# Mathematics (MATH)

MATH 100-0 Quantitative Reasoning (1 Unit)   Analyzing topical, real-life problems from a quantitative perspective. Solving multistep problems using elementary algebra, probability, and statistics. Formal Studies Distro Area

MATH 100-BR Quantitative Reasoning (0.5 Unit)   For participants in Bridge I summer program. Analyzing topical, real-life problems from a quantitative perspective. Solving multistep problems using elementary algebra, probability, and statistics. Taken with HUM 100-1-BR.

MATH 105-6 First-Year Seminar (1 Unit)   Topics vary. WCAS First-Year Seminar

MATH 110-0 Introduction to Mathematics (1 Unit)   Exploration of the beauty of mathematics through a study of the patterns and properties of the natural numbers. Topics include counting, probability, prime numbers, the Euclidean algorithm, and unique factorization. For students with minimal mathematical background. Students may not receive credit for MATH 110-0 after completing a 200-level MATH course or higher. Formal Studies Distro Area

MATH 202-0 Finite Mathematics (1 Unit)   Selected topics from elementary linear algebra and its applications, finite probability, and elementary statistics. For students majoring in the behavioral sciences. Formal Studies Distro Area

MATH 211-0 Short Course in Calculus (1 Unit)   Elements of differential and integral calculus. Students may not receive credit for both MATH 211-0 and any of MATH 212-0 (former), MATH 213-0 (former), MATH 214-0 (former), MATH 218-1, MATH 218-2, MATH 218-3, MATH 220-0 (former), MATH 220-1, MATH 220-2, MATH 224-0 (former), or MATH 226-0. Not suitable for students planning to major in mathematics, the natural sciences, or economics.  Formal Studies Distro Area

MATH 218-1 Single-Variable Calculus with Precalculus (1 Unit)   Functions and graphs. Limits. Continuity. Differentiation. Linearization. Students may not receive credit for both MATH 218-1 and any of MATH 211-0, MATH 212-0 (former), MATH 220-0 (former), or MATH 220-1. Prerequisite: consent of the department. Formal Studies Distro Area

MATH 218-2 Single-Variable Calculus with Precalculus (1 Unit)   Extreme value theorem, mean value theorem, and curve-sketching. Related rates. Optimization. Transcendental and inverse functions. Students may not receive credit for both MATH 218-2 and any of MATH 211-0, MATH 212-0 (former), MATH 220-0 (former), or MATH 220-1. Prerequisite: MATH 218-1 or consent of the department. Formal Studies Distro Area

MATH 218-3 Single-Variable Calculus with Precalculus (1 Unit)   Definite integrals, antiderivatives, and the fundamental theorem of calculus. Areas and volumes. Techniques of integration, numerical integration, and improper integrals. First-order linear and separable ordinary differential equations. Students may not receive credit for both MATH 218-3 and any of MATH 213-0 (former), MATH 220-2, or MATH 224-0 (former). Prerequisite: MATH 218-2 or consent of the department. Formal Studies Distro Area

MATH 218-SG-1 Peer-Guided Study Group: Single-Variable Calculus with Precalculus (0 Unit)   Peer-guided study group for students enrolled in MATH 218-1. Meets weekly in small groups with a peer facilitator, to collaboratively review material, solve practice problems, and clarify concepts. Enrollment optional. Graded S/U.

MATH 218-SG-2 Peer-Guided Study Group: Single-Variable Calculus with Precalculus (0 Unit)   Peer-guided study group for students enrolled in MATH 218-2. Meets weekly in small groups with a peer facilitator, to collaboratively review material, solve practice problems, and clarify concepts. Enrollment optional. Graded S/U.

MATH 218-SG-3 Peer-Guided Study Group: Single-Variable Calculus with Precalculus (0 Unit)   Peer-guided study group for students enrolled in MATH 218-3. Meets weekly in small groups with a peer facilitator, to collaboratively review material, solve practice problems, and clarify concepts. Enrollment optional. Graded S/U.

