## Course Catalog

**MATHEMATICS**

A minor in mathematics is attained upon the completion of five mathematics courses with a grade of C- or better. Three of the courses must be numbered above MA 233M.

**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 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 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 268N: Learnability and Linguistic Theory**

This course introduces the student to language learnability theory within Optimality Theory. Topics will include formal grammars, linguistic typologies, optimization, efficiency of learning algorithms and learnability of grammatical systems. 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 233M.

**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 132M or MA 236N.

**MA 336: Abstract Algebra II**

Continuation of MA 335N, which is prerequisite.

**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 132M.

**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.

**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 233M.

**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 132M or PL 345H and Junior/Senior standing.

**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 233M.

**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.