# MATH - Mathematics

## MATH 2 College Algebra for Calculus

### Credits

#### Requirements

Prerequisite(s): mathematics placement (MP) score of 100 or higher.

#### Quarter offered

Fall, Summer

## MATH 2S College Algebra for Calculus

### Credits

#### Instructor

The Staff

#### Requirements

Prerequisite(s): mathematics placement (MP) score of 100 or higher.

## MATH 2T Preparatory Math: Tutorial

### Credits

#### Instructor

Debra Lewis

#### Requirements

Prerequisite(s): mathematics placement (MP) score of 100 or higher.

#### Repeatable for credit

Yes

#### Quarter offered

Fall

## MATH 3 Precalculus

Inverse functions and graphs; exponential and logarithmic functions, their graphs, and use in mathematical models of the real world; rates of change; trigonometry, trigonometric functions, and their graphs; and geometric series. Students cannot receive credit for both MATH 3 and AM 3.

### Credits

#### Requirements

Prerequisite(s): MATH 2 or mathematics placement (MP) score of 200 or higher. Students may not enroll in or receive credit for MATH 3 after receiving credit with a 'C' or better in AM 11A, MATH 11A, MATH 19A, MATH 20A or equivalents.

#### General Education Code

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 4 Mathematics of Choice and Argument

### Credits

#### Requirements

Prerequisite(s): MATH 2, or mathematics placement (MP) score of 200 or higher, or AP Calculus AB examination score of 3 or higher.

#### General Education Code

SR

## MATH 11A Calculus with Applications

### Credits

#### Requirements

Prerequisite(s): MATH 3 or AM 3; or mathematics placement (MP) score of 300 or higher; or AP Calculus AB exam score of 3 or higher.

#### General Education Code

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 11B Calculus with Applications

### Credits

#### Requirements

Prerequisite(s): MATH 11A or MATH 19A or AM 15A or AP Calculus AB exam score of 4 or 5, or BC exam score of 3 or higher, or IB Mathematics Higher Level exam score of 5 or higher.

#### General Education Code

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 19A Calculus for Science, Engineering, and Mathematics

### Credits

#### Requirements

Prerequisite(s): MATH 3; or mathematics placement (MP) score of 400 or higher; or AP Calculus AB exam score of 3 or higher.

#### General Education Code

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 19B Calculus for Science, Engineering, and Mathematics

### Credits

#### Requirements

Prerequisite(s): MATH 19A or MATH 20A or AP Calculus AB exam score of 4 or 5, or BC exam score of 3 or higher, or IB Mathematics Higher Level exam score of 5 of higher.

#### General Education Code

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 20A Honors Calculus

### Credits

#### Requirements

Prerequisite(s): mathematics placement (MP) score of 500 higher; or AP Calculus AB examination score of 4 or 5; or BC examination of 3 or higher; or IB Mathematics Higher Level examination score of 5 or higher.

#### General Education Code

MF

## MATH 20B Honors Calculus

### Credits

#### Requirements

Prerequisite(s): MATH 20A.

#### General Education Code

MF

## MATH 21 Linear Algebra

### Credits

#### General Education Code

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 22 Introduction to Calculus of Several Variables

Functions of several variables. Continuity and partial derivatives. The chain rule, gradient and directional derivative. Maxima and minima, including Lagrange multipliers. The double and triple integral and change of variables. Surface area and volumes. Applications from biology, chemistry, earth sciences, engineering, and physics. Students cannot receive credit for this course and MATH 23A.

### Credits

#### Requirements

Prerequisite(s): MATH 11B or MATH 19B or MATH 20B or AM 15B or AP calculus BC exam score of 4 or 5.

#### General Education Code

MF

#### Quarter offered

Winter, Summer

## MATH 23A Vector Calculus

Vectors in n-dimensional Euclidean space. The inner and cross products. The derivative of functions from n-dimensional to m-dimensional Euclidean space is studied as a linear transformation having matrix representation. Paths in 3-dimensions, arc length, vector differential calculus, Taylor's theorem in several variables, extrema of real-valued functions, constrained extrema and Lagrange multipliers, the implicit function theorem, some applications. Students cannot receive credit for this course and MATH 22 or AM 30.