MATH 220-1 Single-Variable Differential Calculus (1 Unit)   Limits. Differentiation. Linear approximation and related rates. Extreme value theorem, mean value theorem, and curve-sketching. Optimization. Students may not receive credit for both MATH 220-1 and any of MATH 211-0, MATH 212-0 (former), MATH 213-0 (former), MATH 218-1, MATH 218-2, or MATH 220-0 (former). Formal Studies Distro Area

MATH 220-2 Single-Variable Integral Calculus (1 Unit)   Definite integrals, antiderivatives, and the fundamental theorem of calculus. Transcendental and inverse functions. Areas and volumes. Techniques of integration, numerical integration, and improper integrals. First-order linear and separable ordinary differential equations. Students may not receive credit for both MATH 220-2 and any of MATH 213-0 (former), MATH 214-0 (former), MATH 218-3, or MATH 224-0 (former). Prerequisite: MATH 218-2 or MATH 220-0 (former) or MATH 220-1. Formal Studies Distro Area

MATH 220-SG-1 Peer-Guided Study Group: Single-Variable Differential Calculus (0 Unit)   Peer-guided study group for students enrolled in MATH 220-1. Meets weekly in small groups with a peer facilitator to collaboratively review material, solve practice problems, and clarify concepts. Enrollment optional. Graded S/U.

MATH 220-SG-2 Peer-Guided Study Group: Single-Variable Integral Calculus (0 Unit)   Peer-guided study group for students enrolled in MATH 220-2. Meets weekly in small groups with a peer facilitator to collaboratively review material, solve practice problems, and clarify concepts. Enrollment optional. Graded S/U.

MATH 226-0 Sequences and Series (1 Unit)   Infinite sequences. Infinite series and convergence tests. Power series, Taylor series, Taylor polynomials and error. Complex numbers. Second-order linear ordinary differential equations and power series solutions. Students may not receive credit for both MATH 226-0 and any of MATH 214-0 (former), MATH 224-0 (former), or MATH 281-2. Prerequisite: MATH 218-3 or MATH 220-2. Formal Studies Distro Area

MATH 228-1 Multivariable Differential Calculus for Engineering (1 Unit)   Vectors, vector functions, partial derivatives, Taylor polynomials, and optimization. Emphasis on engineering applications. For McCormick School of Engineering students only. Students may not receive credit for both MATH 228-1 and any of MATH 230-0 (former), MATH 230-1, MATH 281-1, MATH 285-2, MATH 290-2, MATH 291-2, or ES_APPM 252-1. Prerequisite: MATH 218-3 or MATH 214-0 (former) or MATH 220-2 or MATH 224-0 (former). Formal Studies Distro Area

MATH 228-2 Multivariable Integral Calculus for Engineering (1 Unit)   Multiple integration: double integrals, triple integrals, and change of variables. Vector calculus: vector fields, line integrals, surface integrals, curl and divergence, Green's theorem, Stokes' theorem, and the divergence theorem. Emphasis on engineering applications. For McCormick School of Engineering students only. Students may not receive credit for both MATH 228-2 and any of MATH 230-2, MATH 234-0 (former), MATH 281-2, MATH 285-3, MATH 290-3, MATH 291-3, or ES_APPM 252-2. Prerequisite: MATH 228-1 or MATH 230-0 (former) or MATH 230-1 or MATH 281-1 or MATH 285-2 or MATH 290-2 or MATH 291-2 or ES_APPM 252-1. Formal Studies Distro Area

MATH 228-SG-1 Peer-Guided Study Group: Multivariable Calculus for Engineering (0 Unit)   Peer-guided study group for students enrolled in MATH 228-1. Meets weekly in small groups with a peer facilitator to collaboratively review material, solve practice problems, and clarify concepts. Enrollment optional. Graded S/U.

MATH 230-1 Multivariable Differential Calculus (1 Unit)   Vectors, vector functions, partial derivatives, and optimization. Not open to students in the McCormick School of Engineering. Students may not receive credit for both MATH 230-1 and any of MATH 228-1, MATH 230-0 (former), MATH 281-1, MATH 285-2, MATH 290-2, MATH 291-2, or ES_APPM 252-1. Prerequisite: MATH 218-3 or MATH 214-0 (former) or MATH 220-2 or MATH 224-0 (former). Formal Studies Distro Area

