit for 153.xx, 154, 162.xx, or 162.01H.
Exclusions:
Not open to students with credit for 345.
Text:
Lecture Notes, by N. Falkner.
Topics List:
1. Propositional calculus; quantifiers.
2. Simple examples of mathematical proofs.
3. Mathematical induction.
4. Sets and functions: surjections, injections, bijections.
5. Infinite sets: countable and uncountable.
Page 1
2016-2017
Math 3345
Mathematics 3350
Introduction to Mathematical Biology
Spring
3 credits
3 credits
Catalog Description:
Introduction to quantitative and qualitative analysis of several mathematical models for
biological systems.
Purpose:
This course provides students with experience and knowledge in mathematical analysis of
differential equations models, as well as with numerical tools for simulating those models.
Prerequisite:
C- or better in Math 2255, 2415, 5520H; or credit for 255, 415.xx, or 521H.
Text:
Lecture Notes
Topics List:
1. Population dynamics: Logistic growth.
2. Population dynamics: Lotka-Volterra predator-prey model.
3. Modeling specific diseases (e.g. HIV, cancer).
4. Competition models.
5. Dynamics of neurons.
6. Bifurcution theory.
7. Enzyme kinetics.
8. Cells proliferation and death.
Page 1
2016-2017
Math 3350
Mathematics 3532
Mathematical Foundations of Actuarial Science
Spring
3 credits
Catalog Description:
Problem workshop for applications of calculus and probability to actuarial science and risk
management.
Prerequisite:
C- or better in Math 4530, 5530H, or Stat 4201; or credit for 530, 531H, or Stat 420.
Topics List:
1. Random variables.
2. Discrete distributions.
3. Continuous distributions.
4. Central Limit Theorem and law of large numbers.
5. Risk models.
Page 1
2016-2017
Math 3532
Mathematics 3588
Practicum in Actuarial Science
Spring
3 credits
Catalog Description:
Presentations by practicing actuaries on topics drawn from their fields of expertise; oral
presentations by students on selected topics in actuarial science.
Prerequisite:
3rd year standing and completion of second writing course.
Exclusions:
Open only to actuarial science majors.
Text:
None.
Topics List:
2. Problems in life insurance.
3. Problems in property and casualty insurance.
4. Problems in pension consulting.
5. Problems in health care consulting.
6. Risk management.
Page 1
2016-2017
Math 3588
Mathematics 3589
Introduction to Financial Mathematics
Autumn
3 credits
Catalog Description:
Introduction to mathematics used in financial asset pricing, based on the binomial asset pricing
model. This course prepares students for further study of stochastic calculus in continuous time.
Purpose:
This course is designed as an introduction to the concepts encountered in financial mathematics
for students who don’t have a background in continuous-time stochastic calculus.
Prerequisite:
{C- or better in 3345 or credit for 345}; and {C- or better in 4530, 5530H, or Stat 4201, or credit
for 530, 531H, 345 or Stat 420}; or permission of department.
Text:
Stochastic Calculus for Finance I, The Binomial Asset Pricing Model, by Shreve, published by
Springer, ISBN: 9780387249681
Topics List:
1. First principles; assumptions about stock behavior and description of basic financial
instruments; put and call options.
2. Arbitrage, and no-arbitrage pricing.
3. One-period and multi-period models; replication and hedging.
4. Conditional expectations.
5. Martingales and Markov processes.
6. Change of measure.
7. Utility functions and the capital asset pricing model.
8. Stopping times and American derivatives.
9. Random walks and passage times.
Page 1
2016-2017
Math 3589
Mathematics 3607
Beginning Scientific Computing
Autumn, Spring
3 credits
Catalog Description:
3 credits
Introduction to uses of computers to solve problems arising in the physical and biological
sciences, and in engineering and finance.
Prerequisite:
{C- or better in 2255, 2415, or 5520H; and C- or better in 2568 or 5520H}; or:
{credit for 255, 415.xx, or 521H; and credit for 568, 571, or 520H}.
Purpose:
Math 3607 is a course which has three main goals: it introduces students to MATLAB (or
improves their knowledge of MATLAB); it uses MATLAB to solve practical problems from
various areas of mathematics, physics, engineering, business, and finance; and it presents the
numerical analysis needed to use MATLAB effectively. The principle underlying this course is
that the way to learn MATLAB and numerical analysis is by doing it, not by reading about it.
This course is taught in a computer lab and MATLAB will be used to some extent every class.
Textbook:
Learning MATLAB, Problem Solving, and Numerical Analysis through Examples, by Ed
Topics List:
1. MATLAB as a scalar calculator, round-off errors, debugging.
2. Arrays in MATLAB, probability theory, Markov processes.
3. Graphics in MATLAB, applications of probability theory, histograms.
4. Programming in MATLAB, more probability theory, mathematical biology.
5. Function m-files in MATLAB, more Markov processes, chaos.
7. Solving linear systems of equations.
8. Interpolation and approximation.
9. The solution of nonlinear equations and unconstrained optimization.
10. Numerical differentiation and integration
11. Time-evolution ordinary differential equations, boundary-value ordinary differential
equations, stochastic differential equations, examples from many disciplines.
12. Eigenvalues, Fourier series.
Page 1
2016-2017
Math 3607
Mathematics 3618
Theory of Interest
Autumn, Spring, Summer
3 credits
Catalog Description:
3 credits
Financial transactions involving interest: measurement of interest, force of interest, annuitiescertain, introduction to financial derivatives.
Prerequisite:
C- or better in 1152, 2162.xx, 1172, 2182H, 4181H; or credit for 153, 162, 162H, or 191H.
Exclusions: Open only to actuarial science majors and pre-majors, and to math majors.
Text:
Mathematics of Investment & Credit, 5th edition, by Broverman, published by Actex. ISBN:
9781566987677
Topics List:
1. Compound and simple rates of interest and discount, force of interest.
2. Annuity certain and annuity due.
3. Mortgage amortizations.
4. Evaluation of bonds.
5. Durations.
6. Asset and liability matching.
7. Introduction to options, futures, and other derivatives.
Page 1
2016-2017
Math 3618
Mathematics 4181H (Au), 4182H (Sp)
Honors Analysis I, Honors Analysis II
5 credits each
3 credits
Catalog Description:
4181H and 4182H is an enriched honors sequence introducing students to mathematical
underpinnings of calculus. 4181H is the first of the calculus sequence designed to introduce
students to the mathematical underpinnings of analysis. 4182H is a continuation with a rigorous
treatment of multivariable calculus including gradients, multiple integrals, line and surface
integrals, Green’s theorem, the divergence theorem, and Stokes’ Theorem.
