# Courses

## MATH-3510 (3) Introduction to Probability and Statistics

Introduces the basic notions of Probability: random variables, expectation, conditioning, and the standard distributions (Binomial, Poisson, Exponential, Normal). This course also covers the Law of Large Numbers and Central Limit Theorem as they apply to statistical questions: sampling from a random distribution, estimation, and hypothesis testing. Prereqs., MATH 2001 and MATH 2300 or APPM 1360. Credit not granted for this course and MATH 2510 or MATH 4510.

## MATH-3850 (1) Seminar in Guided Mathematics Instruction

Provides Learning Assistants with an opportunity to analyze assessment data for formative purposes, and develop instructional plans as a result of these analyses. These formative assessment analyses will build on the literature in the learning sciences. Students will gain direct experiences interacting with the tools of the trade, especially with actual assessment data and models of instruction. May be repeated up to 3 total credit hours. Restricted to Learning Assistants in Math. Coreq., EDUC 4800.

## MATH-4000 (3) Foundations of Mathematics

Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Prereq., MATH 2001 plus one of 3001, 3130, 3140, or 3210. Same as MATH 5000.

## MATH-4001 (3) Analysis II

Provides a rigorous treatment of infinite series, sequences of functions, and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral, or Fourier analysis). Prereqs., MATH 3001 and MATH 3130.

## MATH-4120 (3) Introduction to Operations Research

Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation, and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Prereqs., MATH 3130 or APPM 3310. Same as MATH 5120 and APPM 4120.

## MATH-4140 (3) Abstract Algebra 2

Covers group actions, Sylow theory, Field theory, and some Galois theory. Prereq., MATH 3140.

## MATH-4200 (3) Introduction to Topology

Introduces the basic concepts of point set topology. Includes topological spaces, metric spaces, homeomorphisms, connectedness, and compactness. Prereqs., MATH 3001 or MATH 4310.

## MATH-4210 (3) Euclidean and Non-Euclidean Geometry II

Continues the study of Euclidean and non-Euclidean geometry from MATH 3210 and examines a more advanced topic from geometry chosen by the instructor (e.g.,projective geometry or three-dimensional geometry). Prereq., MATH 3120.

## MATH-4230 (3) Geometry of Curves and Surfaces

Introduces the modern differential geometry of plane curves, space curves, and surfaces in space. Computers are used, but no prior knowledge of computer programming is required. Prereqs., Calculus 3 and MATH 3130.

## MATH-4330 (3) Fourier Analysis

The notion of Fourier analysis, via series and integrals, of periodic and nonperiodic phenomena is central to many areas of mathematics. Develops the Fourier theory in depth, and considers such special topics and applications as wavelets, Fast Fourier Transforms, seismology, digital signal processing, differential equations, and Fourier optics. Prereq., MATH 3001 or instructor consent. Same as MATH 5330.

## MATH-4430 (3) Ordinary Differential Equations

Involves an elementary systematic introduction to first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness, and numerical solutions. Prereqs., Calculus 3, and MATH 3130 or APPM 3310 (min grade C). Similar to APPM 2360.

## MATH-4440 (3) Mathematics of Coding and Cryptography

Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed; prepares students for the more advanced ECEN 5032 and 5682. Prereq., MATH 3130. Recommended prereqs., MATH 3110 and 3140. Same as MATH 5440.

## MATH-4450 (3) Introduction to Complex Variables

Theory of functions of one complex variable, including integrals, power series, residues, conformal mapping, and special functions. Prereqs., MATH 2400 and 3001.

## MATH-4470 (3) Partial Differential Equations 1

Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green's function, and variational methods. Prereq., MATH 4430 or equivalent. Same as MATH 5470.

## MATH-4510 (3) Introduction to Probability Theory

Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains. Prereqs., MATH 2400, or APPM 2350, and MATH 3130. Credit not granted for this course and APPM 3570, ECEN 3810, or MATH 3510.

## MATH-4520 (3) Introduction to Mathematical Statistics

Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis. Analyzes variance distribution-free methods. Prereq., MATH 4510 or APPM 3570. Same as MATH 5520 and APPM 4520. Credit not granted for this course and MATH 2510.

## MATH-4540 (3) Introduction to Time Series

Stresses basic properties, linear extrapolation, and filtering of stationary random functions. Topics also include spectral analysis and estimation of the power spectrum using computers. Prereqs., MATH 4510/APPM 3570 and MATH 4520/APPM 4520. Same as MATH 5540 and APPM 4540.

## MATH-4650 (3) Intermediate Numerical Analysis 1

Focuses on numerical solution of nonlinear equations,interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Prereqs., APPM 3310 orMath 3130, and knowledge of a programming language. Same as Appm 4650.

## MATH-4660 (3) Intermediate Numerical Analysis 2

Topics include solution of algebraic and transcendental equations, and linear and nonlinear systems of equations. Highlights interpolation, integration, solution of ordinary differential equations, least squares, sources of error and error analysis, computer implementation of numerical methods, matrix eigenvalue problems, and summation of infinite series. See also MATH 4650. Prereq., MATH 4650. Same as APPM 4660.

## MATH-4730 (3) Set Theory

Studies in detail the theory of cardinal and ordinal numbers, definition by recursion, the statement of the continuum hypothesis, simple cardinal arithmetic, and other topics chosen by the instructor. Prereq., MATH 2001 plus one upper division MATH class.

## MATH-4805 (1) Mathematical Teacher Training: Inclusive Pedagogy

Designed to train students to teach mathematics in an inclusive, multicultural environment. Students teach a math course within the McNeill Academic Program (Student Academic Services Center) meeting weekly with faculty and colleagues to learn to re-design curriculum, fine-tune pedagogical practices, create assessments, mentor undergraduate instructor assistants and create an inclusive classroom environment. May be repeated up to 4 total credit hours. Prereqs., senior or graduate standing, experience with college-level instruction.

## MATH-4820 (3) History of Mathematical Ideas

Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Prereq., two upper division courses in mathematics. Recommended prereq., completion of upper division Written Communication requirement.

## MATH-4890 (1-3) Honors Independent Study

Offered for students doing a thesis for departmental honors.

## MATH-5000 (3) Foundations of Mathematics

Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Restricted to graduate students only. Prereqs., MATH 3130 and 3140. Same as MATH 4000. Prerequisites: Restricted to Graduate Students only.