MATH 230-2 Multivariable Integral Calculus (1 Unit)   Multiple integration: double integrals, triple integrals, and the change of variables theorem. Vector calculus: vector fields, line integrals, surface integrals, curl and divergence, Green's theorem, Stokes' theorem, and the divergence theorem. Not open to students in the McCormick School of Engineering. Students may not receive credit for both MATH 230-2 and any of MATH 228-2, MATH 234-0 (former), MATH 281-2, MATH 285-3, MATH 290-3, MATH 291-3, or ES_APPM 252-2. Prerequisite: MATH 228-1 or MATH 230-0 (former) or MATH 230-1 or MATH 281-1 or MATH 285-2 or MATH 290-2 or MATH 291-2 or ES_APPM 252-1. Formal Studies Distro Area

MATH 230-SG-1 Peer-Guided Study Group: Multivariable Differential Calculus (0 Unit)   Peer-guided study group for students enrolled in MATH 230-1. Meets weekly in small groups with a peer facilitator to collaboratively review material, solve practice problems, and clarify concepts. Enrollment optional. Graded S/U.

MATH 240-0 Linear Algebra (1 Unit)   Elementary linear algebra: systems of linear equations, matrix algebra, subspaces, determinants, eigenvalues, eigenvectors, and orthogonality. Students may not receive credit for both MATH 240-0 and any of MATH 281-3, MATH 285-1, MATH 290-1, MATH 291-1, GEN_ENG 205-1, or GEN_ENG 206-1. Prerequisite: MATH 230-1 or MATH 230-0 (former) or MATH 281-1 or ES_APPM 252-1. Formal Studies Distro Area

MATH 250-0 Elementary Differential Equations (1 Unit)   Elementary ordinary differential equations: first-order equations, second-order linear equations, series solutions, and systems of first-order linear equations. Students may not receive credit for both MATH 250-0 and any of MATH 281-3, MATH 360-1, GEN_ENG 205-4, or GEN_ENG 206-4. Prerequisites: MATH 226-0 or MATH 281-2; and MATH 228-2 or MATH 230-2 or MATH 234-0 (former) or MATH 281-2 or MATH 285-3 or MATH 290-3 or MATH 291-3 or ES_APPM 252-2; and MATH 240-0 or MATH 285-1 or MATH 290-1 or MATH 291-1 or GEN_ENG 205-1 or GEN_ENG 206-1. Formal Studies Distro Area

MATH 281-1 Accelerated Mathematics for ISP: First Year (1 Unit)   Multivariable differential and integral calculus. Students may not receive credit for both MATH 281-1 and any of MATH 228-1, MATH 230-0 (former), MATH 230-1, MATH 285-2, MATH 290-2, MATH 291-2, or ES_APPM 252-1. Prerequisite: first-year standing in ISP. Formal Studies Distro Area

MATH 281-2 Accelerated Mathematics for ISP: First Year (1 Unit)   Vector calculus, ordinary differential equations, and infinite series. Students may not receive credit for both MATH 281-2 and any of MATH 226-0, MATH 228-2, MATH 230-2, MATH 234-0 (former), MATH 285-3, MATH 290-3, MATH 291-3, or ES_APPM 252-2. Prerequisite: MATH 281-1. Formal Studies Distro Area

MATH 281-3 Accelerated Mathematics for ISP: First Year (1 Unit)   Linear algebra and systems of ordinary differential equations. Students may not receive credit for both MATH 281-3 and any of MATH 240-0, MATH 250-0, MATH 285-1, MATH 290-1, MATH 291-1, MATH 360-1, GEN_ENG 205-1, GEN_ENG 206-1, GEN_ENG 205-4, or GEN_ENG 206-4. Prerequisite: MATH 281-2. Formal Studies Distro Area

MATH 285-1 Accelerated Mathematics for MMSS: First Year (1 Unit)   Linear algebra: systems of linear equations, linear transformations, determinants, vector spaces, eigenvalues and eigenvectors. Students may not receive credit for both MATH 285-1 and any of MATH 240-0, MATH 281-3, MATH 290-1, MATH 291-1, GEN_ENG 205-1, or GEN_ENG 206-1. Prerequisite: first-year standing in MMSS. Formal Studies Distro Area

MATH 285-2 Accelerated Mathematics for MMSS: First Year (1 Unit)   Linear algebra: orthogonality, symmetric matrices, and quadratic forms. Multivariable differential calculus: vectors, differentiation, vector-valued functions, and optimization. Students may not receive credit for both MATH 285-2 and any of MATH 228-1, MATH 230-0 (former), MATH 230-1, MATH 281-1, MATH 290-2, MATH 291-2, or ES_APPM 252-1. Prerequisite: MATH 285-1. Formal Studies Distro Area