Prerequisite:
4181H: Permission of department.
4182H: B- or better in 4181H, or permission of department.
Purpose of Course:
This two-semester sequence comprises the most intensive first year honors track in mathematics.
It is designed to challenge talented, highly motivated students, regardless of their chosen major
area of study. The courses introduce students to the mathematical underpinnings of calculus and
stimulate the development of mathematical thinking, in addition to covering the material of the
traditional calculus sequence. 4181H and 4182H will fulfill the analysis requirement for a Math
major. The sequence is taught by faculty members in small sections with considerable teacherstudent interaction.
Text:
4181H: Calculus, 4th edition, by Spivak, published by Publish or Perish, ISBN: 9780914098918
Topics List:
4181H:
1. Properties of real numbers
2. Mathematical induction
3. Definition of integral
4. Integrals of polynomials and trigonometric functions.
5. Applications
6. Continuity, limits, derivatives and applications
7. Fundamental Theorem of Calculus and integration techniques
8. Taylor series
9. Sequences and series of numbers and functions
10. Uniform convergence
11. Power series
12. If time permits, some differential equations or complex-valued functions.
Page 1
2016-2017
Math 4181H, 4182H
Mathematics 4181H (Au), 4182H (Sp)
Honors Analysis I, Honors Analysis II
5 credits each
3 credits
4182H:
1. Multivariable calculus (vector approach)
3. Multiple integrals
4. Line and surface integrals
5. Green's Theorem
6. Divergence theorem
7. Stokes' Theorem.
Page 2
2016-2017
Math 4181H, 4182H
Mathematics 4350
Quantitative Neuroscience
Spring
3 credits
Catalog Description:
Introduction to mathematical modeling and computational analysis of neuronal systems, HodgkinHuxley model, dynamical systems methods, neuronal networks, models for neurological disease.
Prerequisite:
Math 1152 (152) or 1157 or permission of instructor.
Purpose:
Mathematical models and computational methods have been very useful in understanding biological
mechanisms underlying neuronal behavior. The Hodgkin‐Huxley model, for example, has formed the
basis for our understanding of how action potentials are generated and how they propagate along a
nerve axon. More recently, mathematical models have been used to help understand cellular
processes responsible for both normal and pathological firing patterns that arise in a wide range of
neuronal systems. Examples include models for sleep rhythms, sensory processing, Parkinsonian
tremor and working memory.
This course provides a detailed introduction to how mathematical and computational methods have
been used to both develop and analyze models that arise in neuroscience. We begin by deriving the
Hodgkin--‐Huxley model and then describe dynamical system methods for analyzing models. After
discussing the dynamics of single neurons, we consider neuronal networks and describe how
different types of population firing patterns depend on biological details, such as the intrinsic
properties of individual neurons and synaptic coupling. We conclude by considering specific
systems, including models for sleep rhythms, olfaction, working memory and neurological disease.
Text:
Foundations of Mathematical Neuroscience, by G. Bard Ermentrout and David H. Terman
Topics List:
1. Overview: Neurons, synapses, neuronal firing patterns
2. Hodgkin‐Huxley Model: Resting potential, Nernst equation, Goldman‐Hodgkin‐Katz
equation, Cable equation, action potential
3. Dynamics I: Introduction to differential equations; phase‐planes; oscillations
4. Dynamics II: Stability analysis, bifurcation theory, numerical methods
5. Single cell dynamics I: Propagating action potentials; rhythmic behavior
6. Single cell dynamics II: Variety of channels, bursting oscillations; dendrites - multi‐
compartment models
7. Synapses: Simple networks
8. Networks: Classification of network behavior; synchrony, role of different types of channels
and coupling
9. Models for sleep: Sleep/wake cycle, Thalamocortical oscillations
10. Parkinson’s disease: Basal ganglia, origin of pathological firing patterns, Deep brain
stimulation
11. Olfaction
12. Vision
13. Stroke
14. Presentation of projects
Page 1
2016-2017
Math 4350
Mathematics 4504
History of Mathematics
Spring
3 credits
Catalog Description:
Development of mathematics from primitive origins to present forms.
development of arithmetic, algebra, geometry, trigonometry, and calculus.
Topics include:
Prerequisite:
C- or better in 2568, 4507, or 5520H; or credit for 568, 571, 507, 580, or 520H; or permission of
department.
Exclusions:
Open only to math majors, or students with graduate standing in Ed T&L. Not open to students
with credit for 504.
Text:
Topics List:
1. Development of arithmetic; Babylonian tablets and Egyptian papyri.
2. Development of geometry: Pythagoras, Thales, Euclid, Archimedes, Ptolemy, and nonEuclidean geometry.
3. Development of algebra and calculus.
Page 1
2016-2017
Math 4504
Mathematics 4507
Geometry
Autumn, Spring
3 credits
Catalog Description:
Topics in Euclidean, spherical, and hyperbolic geometries. Connections to high school
mathematics, calculus, and the theory of groups are emphasized.
Prerequisite:
C- or better in 3345 and in C- or better in 2568 or 5520H; or credit for 345, and credit for 568,
571, or 520H; or graduate standing.
Purpose:
This course treats Euclidean, spherical, and hyperbolic geometry from a unified point of view.
Moreover, in this course students essentially write their own “textbook” with the proofs of a
majority of the theorems left to the student. With this in mind, we hope to encourage the student
to become a “do-er” of mathematics.
Text:
Course notes.
Topics List:
1. Neutral geometry.
2. Euclidean geometry.
3. Spherical geometry.
4. Hyperbolic geometry.
Page 1
2016-2017
Math 4507
Mathematics 4512
Partial Differential Equations
for Science and Engineering
Autumn, Spring, Summer
3 credits
Catalog Description:
Second-order PDEs; boundary value problems; Fourier series; wave, heat and Laplace equations;
applications.