### Credits

#### General Education Code

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 23B Vector Calculus

Double integral, changing the order of integration. Triple integrals, maps of the plane, change of variables theorem, improper double integrals. Path integrals, line integrals, parametrized surfaces, area of a surface, surface integrals. Green's theorem, Stokes' theorem, conservative fields, Gauss' theorem. Applications to physics and differential equations, differential forms.

### Credits

#### Requirements

Prerequisite(s): MATH 23A.

#### General Education Code

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 24 Ordinary Differential Equations

### Credits

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 99 Tutorial

### Credits

#### Quarter offered

Fall, Winter, Spring

## MATH 99F Tutorial

### Credits

#### Repeatable for credit

Yes

#### Quarter offered

Fall, Winter, Spring

## MATH 100 Introduction to Proof and Problem Solving

### Credits

#### Requirements

Prerequisite(s): satisfaction of the Entry Level Writing and Composition requirements; MATH 11A or MATH 19A or MATH 20A; and MATH 21 or AM 10 or AMS 10A.

#### General Education Code

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 101 Mathematical Problem Solving

### Credits

#### General Education Code

PR-E

#### Quarter offered

Fall

## MATH 103A Complex Analysis

### Credits

#### Quarter offered

Winter, Spring, Summer

## MATH 103B Complex Analysis II

### Credits

#### Requirements

Prerequisite(s): MATH 103A.

## MATH 105A Real Analysis

### Credits

## MATH 105B Real Analysis

### Credits

#### Requirements

Prerequisite(s): MATH 105A.

#### Quarter offered

Spring

## MATH 105C Real Analysis

### Credits

#### Requirements

Prerequisite(s): MATH 105B.

## MATH 106 Systems of Ordinary Differential Equations

### Credits

#### Requirements

Prerequisite(s): MATH 21 or AM 10; and either MATH 24 or AM 20; and either MATH 100 or CSE 101.

#### Quarter offered

Winter, Summer

## MATH 107 Partial Differential Equations

### Credits

#### Requirements

Prerequisite(s): MATH 21 or AM 10; and MATH 24 or AM 20; and either MATH 100 or CSE 101; MATH 106 is recommended as preparation.

#### Quarter offered

Spring

## MATH 110 Introduction to Number Theory

### Credits

#### Quarter offered

Fall, Winter, Summer

## MATH 111A Algebra

### Credits

#### Quarter offered

Fall, Winter

## MATH 111B Algebra

### Credits

#### Requirements

Prerequisite(s): MATH 111A.

#### Quarter offered

Spring

## MATH 111T Algebra

### Credits

#### Requirements

Prerequisite(s): MATH 100.

#### Quarter offered

Spring, Summer

## MATH 114 Introduction to Financial Mathematics

### Credits

## MATH 115 Graph Theory

### Credits

#### Quarter offered

Fall

## MATH 116 Combinatorics

### Credits

#### Requirements

Prerequisite(s): MATH 100 or CSE 101. Enrollment is restricted to sophomores juniors, and seniors. Familiarity with basic group theory is recommended.

#### Quarter offered

Spring

## MATH 117 Advanced Linear Algebra

### Credits

#### Quarter offered

Fall, Spring, Summer

## MATH 118 Advanced Number Theory

### Credits

## MATH 120 Coding Theory

### Credits

#### Requirements

Prerequisite(s): MATH 21.

## MATH 121A Differential Geometry

### Credits

#### Requirements

Prerequisite(s): MATH 21 and MATH 23B and either MATH 100 or CSE 101. MATH 105A strongly recommended.

#### Quarter offered

Winter

## MATH 121B Differential Geometry and Topology

### Credits

#### Requirements

Prerequisite(s): MATH 121A.