MATH 285-3 Accelerated Mathematics for MMSS: First Year (1 Unit)   Multivariable integral calculus: multiple integration, line integrals, surface integrals, and vector analysis. Students may not receive credit for both MATH 285-3 and any of MATH 228-2, MATH 230-2, MATH 234-0 (former), MATH 281-2, MATH 290-3, MATH 291-3, or ES_APPM 252-2. Prerequisite: MATH 285-2. Formal Studies Distro Area

MATH 290-1 MENU: Linear Algebra and Multivariable Calculus (1 Unit)   Linear algebra: systems of linear equations, linear transformations, determinants, eigenvalues and eigenvectors. Students may not receive credit for both MATH 290-1 and any of MATH 240-0, MATH 281-3, MATH 285-1, MATH 291-1, GEN_ENG 205-1, or GEN_ENG 206-1. Formal Studies Distro Area

MATH 290-2 MENU: Linear Algebra and Multivariable Calculus (1 Unit)   Linear algebra: orthogonality, symmetric matrices, and quadratic forms. Multivariable differential calculus: vectors, differentiation, vector-valued functions, and optimization. Students may not receive credit for both MATH 290-2 and any of MATH 228-1, MATH 230-0 (former), MATH 230-1, MATH 281-1, MATH 285-2, MATH 291-2, or ES_APPM 252-1. Prerequisite: MATH 290-1. Formal Studies Distro Area

MATH 290-3 MENU: Linear Algebra and Multivariable Calculus (1 Unit)   Multivariable integral calculus: multiple integration, line integrals, surface integrals, and vector analysis. Students may not receive credit for both MATH 290-3 and any of MATH 228-2, MATH 230-2, MATH 234-0 (former), MATH 281-2, MATH 285-3, MATH 291-3, or ES_APPM 252-2. Prerequisite: MATH 290-2. Formal Studies Distro Area

MATH 291-1 MENU: Intensive Linear Algebra and Multivariable Calculus (1 Unit)   Foundations. Linear algebra: systems of linear equations, linear transformations, subspaces, vector spaces, and determinants. The course emphasizes theory and proofs. Students may not receive credit for both MATH 291-1 and any of MATH 240-0, MATH 281-3, MATH 285-1, MATH 290-1, GEN_ENG 205-1, or GEN_ENG 206-1. Prerequisite: consent of the department. Formal Studies Distro Area

MATH 291-2 MENU: Intensive Linear Algebra and Multivariable Calculus (1 Unit)   Linear algebra: eigenvalues and eigenvectors, orthogonality, symmetric matrices, and quadratic forms. Multivariable differential calculus: vectors, differentiation, and vector-valued functions. The course emphasizes theory and proofs. Students may not receive credit for both MATH 291-2 and any of MATH 228-1, MATH 230-0 (former), MATH 230-1, MATH 281-1, MATH 285-2, MATH 290-2, or ES_APPM 252-1. Prerequisite: MATH 291-1. Formal Studies Distro Area

MATH 291-3 MENU: Intensive Linear Algebra and Multivariable Calculus (1 Unit)   Multivariable differential calculus: optimzation. Multivariable integral calculus: multiple integration, line integrals, surface integrals, and vector analysis. The course emphasizes theory and proofs. Students may not receive credit for both MATH 291-3 and any of MATH 228-2, MATH 230-2, MATH 234-0 (former), MATH 281-2, MATH 285-3, MATH 290-3, or ES_APPM 252-2. Prerequisite: MATH 291-2. Formal Studies Distro Area

MATH 300-0 Foundations of Higher Mathematics (1 Unit)

Introduction to fundamental mathematical structures, including sets, functions, equivalence relations, and cardinal numbers. Elementary logic and proof techniques. Students may not receive credit for MATH 300-0 after passing any of MATH 320-1, MATH 321-1, MATH 330-1, or MATH 331-1.

Prerequisite: MATH 240-0 or MATH 281-3 or MATH 285-1 or MATH 290-1 or MATH 291-1 or GEN_ENG 205-1 or GEN_ENG 206-1 or consent of the department.

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MATH 306-0 Combinatorics & Discrete Mathematics (1 Unit)

Discrete mathematics, inductive reasoning, counting problems, binomial coefficients and Pascal's triangle, Fibonacci numbers, combinatorial probability, divisibility and primes, partitions, and generating functions.