Prerequisite:
C- or better in 2173, 2153, 2162.xx, 2182H, or 4182H; or credit for 254.xx, 263.xx, 263.01H, or
264H. Intended for undergraduate and master degree students in Engineering and Science.
Exclusions:
Not open to students with credit for 4557, 512, or 557.
Not open to students with a math major, math minor or actuarial science major.
Purpose of Course:
This course develops problem solving skills with little emphasis on theory. Students should be
able to solve the PDE’s and ODE’s and interpret the solution.
Text:
Partial Differential Equations & Boundary Value Problems, 9th OSU custom edition, by Boyce,
Topics List:
Part I: ODE's via The Laplace Transform (Chapter 6);
Euler's and Bessel's Equation (½ of Chapter 5)
6.1
Definition of the Laplace Transform
6.2
Solution of Initial Value Problems
6.3
Step Functions
6.4
Differential Equations with Discontinuous Forcing Functions
6.5
Impulse Functions
6.6
Convolution Integral
5.4
Euler's Equation; Regular Singular Points
5.5
Series Solution near a Singular Point: Part I
5.6
Series Solution near a Singular Point: Part II
5.7
Bessel's Equation
Midterm I
Page 1
2016-2017
Math 4512
Mathematics 4512
Partial Differential Equations
for Science and Engineering
Autumn, Spring, Summer
3 credits
Part II: Partial Differential Equations and Fourier Series (Chapter 10)
10.1 The Two-Point Boundary Value Problem
10.2 Fourier Series
10.3 Fourier Convergence Theorem
10.4 Even and Odd Functions
App A Heat Conduction Equation: Motivation via Derivation
10.5 Separation of Variables; Heat Conduction in a Rod
10.6 Other Heat Conduction Problems: Nonhomogeneous, Mixed Boundary Conditions
App B Wave Equation: Motivation via Derivation;
10.7 Vibrations of an Elastic String
10.8 Laplace's Equation: Separation in Cartesian Coordinates Dirichelet vs. Neumann
Boundary Conditions
10.8 Separation and Solution in Polar and Cylindrical Coordinates
Midterm II
11.1
11.2
11.2
11.3
11.4
11.5
11.6
Page 2
Part III: Boundary Value Problems (Chapter 11)
Two-point Boundary Value Problems
Sturm-Liouville Boundary Value Problems I
Sturm-Liouville Boundary Value Problems II
Nonhomogeneous Boundary Value Problems
Singular Sturm-Liouville Problems
Bessel Series Expansion: Vibrating Drum
(If time permits: Series of Orthogonal Functions: Mean Convergence)
2016-2017
Math 4512
Mathematics 4530
Probability
Autumn, Spring, Summer
3 credits
Catalog Description:
Combinatorial probability, random variables, independence, expectation, variance.
Purpose:
This is an introductory probability course designed to give students a firm grasp of random
variables, where they occur, and how they are used, and to develop the computational tools
necessary to work with them.
Prerequisite:
C- or better in 2153, 2162.xx, 2173, 2177, 2182H, 4182H; or credit for 254.xx, 263.xx, 263.01H,
or 264H.
Exclusions:
Not open to students with credit for any of 530, 5530H (531H), or Stat 4201 or 420.
Follow-up Courses:
Math 3532 (actuarial science majors), Math 3589 (financial math), Stat 4202.
Text:
Topics List:
I. Discrete probability.
1. First principles: outcome spaces, basic counting techniques, and partitions.
2. Venn diagrams and the inclusion-exclusion principle.
3. Conditional probability and independence; decision trees and Bayes’ Theorem.
4. Discrete random variables; mass and generating functions; joint distributions.
5. Binomial, hypergeometric, geometric, negative binomial, and Poisson variables;
applications and relationships.
6. Statistics on discrete variables.
II. Continuous probability
7. First principles: density functions, calculation of probabilities and statistics.
8. Moments and moment-generating functions.
9. Common distributions and their applications; exponential, gamma, uniform, normal.
10. The central limit theorem and normal approximation to the binomial distribution.
11. Relationships between the exponential, gamma, and Poisson distributions.
12. Hazard rates and survival functions.
13. Cumulative distribution functions, percentiles, and change of variables.
14. Joint distribution of continuous variables; independence and marginal distributions;
density of a function of two variables
Page 1
2016-2017
Math 4530
Mathematics 4545
Analysis Overview
Autumn
4 credits
Catalog Description:
Topics in calculus and analysis.
Prerequisites:
Either C- or better in 2153, 2162.xx, 2173, 2182H, or 4182H; or credit for 254, 263.xx, 263.01H,
264H, or equivalent;
-and- C- or better in Math 2568, 5520H, or equivalent.
Exclusions: Entry to this course is restricted to graduate students in Statistics or Biostatistics
who have permission from the Departments of Statistics or Biostatistics.
Text:
Introduction to Real Analysis, by William F. Trench, Edition1.03, published by Library of
Topics List:
1. Limits and continuity of functions.
2. Derivative, mean value theorem, optimization.
3. Sequences and series, uniform convergence, power series, Taylor's theorem.
4. Riemann integral, substitution, bounded variation, limit properties, Rieman-Stieltjes
integral.
5. Multivariable functions, directional derivatives, chain rule, Taylor's theorem.
6. Inverse and implicit function theorems, Lagrange multipliers, multiple integrals,
Jacobians, differentiation under the integral sign.
Page 1
2016-2017
Math 4545
Mathematics 4547
Introductory Analysis I
Autumn, Spring
3 credits
Catalog Description:
4547-4548 involved advanced calculus covering: sequences, limits, continuity, differentiation,
Riemann integral, sequences and series of functions, Taylor series, and improper integrals.
Prerequisite:
C- or better in 3345, or credit for 345.
Text:
Introduction to Real Analysis, 4th edition, by Bartle & Sherbert, published by Wiley,
ISBN: 9780471433316
Topics List:
1. Sequences and their limits.
2. Bolzano-Weierstrass Theorem and Cauchy’s criterion.
3. Convergence and absolute convergence of series. Tests for convergence.
4. Power series.
5. Continuous functions.
Page 1
2016-2017
Math 4547
Mathematics 4548
Introductory Analysis II
Autumn, Spring
3 credits
Catalog Description:
4547-4548 involved advanced calculus covering: sequences, limits, continuity, differentiation,
Riemann integral, sequences and series of functions, Taylor series, and improper integrals.
