**MA 104M: Survey of Mathematics**

Applications of mathematics to real problems. Probability, statistics, number theory, graph theory, fractals, chaos theory and other advanced math topics.

**MA 105M: Precalculus**

Algebraic, exponential, logarithmic and trigonometric functions. Analytic geometry, curve sketching, mathematical induction, equations and inequalities.

**MA 129M: Math in Visual Effects (VFX)**

Creation of visual effects (VFX) used in movies, video games, and the web with a particular emphasis on the underlying mathematical representations used. Students will create and analyze a portfolio of effects. No prerequisites.

**MA 131M: Calculus I**

First in three-course sequence. Techniques of differentiation and integration, limits, continuity, the Mean Value Theorem, curve sketching, Riemann sums and the Fundamental Theorem of Calculus. Applications in the sciences.

**MA 132M: Calculus II**

Continuation of MA 131M. Exponential, logarithmic and trigonometric functions, formal integration techniques, Taylor polynomials and infinite series. Prerequisite: MA 131M.

**MA 133M: Statistics, an Introduction**

Concepts, methods and applications of statistics in the natural sciences. Elementary probability theory, random variables, discrete and continuous probability distributions. Statistics and sampling distributions, estimation and hypothesis testing, linear regression. Credit is given for only one of MA 133M or one of the behavioral science statistics courses, but not both.

**MA 233M: Calculus III**

Continuation of MA 132M. Three-dimensional analytic and vector geometry, partial and directional derivatives, extremes of functions of several variables, multiple integration, line and surface integrals, Green's and Stoke's Theorem. Prerequisite: MA 132M.

**MA 234N: Differential Equations**

Existence and uniqueness theorems, nth-order linear differential equations, Laplace transforms, systems of ordinary differential equations, series solutions and numerical methods. Prerequisite: MA 132M.

**MA 236N: Linear Algebra**

Vector spaces, linear transformations, matrices, eigenvalues, eigenvectors and systems of linear equations. Prerequisite: MA 131M.

**MA 237N: Introduction to Mathematical Thinking**

Abstract mathematical reasoning and exposition, emphasizes writing and understanding mathematical proof, propositional and predicate calculus, relations, functions, construction and properties of number systems. Prerequisite: MA 132M.

**MA 238: Optimization Techniques**

Classical techniques for optimizing univariate and multivariate functions with or without constraints. Linear programming through simplex method, duality theory. Non-linear programming through Lagrange multipliers, quadratic and convex conforms. Prerequisite: MA 233M.

**MA 303: Mathematical Biology**

Learn mathematical and computational tools to study biological systems. Topics range from the molecular to population level from areas such as biology, ecology, evolution, and epidemiology. Prerequisite: MA 131M

**MA 304: Mathematics for Sustainability**

Learn mathematical techniques and use them to answer real-world questions about topics such as renewable energy, climate change, recycling programs, population growth, etc. Prerequisite: MA 131M.

**MA 333: Probability and Statistics I**

First in two-course sequence covering probability theory, random variables, random sampling, various distribution functions, point and interval estimation, tests of hypotheses, regression theory, non-parametric tests. Prerequisite: MA 132M.

**MA 334: Probability and Statistics II**

Continuation of MA 333, which is prerequisite.

**MA 335N: Abstract Algebra I**

First in two-course sequence covering integers, groups, rings, integral domains, vector spaces, development of fields. Prerequisite: MA 237N or CS 150M.

**MA 336: Abstract Algebra II**

Continuation of MA 335N, which is prerequisite.

**MA 337N: Number Theory**

An introduction to number-theoretic topics, including divisibility, prime numbers, congruence, modular arithmetic, arithmetic functions, primitive roots, and applications to cryptography.

**MA 339N: Combinatorics**

Problem solving that deals with finite sets. Permutations and combinations, generating functions, recurrence relations, Polya's theory of counting, fundamentals of graph theory, difference equations and enumeration techniques. Prerequisite: MA 237N or CS 150M.

**MA 340: Dynamical Systems**

An introduction to dynamical systems, chaos and fractals. Dynamic modeling, stability analysis, bifurcation theory, strange attractors, self-similarity, iterated function systems. Prerequisite: MA 234N.

**MA 341: Numerical Analysis**

Methods for solving an equation or systems of equations. Interpolating polynomials, numerical integration and differentiation, numerical solutions of ordinary and partial differential equations, boundary value problems. Prerequisite: MA 233M.

**MA 351: Fourier Analysis**

Introduction to Fourier series, Fourier transforms and discrete Fourier transforms. Computer simulation and analysis of various physical phenomena using Fourier software packages, including the fast Fourier transform algorithm. Prerequisite: MA 234N.

**MA 365N: Cognitive Linguistics**

How are cognitive functions structured and computed in the brain? This course investigates how grammars are organized in neural networks and capture linguistic patterns. Topics include formal grammars, optimization, typologies, and tensor product representations of cognitive architectures.

**MA 375: Differential Geometry**

This course covers curves and surfaces in Euclidean 3-dimensional space. Topics include curvature and torsion of curves, the Frenet frame, Gaussian and mean curvature of surfaces, geodesics, isometries, Gauss' Theorema Egregium, and interesting applications. Prerequisites: MA 233M, MA 236N

**MA1 410: Mathematics Seminar-1st semester**

Required of all Juniors and Seniors majoring in mathematics. One course credit upon satisfactory completion of two-years participation. Mathematical processes from a historical and cultural perspective.

**MA2 410: Mathematics Seminar-2nd semester**

Continuation of Mathematics Seminar. Four semesters required for one course credit. Prerequisite: MA1 410.

**MA3 410: Mathematics Seminar-3rd semester**

Continuation of Mathematics Seminar. Four semesters required for one course credit. Prerequisites: MA1 410 and MA2 410.

**MA4 410: Mathematics Seminar-4th semester**

Continuation of Mathematics Seminar. Four semesters required for one course credit. Prerequisites: MA1 410, MA2 410 and MA3 410.

**MA 411: Introduction to Topology**

Introduction to point-set topology emphasizing connectedness, compactness, separation properties, continuity, homeomorphisms and metric and Euclidean spaces. Prerequisite: MA 237N or CS 150M.

**MA 421: Partial Differential Equations**

Initial and boundary value problems. Separation of variables, d'Alembert solution, Green's functions, Fourier series, Bessel functions, Legendre polynomials, Laplace transforms and numerical methods. Prerequisite: MA 234N.

**MA 422: Mathematical Logic**

Topics include Propositional and Predicate Calculus, Recursion Theory, set Theory, Godel's completeness Theorem and Godel's Incompleteness Theorems. This course does not fulfill the Natural Science Academic Area requirement. Prerequisite: MA 237N or CS 150M or PL 210M.

**MA 433: Real Analysis I**

First in two-course sequence covering point-set topology, limits, continuity, derivatives, functions of bounded variation, Riemann-Stieltjes integrals, infinite series, function spaces and sequences of functions. Prerequisite: MA 237N or CS150M.

**MA 434: Real Analysis II**

Continuation of MA 433, which is prerequisite.

**MA 445: Complex Analysis**

Analytic functions, contour integrals, residues, linear transformations of the complex plane, Laurent Series, conformal mappings and Poisson Integrals. Prerequisite: MA 233M.

**MA 498: Comprehensive Examination**

**MA 499: Senior Thesis**

Senior mathematics majors may, upon invitation of the mathematics faculty, do research and write a thesis under the direction of a member of that faculty.