Prerequisite: MATH 240-0 or MATH 281-3 or MATH 285-1 or MATH 290-1 or MATH 291-1 or GEN_ENG 205-1 or GEN_ENG 206-1.

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MATH 308-0 Graph Theory (1 Unit)

Introduction to graph theory: graphs, trees, matchings, planar graphs, and colorings. Additional topics as time permits.

Prerequisite: MATH 291-1 or MATH 300-0 or MATH 306-0.

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MATH 310-1 Probability and Stochastic Processes (1 Unit)

Axioms of probability. Conditional probability and independence. Random variables. Joint distributions. Expectation. Limit theorems: the weak law of large numbers and the central limit theorem. Students may not receive credit for both MATH 310-1 and any of MATH 311-1, MATH 314-0, MATH 385-0, STAT 320-1, STAT 383-0, IEMS 202-0, or ELEC_ENG 302-0. Prerequisite or corequisite: MATH 226-0 or MATH 281-2; and MATH 228-2 or MATH 230-2 or MATH 234-0 (former), or MATH 281-2 or MATH 285-3 or MATH 290-3 or MATH 291-3 or ES_APPM 252-2.

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MATH 310-2 Probability and Stochastic Processes (1 Unit)

Discrete-time Markov chains, recurrence and transience. Students may not receive credit for both MATH 310-2 and MATH 311-2.

Prerequisites: MATH 240-0 or MATH 281-3 or MATH 285-1 or MATH 290-1 or MATH 291-1 or GEN_ENG 205-1 or GEN_ENG 206-1; and MATH 310-1 or MATH 311-1 or MATH 314-0 or MATH 385-0 or STAT 320-1 or STAT 383-0 or IEMS 202-0 or ELEC_ENG 302-0.

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MATH 310-3 Probability and Stochastic Processes (1 Unit)

Continuous-time Markov chains, queues, population growth models. Brownian motion and other diffusion processes. Additional topics as time permits. Students may not receive credit for both MATH 310-3 and MATH 311-3.

Prerequisite: MATH 310-2 or MATH 311-2.

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MATH 311-1 MENU: Probability and Stochastic Processes (1 Unit)

Probability spaces. Random variables. Independence. Distributions. Generating functions. The central limit theorem. Students may not receive credit for both MATH 311-1 and any of MATH 310-1, MATH 314-0, MATH 385-0, STAT 320-1, STAT 383-0, IEMS 202-0, or ELEC_ENG 302-0.

Prerequisite: MATH 226-0 or MATH 281-2; and MATH 291-3, or MATH 300-0 and any one of MATH 290-3, MATH 281-2, MATH 285-3 or ES_APPM 252-2; or consent of the department. Recommended: MATH 320-1 or MATH 321-1.

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MATH 311-2 MENU: Probability and Stochastic Processes (1 Unit)

Markov chains, convergence of random variables, random processes, renewals, and queues. Students may not receive credit for both MATH 311-2 and MATH 310-2.

Prerequisite: MATH 311-1 or consent of the department.

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MATH 311-3 MENU: Probability and Stochastic Processes (1 Unit)

Stationary processes, martingales, and diffusion processes. Students may not receive credit for both MATH 311-3 and MATH 310-3.

Prerequisite: MATH 311-2 or consent of the department.

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MATH 314-0 Probability and Statistics for Econometrics (1 Unit)

Introduction to probability theory and statistical methods, including properties of probability distributions, sampling distributions, estimation, confidence intervals and hypothesis testing. For students planning to take ECON 381-1. Students may not receive credit for both MATH 314-0 and any of MATH 310-1, MATH 311-1, MATH 385-0, STAT 320-1, STAT 383-0, IEMS 202-0, or ELEC_ENG 302-0. Prerequisite or corequisite: MATH 226-0 or MATH 281-2; and MATH 228-2 or MATH 230-2 or MATH 234-0 (former) or MATH 281-1 or MATH 285-3 or MATH 290-3 or MATH 291-3 or ES_APPM 252-2.

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MATH 320-1 Real Analysis (1 Unit)

Analysis on the real line: axiomatic development of the real number system, sequences and series of real numbers, continuity, and differentiability. Students may not receive credit for both MATH 320-1 and MATH 321-1.