Prerequisite:
C- or better in 4547, or credit for 548.
Text:
Introduction to Real Analysis, 4th edition, by Bartle & Sherbert, published by Wiley,
ISBN: 9780471433316
Topics List:
1. Uniform continuity.
2. Derivatives.
3. Mean Value Theorem, L’Hopital’s rule.
4. Taylor series.
5. Riemann integral.
6. Exponential and logarithmic functions.
7. Sequences and series of functions.
Page 1
2016-2017
Math 4548
Mathematics 4551
Vector Analysis
Autumn, Spring
3 credits
Catalog Description:
Vector operations; Jacobian and change of variables; div, grad and curl; Green's Stokes', and
divergence theorems; applications.
Prerequisite:
C- or better in 2153, 2162.xx, 2173, or 2182H; or credit for 254.xx, 263.xx or 263.01H.
Exclusions:
Not open to students with credit for Math 4182H, 264H, 513 or 551.
Text:
Topics List:
1. Vector operations, multiple integrals, line and surface integrals.
2. Vector operators: div, grad, and curl.
3. Jacobians and change of variables.
4. Green's Theorem, Stokes theorem.
5. Divergence Theorem.
6. Applications.
Page 1
2016-2017
Math 4551
Mathematics 4552
Complex Analysis
Spring, Summer
3 credits
Catalog Description:
Introduction to analytic functions of a complex variable, integral theorems, power series,
residues, conformal mapping.
Prerequisite:
C- or better in 2153, 2162.xx, 2173, 2182H, or 4182H; or credit for 254.xx, 263.xx, 263.01H, or
264H.
Exclusions:
Not open to students with credit for Math 5522H, 552 or 514.
Purpose:
This course provides a comprehensive introduction to complex analysis, emphasizing
applications that are useful in science and engineering.
Text:
Complex Variables and Applications, 8th edition, by Brown & Churchill, published by McGrawHill, ISBN: 0073051942
Topics List:
Complex numbers, polar form (Ch. 1)
Analyticity, Cauchy-Riemann equations (Ch. 2)
Elementary functions (Ch. 3)
Cauchy integral theorem and consequences (Ch. 4)
Midterm 1
Power series (Ch. 5)
Residues and poles (Ch. 6)
Applications of residues (Ch. 7)
Mapping by elementary functions (Ch. 8)
Conformal mapping (Ch. 9)
Midterm 2
Applications of conformal mapping (Ch. 10)
Schwarz-Christoffel transformation (Ch. 11)
Poisson integral, Dirichlet problem (Ch. 12)
Page 1
2016-2017
Math 4552
Mathematics 4556
Dynamical Systems
Autumn
3 credits
5 credits
Catalog Description:
Systems of linear, first-order differential equations; existence and uniqueness theorems;
numerical methods; qualitative theory (phase plane analysis, linearization, stability, limit cycles);
and physical applications.
Prerequisite:
C- or better in 2153, 2162.xx, 2173, 2182H, or 4182H; or credit for 254.xx, 263, 263H, or 264H.
Text:
Nonlinear Dynamics and Chaos, Steven H. Strogatz, published by Westview Press, ISBN
9780738204536
Topics List:
1. One-dimensional flows: geometric way of thinking; fixed points and stability; population
growth and other applications.
2. Bifurcations in one-dimensional flows: saddle-node, transcritical and pitchfork
bifurcations; imperfect bifurcations.
3. Theory: existence; uniqueness; continuous dependence.
4. Phase planes: phase portraits; vector fields; nullclines; fixed points; stability;
linearization.
5. Linear systems: classification of linear systems; what does the linear system say about the
nonlinear system?
6. Limit cycles; introduction; Poincare-Bendixson theorem; conservative systems.
7. Bifurcations of two-dimensional flows; saddle-node, transcritical, and pitchfork
bifurcations; Hopf bifurcation theorem.
8. XPPAUT: phase planes; bifurcations; applications.
9. Global bifurcations: homoclinic orbits; Poincare map; stability of periodic orbits.
10. Singular perturbations: Relaxation oscillator; averaging.
11. Applications: (e.g., Neurons).
12. One-dimensional maps: Logistic map.
13. Smale horseshoe: symbolic dynamics.
14. Applications.
Page 1
2016-2017
Math 4556
Mathematics 4557
Partial Differential Equations
Autumn, Spring
3 credits
5 credits
Catalog Description:
First and second-order PDE’s; existence and uniqueness, initial and boundary value problems,
Fourier series; Green's functions; wave, heat and Laplace equations; nonlinear PDE’s;
applications.
Prerequisite:
C- or better in 2255, 2415, 4556, or 5520H; or credit for 255, 415.xx, or 521H.
Exclusions:
Not open to students with credit for Math 4512 or 512.
Text:
Wiley, ISBN: 0471548685.
Topics List:
1. Definition of a PDE, linearity; solution of first-order linear (transport) equation; modeling
with PDEs.
2. Well-posed problems, initial- and boundary conditions; secondorder equations;
classification into types; the wave equation.
3. Causality and energy; diffusion equation; diffusion on the whole line.
4. Solution of the wave and diffusion equations on a half-line; diffusion and waves with
sources.
5. Separation of variables for the wave equation, Dirichlet, Neumann and Robin conditions.
6. Fourier series; sine and cosine series; orthogonality and general Fourier series;
completeness and convergence.
7. Midterm. Gibbs phenomenon.
8. Laplace’s equation; maximum principle; rectangular coordinates.
9. Poisson’s formula; Laplace’s equation in circular coordinates.
10. Green’s identities; maximum principle; Dirichlet principle; Green’s second identity.
11. Green’s functions; symmetry; half-space and sphere.
12. Wave equation in two and three dimensions; energy; causality; Huyghens’ principle.
13. Rays and characteristics; relativistic geometry; sources; the diffusion equation.
14. The Schrödinger equation; the hydrogen atom.
Page 1
2016-2017
Math 4557
Mathematics 4568
Linear Algebra for Engineering Graduate Students
Autumn, Spring, Summer
3 credits
Catalog Description:
Matrix algebra, vector spaces and linear maps, bases and dimension, eigenvalues and
eigenvectors, applications.