## MATH 124 Introduction to Topology

### Credits

#### Quarter offered

Fall

## MATH 128A Classical Geometry: Euclidean and Non-Euclidean

### Credits

#### Quarter offered

Spring

## MATH 128B Classical Geometry: Projective

### Credits

#### Requirements

Prerequisite(s): MATH 21.

## MATH 129 Algebraic Geometry

### Credits

#### Quarter offered

Winter

## MATH 130 Celestial Mechanics

### Credits

#### Requirements

Prerequisite(s): MATH 19A and 19B; and MATH 23A or PHYS 5A or PHYS 6A; MATH 21 and MATH 24 strongly recommended.

## MATH 134 Cryptography

### Credits

#### Quarter offered

Winter

## MATH 140 Industrial Mathematics

### Credits

#### Instructor

The Staff

## MATH 145 Introductory Chaos Theory

### Credits

#### Requirements

Prerequisite(s): MATH 22 or MATH 23A; MATH 21; MATH 100 or CSE 101. Concurrent enrollment in MATH 145L is required.

## MATH 145L Introductory Chaos Laboratory

### Credits

#### Requirements

Concurrent enrollment in MATH 145 is required.

## MATH 148 Numerical Analysis

### Credits

#### Requirements

Prerequisite(s): MATH 22 or MATH 23A; and MATH 21 or AM 10; and MATH 24 or AM 20; and MATH 100 or CSE 101. Concurrent enrollment in MATH 148L is required.

#### Quarter offered

Spring

## MATH 148L Numerical Analysis Laboratory

### Credits

#### Requirements

Concurrent enrollment in MATH 148 is required.

#### Quarter offered

Spring

## MATH 152 Programming for Mathematics

### Credits

#### Requirements

Prerequisite(s): MATH 100.

#### General Education Code

MF

#### Quarter offered

Winter

## MATH 160 Mathematical Logic I

### Credits

#### Quarter offered

Spring

## MATH 161 Mathematical Logic II

### Credits

#### Requirements

Prerequisite(s): MATH 100 or equivalent, or by permission of instructor.

## MATH 181 History of Mathematics

### Credits

#### Requirements

Prerequisite(s): MATH 19B or MATH 20B. MATH 100 is strongly recommended for preparation.

#### General Education Code

TA

#### Quarter offered

Winter, Summer

## MATH 192 Dir Stu Teach

### Credits

## MATH 194 Senior Seminar

### Credits

#### Requirements

Prerequisite(s): satisfaction of the Entry Level Writing and Composition requirements; MATH 103A or MATH 105A or MATH 110 or MATH 111A or MATH 111T or MATH 117. Enrollment priority is given to seniors; juniors may request permission from the undergraduate vice chair.

#### Quarter offered

Winter, Spring

## MATH 195 Senior Thesis

### Credits

#### Repeatable for credit

Yes

#### Quarter offered

Fall, Winter, Spring

## MATH 199 Tutorial

### Credits

#### Repeatable for credit

Yes

#### Quarter offered

Fall, Winter, Spring

## MATH 199F Tutorial

### Credits

#### Repeatable for credit

Yes

## MATH 200 Algebra I

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Repeatable for credit

Yes

#### Quarter offered

Fall

## MATH 201 Algebra II

### Credits

#### Requirements

Prerequisite(s): MATH 200 is recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 202 Algebra III

### Credits

#### Requirements

Prerequisite(s): MATH 201 is recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 203 Algebra IV

### Credits

#### Requirements

Prerequisite(s): MATH 200, MATH 201, and MATH 202. Enrollment is restricted to graduate students.

#### Quarter offered

Fall

## MATH 204 Analysis I

### Credits

#### Requirements

Prerequisite(s): MATH 105A and MATH 105B are recommended as preparation.Enrollment is restricted to graduate students.

#### Quarter offered

Fall

## MATH 205 Analysis II

^{p}spaces, derivative of a measure, the Radon-Nikodym theorem, and the fundamental theorem of calculus.