Prerequisite: MATH 226-0 or MATH 281-2; and MATH 300-0 or MATH 291-3; or consent of the department.

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MATH 320-2 Real Analysis (1 Unit)

Analysis on the real line: the Riemann integral and sequences and series of functions. Additional topics as time permits. Students may not receive credit for both MATH 320-2 and MATH 321-2.

Prerequisite: MATH 320-1 or MATH 321-1.

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MATH 320-3 Real Analysis (1 Unit)

Analysis on Euclidean spaces: the topology of Euclidean spaces, limits, continuity, and differentiability, including the inverse and implicit function theorems. Additional topics as time permits. Students may not receive credit for both MATH 320-3 and MATH 321-2.

Prerequisite: MATH 320-2.

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MATH 321-1 MENU: Real Analysis (1 Unit)

Analysis on metric spaces: the real number system, the topology of metric spaces, sequences and series, continuity, and differentiability. Students may not receive credit for both MATH 321-1 and MATH 320-1.

Prerequisite: consent of the department.

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MATH 321-2 MENU: Real Analysis (1 Unit)

Analysis on metric spaces: the Riemann integral, sequences and series of functions, and functions of several variables, including the inverse and implicit function theorems. Students may not receive credit for both MATH 321-2 and either MATH 320-2 or MATH 320-3.

Prerequisite: MATH 321-1.

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MATH 321-3 MENU: Real Analysis (1 Unit)

Lebesgue measure and the Lebesgue integral. Additional topics as time permits.

Prerequisite: MATH 321-2.

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MATH 325-0 Complex Analysis (1 Unit)

Complex numbers. Analytic functions. Cauchy's theorem and the Cauchy integral formula. Series. Residues. Students may not receive credit for both MATH 325-0 and either MATH 382-0 or ES_APPM 312-0.

Prerequisites: MATH 226-0 or MATH 281-2; and MATH 228-2 or MATH 230-2 or MATH 234-0 (former) or MATH 281-2 or MATH 285-3 or MATH 290-3 or MATH 291-3 or ES_APPM 252-2; and MATH 240-0 or MATH 281-3 or MATH 285-1 or MATH 290-1 or MATH 291-1 or GEN_ENG 205-1 or GEN_ENG 206-1.

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MATH 327-0 Mechanics for Mathematicians (1 Unit)

Fundamental mathematical ideas arising in classical mechanics: Newtonian mechanics, Lagrangian formalism and the calculus of variations, motion with constraints, symmetries and conservation laws, Hamiltonian mechanics, and Liouville's theorem. No prior knowledge of physics required. Students may not receive credit for MATH 327-0 after taking PHYSICS 330-1.

Prerequisites: MATH 226-0 or MATH 281-3; and MATH 228-2 or MATH 230-2 or MATH 234-0 (former) or MATH 281-2 or MATH 285-3 or MATH 290-3 or MATH 291-3 or ES_APPM 252-2; and MATH 240-0 or MATH 281-3 or MATH 285-1 or MATH 290-1 or MATH 291-1 or GEN_ENG 205-1 or GEN_ENG 206-1.

Formal Studies Distro Area Interdisciplinary Distro - See Rules Natural Sciences Distro Area

MATH 330-1 Abstract Algebra (1 Unit)

Group theory. Students may not receive credit for both MATH 330-1 and MATH 331-1.

Prerequisite: MATH 291-1 or MATH 300-0.

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MATH 330-2 Abstract Algebra (1 Unit)

Ring theory, including polynomial rings. Module theory. Students may not receive credit for both MATH 330-2 and MATH 331-2. Prerequisite: MATH 330-1 or MATH 331-1.Ring theory, including polynomial rings. Module theory. Students may not receive credit for both MATH 330-2 and MATH 331-2.

Prerequisite: MATH 330-1 or MATH 331-1.

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MATH 330-3 Abstract Algebra (1 Unit)

Field theory and Galois theory. Students may not receive credit for both MATH 330-3 and MATH 331-3.

Prerequisite: MATH 330-2 or MATH 331-2.

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MATH 331-1 MENU: Abstract Algebra (1 Unit)

Group theory, including the Sylow theorems. Students may not receive credit for both MATH 331-1 and MATH 330-1.

Prerequisite: consent of the department.

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MATH 331-2 MENU: Abstract Algebra (1 Unit)

Ring theory, including polynomial rings. Module theory, including canonical forms of operators on vector spaces. Students may not receive credit for both MATH 331-2 and MATH 330-2.