Prerequisite:
C- or better in 2153, 2162.xx, 1172, 2182H or 4182H; or credit for 254, 263.xx, 263.01H or 264H
Exclusions:
Restricted to graduate students in engineering. Not open to students with credit for 2568 (568),
5101 (601), 5520H (520H) or 572.
Text:
Introduction to Linear Algebra, 5th edition, by L.W. Johnson, R.D. Riess, and J.T. Arnold,
Topics List:
1.1
1.2
1.3
1.5
1.6
1.7
1.9
Part I
Introduction to Matrices and Systems of linear equations
Echelon Form and Gaussian-Jordan Elimination
Consistent Systems of linear Equations
Matrix Operations
Algebraic Properties of Matrix operations
Linear Independence and Nonsingular Matrices
Matrix Inverses and Their Properties
Midterm 1
2.1
2.2
2.3
3.1
3.2
3.3
3.4
3.5
5.2
5.3
5.4
3.6
3.7
Page 1
Part II
Vectors in The Plane (Review only because it was done in 1152)
Vectors in Space (Review only because it was done in 1152)
The Dot Product and The Cross
Introduction
Vector Space Properties of ℝn
Examples of Subspaces
Bases for Subspaces
Dimension
Vector Spaces
Subspaces
Linear Independence, Bases, and Coordinates
Orthogonal Bases for Subspaces
Linear Transformation from ℝn to ℝm
2016-2017
Math 4568
Mathematics 4568
Linear Algebra for Engineering Graduate Students
Autumn, Spring, Summer
3 credits
Midterm 2
4.1
4.2
4.4
4.5
4.6
4.7
Part III
The Eigenvalue Problem for 2x2 Matrices
Determinants and the Eigenvalue Problem
Eigenvalues and Characteristic Polynomial
Eigenvectors and Eigenspaces
Complex Eigenvalues and Eigenvectors
Similarity Transformations and Diagonalization
Final
Page 2
2016-2017
Math 4568
Mathematics 4573
Elementary Number Theory
Spring (odd years)
3 credits
Catalog Description:
Prime numbers, modular arithmetic, Diophantine equations, combinatorial analysis; introduction
to concepts of abstract algebra.
Purpose:
To introduce students to some topics in number theory at the upper undergraduate level and
make connections to other areas of mathematics, such as combinatorics and abstract algebra.
Prerequisite:
C- or better in 3345 or 4181H; or credit for 345 or 264H.
Exclusions:
Not open to students with credit for Math 5576H, 576H or 573.
Follow-up Courses:
4580-4581; or for students with an honors background, 5590H-5591H
Text:
An Introduction to the Theory of Numbers, 5th edition, by Niven, Zuckerman & Montgomery,
Topics List:
1. Prime numbers and factorization
2. Congruences and modular arithmetic; the Euler phi-function ø(n).
3. Fermat’s “Little” Theorem. Primitive roots.
5. Numerical Functions of number theory; multiplicative functions and Moebius inversion
6. Diophantine equations.
7. Number theory from an algebraic viewpoint; groups, rings and fields.
8. Possible additional topics: continued fractions, Pell’s equation, and elliptic curves.
Page 1
2016-2017
Math 4573
Mathematics 4575
Combinatorial Mathematics
Spring (even years)
3 credits
Catalog Description:
Enumerative techniques, combinatorial identities, graph theory, algorithms, error correcting
codes
Purpose for the Course:
Combinatorics and discrete mathematics are increasingly important, particularly for their
applications in computer science. This course will give a brief overview of this subject.
Prerequisite:
C- or better in 2568 or 5520H; credit for 568, 571, or 520H.
Exclusions:
Not open to students with credit for Math 5529H.
Topics List:
1. Counting principles: factorials, permutations and combinations, binomial coefficients,
Stirling numbers, double counting.
2. Combinatorial identities: bijections, binomial theorem, generating functions.
3. Graph theory: bridges of Konigsberg, Eulerian circuits, trees, edge coloring, vertex
coloring, planar graphs, Kempe's proof of the 5-color theorem
4. Error correcting codes: sphere packing bound, Hamming codes
5. (Optional.) Algorithms: Djkstra's algorithm for minimum spanning tree, depth first and
breadth first algorithms for trees, greedy algorithm for graph coloring.
Page 1
2016-2017
Math 4575
Mathematics 4578
Discrete Mathematical Models
Spring
4 credits
Catalog Description:
Homogeneous and non-homogeneous difference equations of one or several variables, Markov
chains, graph theory, network flows.
Prerequisite:
{C- or better in 2568 or 5520H; and C- or better in 4530, 5530H or Stat 420}; or {credit for 568,
571, or 520H; and credit for 530, 531H, or Stat 420}.
Exclusions: Not open to students with credit for 578.
Topics List:
1. Homogenous and non-homogeneous difference equations.
2. Application in finance, genetics, economics.
3. Matrix methods, nonlinear equations, stability, bifurcation, harvesting.
4. Application of Markov chains with absorbing and non-absorbing states, limiting
behavior.
5. Graph theoretical algorithms, network flows, applications.
6. Linear/integer programming.
Comment:
This course requires the student to use a programming language chosen by the instructor to
complete required course work.
Page 1
2016-2017
Math 4578
Mathematics 4580
Abstract Algebra I
Autumn, Spring
3 credits
Catalog Description:
4580-4581 includes elementary number theory, group theory, vector spaces and linear
transformation, and field theory.
Prerequisite:
{C- or better in 3345, and
C- or
{credit for 345; and credit for 568, 571, or 520H}.
better
in
2568
or
5520H}
or
Exclusions:
Not open to students with credit for 581 or 591H.
Purpose:
Math 4580-4581 constitutes a two-semester sequence on abstract algebra, intended to familiarize
students with the principal concepts, mode of thinking, and important theorems in this subject
area. Considerable emphasis is placed on connections between this material and the traditional
topics of high school mathematics - Euclidean geometry, polynomial equations, and
trigonometry.
Math 4580 begins with a brief review of elementary number theory. Groups are introduced in the
context of geometrical symmetry. There is a study of number systems along with an introduction
to the theory of polynomial equations. Finally, this is all applied to the constructibility problem
for regular polygons.