### Credits

#### Requirements

Prerequisite(s): MATH 204. Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 206 Analysis III

### Credits

#### Requirements

Prerequisite(s): MATH 204 and MATH 205 recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 207 Complex Analysis

### Credits

#### Requirements

Prerequisite(s): MATH 103 is recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 208 Manifolds I

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Fall

## MATH 209 Manifolds II

### Credits

#### Requirements

Prerequisite(s): MATH 208. MATH 201 is recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 210 Manifolds III

### Credits

#### Requirements

Prerequisite(s): MATH 208 and MATH 209 recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 211 Algebraic Topology

### Credits

#### Requirements

Prerequisite(s): MATH 200, MATH 201, and MATH 202 recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 212 Differential Geometry

### Credits

#### Requirements

Prerequisite(s): MATH 208. Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 213A Partial Differential Equations I

*Partial Differential Equations;*which includes transport equations; Laplace equations; heat equations; wave equations; characteristics of nonlinear first-order PDE; Hamilton-Jacobi equations; conservation laws; some methods for solving equations in closed form; and the Cauchy-Kovalevskaya theorem.

### Credits

#### Requirements

MATH 106 and MATH 107 are recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 213B Partial Differential Equations II

### Credits

#### Requirements

Prerequisite(s): MATH 106, MATH 107, and MATH 213A are recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 214 Theory of Finite Groups

### Credits

#### Requirements

Prerequisite(s): MATH 200 and MATH 201 recommended as preparation. Enrollment is restricted to graduate students.

## MATH 215 Operator Theory

### Credits

#### Requirements

Prerequisite(s): MATH 204, MATH 205, MATH 206, and MATH 207 are recommended as preparation. Enrollment is restricted to graduate students.

## MATH 216 Advanced Analysis

### Credits

#### Requirements

Prerequisite(s): MATH 204, MATH 205, and MATH 206 recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 217 Advanced Elliptic Partial Differential Equations

### Credits

#### Requirements

Prerequisite(s): MATH 204, MATH 205, and MATH 206 recommended as preparation. Enrollment is restricted to graduate students.

## MATH 218 Advanced Parabolic and Hyperbolic Partial Differential Equations

### Credits

## MATH 219 Nonlinear Functional Analysis

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 220A Representation Theory I

### Credits

#### Requirements

Prerequisite(s): MATH 200, MATH 201, and MATH 202. MATH 225A and MATH 227 recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 220B Representation Theory II

### Credits

#### Requirements

Prerequisite(s): MATH 220A. Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 222A Algebraic Number Theory

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Fall

## MATH 222B Algebraic Number Theory

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 223A Algebraic Geometry I

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 223B Algebraic Geometry II

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 225A Lie Algebras

### Credits

#### Requirements

Prerequisite(s): MATH 201 and MATH 202 recommended as preparation Enrollment is restricted to graduate students.

#### Quarter offered

Fall

## MATH 225B Infinite Dimensional Lie Algebras

### Credits

#### Requirements

Prerequisite(s): MATH 225A. Enrollment is restricted to graduate students.

## MATH 226A Infinite Dimensional Lie Algebras and Quantum Field Theory I

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 226B Infinite Dimensional Lie Algebras and Quantum Field Theory II

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 227 Lie Groups

### Credits

#### Requirements

Prerequisite(s): MATH 200, MATH 201, MATH 204, and MATH 208. Enrollment is restricted to graduate students.

#### Quarter offered

Fall

## MATH 228 Lie Incidence Geometries

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 229 Kac-Moody Algebras

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 232 Morse Theory

### Credits

#### Requirements

Prerequisite(s): MATH 208, MATH 209, MATH 210, MATH 211, and MATH 212 recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 233 Random Matrix Theory

### Credits

#### Requirements

Prerequisite(s): MATH 103, MATH 204, and MATH 205; MATH 117 recommended as preparation. Enrollment is restricted to graduate students.