Prerequisite: MATH 331-1.

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MATH 331-3 MENU: Abstract Algebra (1 Unit)

Field theory and Galois theory. Students may not receive credit for both MATH 331-3 and MATH 330-3.

Prerequisite: MATH 331-2.

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MATH 334-0 Linear Algebra: Second Course (1 Unit)

Vector spaces. Linear maps. Eigenvalues, eigenvectors and invariant subspaces. Inner product spaces. Canonical forms of operators on real and complex vector spaces.

Prerequisite: MATH 300-0 or MATH 291-2.

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MATH 336-1 Introduction to the Theory of Numbers (1 Unit)

Divisibility and prime numbers. Congruences. Quadratic reciprocity. Diophantine equations.

Prerequisite: MATH 228-1 or MATH 230-1 or MATH 281-1 or MATH 285-2 or MATH 290-2 or MATH 291-2 or ES_APPM 252-1.

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MATH 336-2 Introduction to the Theory of Numbers (1 Unit)

Topics in analytic and algebraic number theory.

Prerequisite: MATH 336-1.

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MATH 340-0 Geometry (1 Unit)

Axioms for Euclidean geometry. Non-Euclidean geometry. Projective geometry. Introduction of coordinate systems from the axioms. Quadrics. Erlangen program. Introduction to plane algebraic curves.

Prerequisite: MATH 300-0 or MATH 291-1.

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MATH 342-0 Introduction to Differential Geometry (1 Unit)

Differential geometry of curves and surfaces in three-dimensional space: curves, regular surfaces, the Gauss map, and additional topics as time permits.

Prerequisites: MATH 226-0 or MATH 281-2; and MATH 228-2 or MATH 230-2 or MATH 234-0 (former) or MATH 281-2 or MATH 285-3 or MATH 290-3 or MATH 291-3 or ES_APPM 252-2; and MATH 240-0 or MATH 281-3 or MATH 285-1 or MATH 290-1 or MATH 291-1 or GEN_ENG 205-1 or GEN_ENG 206-1.

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MATH 344-1 Introduction to Topology (1 Unit)

Topological spaces, continuity, connectedness, compactness, countability and separation axioms.

Prerequisite: MATH 320-1 or MATH 321-1.

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MATH 344-2 Introduction to Topology (1 Unit)

The fundamental group. Classification of covering spaces. Additional topics as permits.

Prerequisites: MATH 344-1, and either MATH 330-1 or MATH 331-1.

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MATH 351-0 Fourier Analysis and Boundary Value Problems (1 Unit)

Fourier series with applications to partial differential equations arising in physics and engineering. Students may not receive credit for both MATH 351-0 and any of MATH 381-0, MATH 360-2, or ES_APPM 311-2.

Prerequisite: MATH 250-0 or MATH 281-3 or MATH 360-1 or GEN_ENG 206-4 or GEN_ENG 206-4.

Formal Studies Distro Area

MATH 353-0 Qualitative Theory of Differential Equations (1 Unit)

Qualitative theory of ordinary differential equations: linear systems, phase portraits, periodic solutions, stability theory, Lyapunov functions, and chaos. Students may not receive credit for both MATH 353-0 and MATH 360-2.

Prerequisite: MATH 250-0 or MATH 281-3 or MATH 360-1 or GEN_ENG 205-4 or GEN_ENG 206-4.

Formal Studies Distro Area

MATH 354-0 Chaotic Dynamical Systems (1 Unit)   Chaotic phenomena in deterministic discrete dynamical systems, primarily through iteration of functions of one variable. Prerequisite: MATH 240-0 or MATH 281-3 or MATH 285-1 or MATH 290-1 or MATH 291-1 or GEN_ENG 205-1 or GEN_ENG 206-1. Formal Studies Distro Area

MATH 360-1 MENU: Applied Analysis (1 Unit)

Linear ordinary differential equations, systems of linear ordinary differential equations, and applications. Students may not receive credit for both MATH 360-1 and any of MATH 250-0, MATH 281-3, GEN_ENG 205-4, GEN_ENG 206-4.

Prerequisite: MATH 226-0 or MATH 281-2; and MATH 290-3 or MATH 291-3.