Text:
An Introduction to Abstract Algebra, by Ronald Solomon (in-house notes).
Topics List:
0. Equivalence Relations and the Integers
1. Isometrics
2. Congruences and Groups
3. The Isometrics of ℝ2 and Symmetry Groups
4. The Integers, Polynomials, and their Generalizations
5. Rational Numbers, Real Numbers and Decimals
6. Roots and the Complex Numbers
7. The Cyclotomic Polynomials
8. Fermat and the Gaussian Integers
9. Constructible Numbers
10. Some Linear Algebra and a Nonconstructibility Criterion
11. The Method of Mr. Gauss
Page 1
2016-2017
Math 4580
Mathematics 4581
Abstract Algebra II
Autumn, Spring
3 credits
Catalog Description:
4580-4581 includes elementary number theory, group theory, vector spaces and linear
transformation, and field theory.
Prerequisite:
C- or better in Math 4580; or credit for 5590H or 581.
Exclusions:
Not open to students with credit for 582 or 592H.
Purpose:
Math 4580-4581 constitutes a two-semester sequence on abstract algebra, intended to familiarize
students with the principal concepts, mode of thinking, and important theorems in this subject
area. Considerable emphasis is placed on connections between this material and the traditional
topics of high school mathematics - Euclidean geometry, polynomial equations, and
trigonometry. Math 4581 deepens the theory of groups and of polynomial equations,
culminating in Galois' theory of equations and the classification of finite symmetry groups in ℝ3.
Text:
Notes on Abstract Algebra, by Ron Solomon (in-house notes)
Topics List:
1. Permutation groups, orbits, and Lagrange's Theorem
2. The Orbit Counting Formula
3. Imaginaries and Galois fields
4. Gaussian integers and Fermat's two squares theorem
5. Review and Midterm 1
6. Symmetric polynomials and the Fundamental Theorem of Algebra
7. Nonconstructibility and a Lagrange Theorem for fields
8. Galois' Theory of Equations
9. The Galois Correspondence
10. Review and Midterm 2
11. The isometry group of ℝ2
12. Linear algebra in ℝ3
13. The Platonic solids and their symmetries
14. The finite subgroups of SO(3)
Page 1
2016-2017
Math 4581
Mathematics 5520H
Honors Linear Algebra and Differential Equations
Autumn
5 credits
Catalog Description:
Linear transformations and matrices, spectral theorem, ordinary differential equations, existence
and uniqueness theorems, phase space, stability, oscillations.
Prerequisite:
C or better in 4182H or in both 2182H and 3345; or C or better in 264H or in both 263H and
345; or permission of department.
Text:
Linear Algebra: An Introductory Approach, revised 4th edition, by Curtis, published by Springer,
ISBN: 9780387909929
ISBN: 9780486659428
Topics List:
1. Vector spaces and linear transformations.
2. Systems of equations, determinants.
3. Spectral theorem.
4. Ordinary, linear and nonlinear differential equations.
5. Existence and uniqueness theorems.
6. Phase space, stability, and periodic points.
Page 1
2016-2017
Math 5520H
Mathematics 5522H
Honors Complex Analysis
Spring
5 credits
Catalog Description:
Theoretical treatment of complex analysis.
Prerequisite:
C or better in 5520H or permission of department.
Text:
Vary, for example:
 An Introduction to Complex Function Theory, by B.P. Palka
 Elementary Theory of Analytic Functions of One or Several Complex Variables, by H.
Cartan
 Complex Analysis, 2nd edition, by Bak-Newman
 Complex Analysis with Applications, by Silverman
Topics List:
1. Complex numbers, Riemann's sphere. Complex functions, elementary functions, Möbius
transformations.
2. Holomorphic functions, Cauchy-Riemann equations.
3. Line integrals. Cauchy’s integration theorem and its consequences.
4. Harmonic functions.
5. Sequences and series of holomorphic functions. Power series, analytic functions.
6. Isolated singularities, meromorphic functions, the calculus of residues.
7. Conformal mappings, the Riemann mapping theorem.
8. Geometric principles.
9. Mittag-Leffler's and Weierstrass's expansions of meromorphic functions.
10. Analytic continuation, Riemann surfaces.
11. Applications to number theory, geometry, physics.
Page 1
2016-2017
Math 5522H
Mathematics 5529H
Honors Combinatorics
Autumn (even numbered years)
5 credits
Catalog Description:
Techniques of combinatorial mathematics; connections with geometry, algebra, analysis, and
probability.
Prerequisite:
C or better in 4182H, or in both 2182H and 3345; or credit for 264H, or for both 263H and 345;
or permission of department.
Text:
Vary, for example:
ISBN: 9780387955858
 Proofs from the Book, 4th edition, by Aigner, Ziegler & Hofmann, published by Springer,
ISBN: 9783642008559
Cambridge University Press, ISBN: 9780521338936
Topics List:
1. Counting principles.
2. Generating functions.
3. Combinatorial probability.
4. Finite fields and applications.
5. Theory of partitions.
6. Famous graphs.
7. Ramsey theory.
8. Permutation groups.
Page 1
2016-2017
Math 5529H
Mathematics 5530H
Honors Probability
Spring (odd numbered years)
5 credits
Catalog Description:
Theoretical treatment of probability, with applications within and outside mathematics.
Prerequisite:
C or better in 5529H, or permission of department.
Purpose of Course:
The acquaintance with rigorous probability theory, its history and its multiple connections, will
better prepare honor students for graduate studies and will help them get involved in research at
earlier stages of their careers.
Text:
Vary, for example:
 Heads and Tails. An Introduction to Limit Theorems in Probability, E. Lesigne, AMS,
ISBN 0821837141
 Elementary Probability Theory with Stochastic Processes, Kai Lai Chung
 Elementary Probability Theory, Kai Lai Chung and Farid AitSahlia,, 4th Edition,
Springer, 2003
Topics List:
1. Historical origins of probability.
2. Diverse ways of sampling, allocation, models.
3. Random variables, expectation, moments.
4. Important distributions.
5. Limit theorems: law of large numbers, central limit theorem.
6. Random walks and Markov chains.
7. Statistical independence in analysis and number theory.
Page 1
2016-2017
Math 5530H
Mathematics 5540H
Honors Differential Geometry
Spring (even numbered years)
5 credits
Catalog Description:
Geometry of curves and surfaces in 3-dimensional space, curvature, geodesics, Gauss-Bonnet
Theorem, Riemannian metrics.