## MATH 234 Riemann Surfaces

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 235 Dynamical Systems Theory

### Credits

## MATH 238 Elliptic Functions and Modular Forms

### Credits

#### Requirements

Prerequisite(s): MATH 200, MATH 201, MATH 202, and either MATH 207 or MATH 103A are recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Fall

## MATH 239 Homological Algebra

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 240A Representations of Finite Groups I

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 240B Representations of Finite Groups II

### Credits

#### Requirements

Prerequisite(s): MATH 200, MATH 201, MATH 202, MATH 203, and MATH 240A recommended. Enrollment is restricted to graduate students.

## MATH 246 Representations of Algebras

### Credits

#### Requirements

Prerequisite(s): MATH 200, MATH 201, and MATH 202. Enrollment is restricted to graduate students.

## MATH 248 Symplectic Geometry

### Credits

#### Requirements

Prerequisite(s): MATH 204; MATH 208 and MATH 209 are recommended as preparation. Enrollment is restricted to graduate students.

## MATH 249A Mechanics I

### Credits

#### Requirements

MATH 208 and MATH 209 recommended as preparation. Enrollment is restricted to graduate students.

## MATH 249B Mechanics II

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 249C Mechanics III

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 252 Fluid Mechanics

### Credits

#### Requirements

Prerequisite(s): MATH 106 and MATH 107 are recommended as preparation. Enrollment is restricted to graduate students.

## MATH 254 Geometric Analysis

### Credits

#### Requirements

MATH 204, MATH 205, MATH 209, MATH 212, and MATH 213A recommended as preparation. Enrollment is restricted to graduate students.

#### Quarter offered

Spring

## MATH 256 Algebraic Curves

### Credits

#### Requirements

MATH 200, MATH 201, MATH 202, MATH 203, MATH 204, and MATH 207 are recommended as preparation. Enrollment is restricted to graduate mathematics and physics students.

## MATH 260 Combinatorics

### Credits

#### Requirements

Enrollment is restricted to graduate students.

## MATH 264 Inverse Problems and Integral Geometry

### Credits

#### Instructor

The Staff

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Fall

## MATH 280 Topics in Analysis

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Repeatable for credit

Yes

## MATH 281 Topics in Algebra

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Repeatable for credit

Yes

## MATH 282 Topics in Geometry

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Repeatable for credit

Yes

## MATH 283 Topics in Combinatorial Theory

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Repeatable for credit

Yes

## MATH 284 Topics in Dynamics

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Repeatable for credit

Yes

## MATH 285 Topics in Partial Differential Equations

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Repeatable for credit

Yes

## MATH 286 Topics in Number Theory

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Repeatable for credit

Yes

## MATH 287 Topics in Topology

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Repeatable for credit

Yes

## MATH 288A Pedagogy of Mathematics

### Credits

#### Instructor

Pedro Morales

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Fall

## MATH 288B Pedagogy of Mathematics

### Credits

#### Instructor

Pedro Morales

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Winter

## MATH 292 Seminar

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Fall, Winter, Spring

## MATH 296 Special Student Seminar

### Credits

#### Requirements

Enrollment is restricted to graduate students.

#### Quarter offered

Fall, Winter, Spring

## MATH 297A Independent Study

### Credits

#### Repeatable for credit

Yes

## MATH 297B Independent Study

### Credits

#### Repeatable for credit

Yes

## MATH 297C Independent Study

### Credits

#### Repeatable for credit

Yes

## MATH 298 Master's Thesis Research

### Credits

#### Quarter offered

Fall, Winter, Spring

## MATH 299A Thesis Research

### Credits

#### Repeatable for credit

Yes

## MATH 299B Thesis Research

### Credits

#### Repeatable for credit

Yes

## MATH 299C Thesis Research

### Credits

#### Repeatable for credit

Yes

Cross-listed courses that are managed by another department are listed at the bottom.