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MATH 360-2 MENU: Applied Analysis (1 Unit)

Qualitative analysis of systems of ordinary differential equations. Linear partial differential equations. Fourier series and orthogonal functions. Applications. Students may not receive credit for both MATH 360-2 and any of MATH 381-0, MATH 351-0, or ES_APPM 311-2.

Prerequisite: MATH 360-1.

Formal Studies Distro Area

MATH 366-0 Mathematical Models in Finance (1 Unit)   Cash flow computations. Basic financial concepts (stocks, bonds, options, arbitrage, hedging) and put-call parity. Binomial tree models. Risk-neutral valuation. Random walk and Brownian motion as a tool for modeling fluctuations. Options pricing. Applications of the central limit theorem. The Black-Scholes formula and partial differential equation. Numerical approximations. Some familiarity with differential equations is desirable. Prerequisites: MATH 240-0 or MATH 281-3 or MATH 285-1 or MATH 290-1 or MATH 291-1 or GEN_ENG 205-1 or GEN_ENG 206-1; and MATH 310-1 or MATH 311-1 or MATH 314-0 or MATH 385-0 or STAT 320-1 or STAT 383-0 or IEMS 202-0 or ELEC_ENG 302-0. Formal Studies Distro Area

MATH 368-0 Introduction to Optimization (1 Unit)

Methods and concepts of optimization theory: linear programming, duality, convexity, and Kuhn-Tucker theory.

Prerequisites: MATH 226-0 or MATH 281-2; and MATH 291-3, or MATH 300-0 and one of MATH 228-2, MATH 230-2, MATH 234-0 (former), MATH 281-2, MATH 285-3, MATH 290-3, or ES_APPM 252-2.

Formal Studies Distro Area

MATH 370-0 Mathematical Logic (1 Unit)

Mathematical formulation and rigorous discussion of logical systems, particularly the propositional calculus and the functional calculi of first and second order. Well-formed formulae, formal languages, proofs, tautologies, effective procedures, deduction theorems, axiom schemata.

Prerequisite: MATH 300-0 or MATH 291-3 or consent of the instructor.

Formal Studies Distro Area

MATH 381-0 Fourier Analysis and Boundary Value Problems for ISP (1 Unit)   Fourier series. Hilbert spaces and orthogonal functions. Parseval's theorem. Poisson summation formula and lattice points. Fourier integrals: Gaussian functions. Fourier inversion formula. Convolution. Sturm-Liouville theory. Applications to partial differential equations. Heat and wave equations. For ISP students only. Students may not receive credit for both MATH 381-0 and any of MATH 351-0, MATH 360-2, or ES_APPM 311-2. Prerequisites: MATH 281-3 and PHYSICS 125-3. Formal Studies Distro Area

MATH 382-0 Complex Analysis for ISP (1 Unit)   Complex numbers. Analytic functions. Cauchy's theorem and the Cauchy integral formula. Series. Residues. For ISP students only. Students may not receive credit for both MATH 382-0 and either MATH 325-0 or ES_APPM 312-0. Prerequisites: MATH 281-3 and PHYSICS 125-3. Formal Studies Distro Area

MATH 385-0 Probability and Statistics for MMSS (1 Unit)   Probability theory and its applications in the social sciences. Students may not receive credit for both MATH 385-0 and any of MATH 310-1, MATH 311-1, MATH 314-0, STAT 320-1, STAT 383-0, IEMS 202-0, or ELEC_ENG 302-0. Prerequisite: second-year standing in MMSS. Formal Studies Distro Area

MATH 386-1 Econometrics for MMSS (1 Unit)   Econometric methods. Students may not receive credit for both MATH 386-1 and ECON 381-1. Prerequisite: MATH 385-0. Formal Studies Distro Area

MATH 386-2 Econometrics for MMSS (1 Unit)   Econometric methods. Students may not receive credit for both MATH 386-2 and ECON 381-2. Prerequisite: MATH 386-1. Formal Studies Distro Area

MATH 395-0 Undergraduate Seminar (1 Unit)   Topics in modern mathematics and relationships among different branches of mathematics. May be taken for only 1 unit of credit at a time but may be repeated for credit with change of topic. Prerequisite: consent of the department.

MATH 399-0 Independent Study (1 Unit)   Independent learning under the direction of a faculty adviser. Students must obtain departmental approval for a plan of study before enrolling in MATH 399-0. Prerequisite: consent of the department.