Prerequisite:
C or better in 5520H, or in both 2182H and 2568; or credit for 520H, or in both 263.01H and
568; or permission of department.
Text:
Text vary, for example:
 Differential Geometry of Curves and Surfaces, DoCarmo
 Elements of Differential Geometry, R. Milman and G. Rarker
Topics List:
1. Geometry of curves; Frenet-Serret equations.
2. Curvature of surfaces, First Fundamental Form, Gauss's Theorema Egregium.
3. Geodesics, exponential map.
4. Isometries, conformal mappings; mapmaking.
5. Gauss-Bonnet Theorem.
6. Riemannian metrics, non-Euclidean geometry.
Page 1
2016-2017
Math 5540H
Mathematics 5576H
Honors Number Theory
Autumn (odd numbered years)
5 credits
Catalog Description:
Elementary analytic and algebraic number theory, tracing its unifying role in the development of
mathematics through history.
Prerequisite:
C or better in 4182H, or in both 2182H and 3345; or credit for 264H, or for both 263H and 345;
or permission of department.
Purpose of Course:
The intention of this course is to present number theory, the "Queen of Mathematics" through its
historical development. Being one of the oldest mathematical disciplines, number theory, in the
course of its history, both benefited from and contributed to such major mathematical areas as
geometry, algebra and analysis. These courses will be especially beneficial for honor students
planning to pursue careers in mathematics, physics, computer science and education, but may be
of interest to engineering students as well.
Text:
Vary, for example:
 An Introduction to the Theory of Numbers, 6th edition, by Hardy, Wright, Heath &
 An Introduction to the Theory of Numbers, I. Niven, H.S. Zukkerman, H.L. Montgomery
 Number Theory: An Introduction to Mathematics, Parts A and B, by William A. Coppel,
Springer-Velag.
Topics List:
1. Review of Egyptian and Mesopotamian Mathematics. Greek tradition. Three classical
Greek problems (cube doubling, angle trisection, circle quadrature).
2. Famous irrationalities.
3. Continued fractions and applications thereof (quadratic surds, Pell’s equation,
Diophantine approximations, etc.)
4. More on diophantine approximation. Algebraic numbers. Liouville numbers. A glimpse
into the Thue-Siegel-Roth Theorem.
5. Uniform distribution modulo one. Weyl criterion. Some important sequences. PisotVijayaraghavan numbers. Formulation and discussion of Margulis’ solution of
Oppenheimer’s conjecture.
6. Normal numbers. Champernoun’s example. Almost every number is normal. LevyKhinchine Theorem on normality of continued fractions.
7. Infinitude of primes. Euler’s identity. Chebyshev’s Theorem. Bertrand’s Postulate.
Dirichlet’s Theorem on primes in progressions. Average rate of growth of classical
number-theoretical functions.
8. Finite fields. Wedderburn’s Theorem. Applications: Latin Squares and Cryptography.
Page 1
2016-2017
Math 5576H
Mathematics 5576H
Honors Number Theory
Autumn (odd numbered years)
5 credits
10. Pythagorean triangles. Representation of integers as sums of squares. Quaternions,
Cayley’s octavas. Hurwitz’ Theorem. Minkowski’s geometry of numbers.
11. p-adic numbers, their construction and axiomatic characterization (Ostrowski’s
Theorem). Minkowski-Hasse principle.
12. Fermat’s last theorem. Some easy cases. A glimpse into modern developments (elliptic
curves, Mordell-Weil Theorem, etc.).
Page 2
2016-2017
Math 5576H
Mathematics 5590H (Au), 5591H, (Sp)
Honors Abstract Algebra I
Honors Abstract Algebra II
5 credits each
Catalog Description:
5590H and 5591H includes elementary number theory, group theory, ring theory, abstract linear
algebra, field theory, and Galois theory.
Prerequisite:
5590H: C or better in 5520H or in 520H, or permission of department.
5591H: C or better in 5590H or permission of department.
Text:
Vary, for example:
 Abstract Algebra, 3rd edition, by Dummit & Foote, published by Wiley, ISBN:
9780471433349
 Algebra, by M. Artin
 Topics in Algebra, by I. Herstein
Topics List:
5590H:
1. Integers, unique factorization; congruences, Euler function.
2. Groups, subgroups, homomorphisms and isomorphisms, normal subgroups, quotient
groups, permutation groups, cyclic groups, Cauchy Theorems, Sylow's Theorems; direct
products, fundamental theorem for finite Abelian group; G-sets.
3. Rings, subrings, ideals, morphisms, polynomial rings, prime and maximal ideals.
4. Commutative rings, factorization theory, Euclidean rings, principal ideal rings, unique
factorization domains, Gauss' lemma; illustrations in the integers of quadratic number
fields.
5. Modules over commutative rings, submodules, quotients and direct sums; fundamental
theorem for modules over principal ideal domains.
5591H:
1. Vector spaces (as a special case of modules); linear maps and matrices, canonical forms,
dual spaces.
2. The theory of determinants.
3. Bilinear and quadratic forms; inner product and unitary spaces; principal axis theorem.
4. Fields, algebraic and transcendental (extensions), existence of closure (over countable
fields), tests for polynomial irreducibility; normality, separability, field automorphisms.
5. Galois theory, the subgroup-subfield correspondence theorem, group theory
interrelations; extensions of finite fields, cyclotomic extensions.
6. Solvable groups and solvability by radicals.
Page 1
2016-2017
Math 5590H, 5591H
Mathematics 5630
Life Contingencies I
Autumn
3 credits
Catalog Description:
5630-5631 introduces students to the mathematical theory of contingencies. Includes material
from examinations by the Society of Actuaries and the Casualty Actuarial Society.
Prerequisite:
C- or better in 3618 and C- or better in 4530, 5530H, or Stat 4201; or credit for 530, 531H, or
Stat 420; or permission of department.
Exclusions:
Open only to actuarial science majors.
Text:
Actuarial Mathematics for Life Contingent Risks, by Dickson, Hardy & Waters, published by
Cambridge, ISBN: 9780521118255
Topics List:
1. Survival distributions.
2. Individual risk models.
3. Life tables.
4. Topics from life insurance.
5. Life annuities.
Page 1
2016-2017
Math 5630
Mathematics 5631
Life Contingencies II
Spring
3 credits
Catalog Description:
5630-5631 introduces students to the mathematical theory of contingencies. Includes material
from examinations by the Society of Actuaries and the Casualty Actuarial Society.
Prerequisite:
C- or better in Math 5630, or credit for 630.
Exclusions:
Open only to actuarial science majors, and to MMS students specializing in Financial Math.
Text:
Actuarial Mathematics for Life Contingent Risks, by Dickson, Hardy & Waters, published by
Cambridge, ISBN: 9780521118255.
Topics List:
1. Benefit reserve.
2. Multiple life functions.
3. Multiple decrement models.
4. Random and deterministic survivorship group.
5. Valuation of pension plans.
6. Applications.
Page 1
2016-2017
Math 5631
Mathematics 5632
Financial Economics
Autumn, Spring, Summer
3 credits
Catalog Description:
Introduction to the evaluation of options, futures, and other derivatives, interest models and risk
management techniques. Includes material from examinations by the Society of Actuaries and
the Casualty Actuarial Society.
Prerequisite:
{C- or better in 3618, or credit for 618, or permission of department} –and– {C- or better in 4530
or Stat 4201 or credit for 530 or Stat 420}.
Exclusions:
Restricted to actuarial science majors, math majors, and students with graduate standing.
Text:
Derivatives Markets, 2nd
ISBN: 9780321280305
edition,
by
McDonald,
published
by
Topics List:
1. Option relationships.
2. Binomial option pricing.
3. Black-Scholes formula.
4. Market making and delta hedging.
5. Exotic options.
6. Brownian motions and Ito's Lemma.
7. Interest rate models.
Page 1
2016-2017
Math 5632
Mathematics 5633
Loss Models I
Autumn
3 credits
Catalog Description:
5633-5634 introduces students to the construction and evaluation of actuarial models, with topics
covered by examinations of the Society of Actuaries and the Casualty Actuarial Society.
Prerequisite:
{C- or better in 4530, 5530H, Stat 4201, or credit for 530, 531H, or Stat 420}; and {C- or better
in Stat 4202 or credit for Stat 421}.
Exclusions:
Open only to actuarial science majors and to MMS students specializing in Financial Math.
Text:
Loss Models: From Data to Decisions, 4th edition, by Klugman, Panjer and Willmot, published
by Wiley, ISBN: 9781118315323.
Topics List:
1. Measures of risk.
2. Characteristics of actuarial models.
3. Severity models.
4. Frequency models.
5. Aggregate loss models.
Page 1
2016-2017
Math 5633
Mathematics 5634
Loss Models II
Spring
3 credits
Catalog Description:
5633-5634 introduces students to the construction and evaluation of actuarial models, with topics
covered by examinations of the Society of Actuaries and the Casualty Actuarial Society.
Prerequisite:
C- or better in 5633.
Exclusions:
Open only to actuarial science majors and to MMS students specializing in Financial Math.
Topics List:
1. Estimation of data.
2. Parameter estimation.
3. Model selection.
4. Simulation.
5. Credibility.
Page 1
2016-2017
Math 5634
Mathematics 5756, 5757
Modern Mathematical Methods of Relativity I, II
Autumn (even years), Spring (odd years)
3 credits
Catalog Description:
Special relativity as moving frames; tensors, exterior algebra and exterior calculus; differentiable
manifolds and space time structures; parallel transport, torsion and curvatures, metric
compatibility; structure equations of differential geometry.
Prerequisite:
Multivariable differential calculus and linear algebra (e.g. Math 2568 and/or 5101). A physics
course (e.g. Physics 133 or higher). No prior knowledge of tensor calculus is assumed.
However, we do assume a mature attitude towards mathematics and physics.
Purpose:
Develop from the bottom up the fundamental mathematical concepts and methods responsible
for the successes in 20th century physics, mathematics, and theoretical engineering. Thus Math
5756 concretizes these developments in terms of:
a) Special Relativity as the cognitive bridge to 20th century geometry
b) Multilinear algebra as a source of geometrical structures,
c) Linear algebra’s marriage to multi-variable calculus
d) differential geometry as a three level hierarchy characterized by its
 Differential structure
 Parallel transport structure (a.k.a. covariant derivative)
 Metric structure
e) The exterior calculus
f) Cartan’s two structural equations for the various flavors of differential geometry, and
their application to
g) The Cartan-Misner calculus
Text:
a)
b)
c)
d)
Page 1
Gravitation by C. W. Misner, K. S. Thorne, and J. A. Wheeler.
Selections from Mathematical Methods of Classical Mechanics by V.I. Arnold.
Selections from Lecture Notes on Elementary Topology and Geometry by I. M. Singer.
Selections from Spacetime Physics, 2nd edition, by E. Taylor and J.A. Wheeler
2016-2017
Math 5756, 5757
Mathematics 5756, 5757
Modern Mathematical Methods of Relativity I, II
Autumn (even years), Spring (odd years)
3 credits
Topics List:
Math 5756 (Autumn):
A rapid course in special relativity: spacetime geometry, event horizons and accelerated frames;
• tensors, metric geometry vs symplectic geometry;
• exterior calculus, Maxwell field equations;
• manifolds, Lie derivatives, and Hamiltonian dynamics in phase space;
• parallel transport, torsion, tensor calculus;
• curvature and Jacobi’s equation of geodesic deviation;
• Cartan’s two structural equations, metric induced properties, and Cartan-Misner
curvature calculus.
Math 5757 (Spring):
•
•
•
•
•
Page 2
Geodesics: Hamilton-Jacobi theory, the principle of constructive interference;
stress-energy tensor: hydrodynamics in curved spacetime and Einstein field equations;
The conservation laws and the Bianch identities mathematized in terms of the “Boundary
of a Boundary is zero (@ @ ­ = 0)” Principle.
Solutions to the Einstein’s field equations: stars, black holes, gravitational collapse,
geometry and dynamics of the universe;
vector harmonics, tensor harmonics, acoustic and gravitational waves in violent
relativistic backgrounds.
2016-2017
Math 5756, 5757
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