## Mathematical Science Course Descriptions (MATH)

Prerequisite chart for

MATH 140 (GQ) — Calculus With Analytic Geometry I (4)
Functions, limits; analytic geometry; derivatives, differentials, applications; integrals, applications. Students may only take one course for credit from MATH 110, 140, 140A, 140B, and 140H.
Prerequisite: MATH 022, MATH 026; or MATH 040 or MATH 041 or satisfactory performance on the mathematics placement examination

MATH 141 (GQ) — Calculus with Analytic Geometry II (4)
Derivatives, integrals, applications; sequences and series; analytic geometry; polar coordinates. Students may take only one course for credit from MATH 141, 141B, and 141H.
Prerequisite: MATH 140, MATH 140A, MATH 140B or MATH 140H

MATH 220 (GQ) — Matrices (2-3)
Systems of linear equations; matrix algebra; eigenvalues and eigenvectors; linear systems of differential equations.
Prerequisite: MATH 110, MATH 140 or MATH 140H

MATH 230 — Calculus and Vector Analysis (4)
Three-dimensional analytic geometry; vectors in space; partial differentiation; double and triple integrals; integral vector calculus. Students who have passed either Math 231 or 232 may not schedule Math 230 or 230H for credit.
Prerequisite: MATH 141 or MATH 141H

MATH 250 — Ordinary Differential Equations (3)
First- and second-order equations; special functions; Laplace transform solutions; higher order equations. Students who have passed MATH 251 may not schedule this course for credit.
Prerequisite: MATH 141

MATH 251 — Ordinary and Partial Differential Equations (4)
First- and second-order equations; special functions; Laplace transform solutions; higher order equations; Fourier series; partial differential equations.
Prerequisite: MATH 141 or MATH 141H

STAT 301 — Statistical Analysis I (3)
Probability concepts; nature of statistical methods; elementary distribution and sampling theory; fundamental ideas relative to estimation and testing hypotheses.
Prerequisite: 3 credits of calculus

MATH 315 — Foundations of Mathematics (3)
A consideration of selected topics in the foundations of mathematics, with emphasis on development of basic meaning and concepts.
Prerequisite: MATH 141

MATH 318 (STAT 318) — Elementary Probability (3)
Combinatorial analysis, axioms of probability, conditional probability and independence, discrete and continuous random variables, expectation, limit theorems, additional topics. Students who have passed either MATH(STAT) 414 or 418 may not schedule this course for credit.
Prerequisite: MATH 141

MATH 401 — Introduction to Analysis I (3)
Review of calculus, properties of real numbers, infinite series, uniform convergence, power series. Students who have passed Math 403 may not schedule this course.
Prerequisite: MATH 230 or MATH 231

MATH 412 — Fourier Series and Partial Differential Equations (3)
Orthogonal systems and Fourier series; derivation and classification of partial differential equations; eigenvalue function method and its applications; additional topics.
Prerequisite: MATH 230; MATH 250 or MATH 251

MATH 421 — Complex Analysis (3)
Infinite sequences and series; algebra and geometry of complex numbers; analytic functions; integration; power series; residue calculus; conformal mapping, applications.
Prerequisite: MATH 230, MATH 232 or MATH 405; MATH 401 or MATH 403

MATH 425 — Introduction to Operations Research (3)
Nature of operations research, problem formulation, model construction, deriving solution from models, allocation problems, general linear allocation problems, inventory problems.
Prerequisite: MATH 141 and MATH 220

MATH 427 — Foundations of Geometry (3)
Euclidean and various non-Euclidean geometries and their development from postulate systems. Students who have passed MATH 427 may not schedule MATH 471.
Prerequisite: MATH 230 or MATH 231

MATH 430 — Linear Algebra and Discrete Models I (3)
Vector spaces, linear transformations, matrices determinants, characteristic values and vectors, systems of linear equations, applications to discrete models.
Prerequisite: MATH 220

MATH 431 — Linear Algebra and Discrete Models II (3)
Vector spaces, linear transformations, matrices, determinants, characteristic values and vectors, systems of linear equations, applications to discrete models.
Prerequisite: MATH 430

MATH 435 — Basic Abstract Algebra (3)
Elementary theory of groups, rings, and fields. Students who have passed MATH 435 may not schedule MATH 470.
Prerequisite: MATH 311W or MATH 315

MATH 449 — Applied Ordinary Differential Equations (3)
Differential and difference equations and their application to biology, chemistry, and physics; techniques in dynamical systems theory.
Prerequisites: MATH 250 or MATH 251

MATH 450 — Mathematical Modeling (3)
Constructing mathematical models of physical phenomena; topics include pendulum motion, polymer fluids, chemical reactions, waves, flight, and chaos.
Prerequisite: either MATH 315 and MATH 430 or MATH 405 or MATH 412

MATH 455 — Introduction to Numerical Analysis I (3)
Floating point computation, numerical rootfinding, interpolation, numerical quadrature, direct methods for linear systems. Students may take only one course for credit from MATH 451 and MATH 455.
Prerequisite: CMPSC 201, CMPSC 202 or CMPSC 121; MATH 220; MATH 230 or MATH 231

MATH 465 — Number Theory (3)
Elements, divisibility of numbers, congruences, residues, and forms.
Prerequisite: MATH 311W

MATH 468 — Mathematical Coding Theory (3)
Shannon's theorem, block codes, linear codes, Hamming codes, Hadamard codes, Golay codes, Reed-Muller codes, bounds on codes, cyclic codes.
Prerequisite: MATH 311W; advanced calculus

MATH 475W — History of Mathematics (3)
A global survey of the history of mathematics as viewed as a human response to cultural, political, economic, and societal pressures.
Prerequisite: MATH 315 or MATH 311W

MATH 496 — Independent Studies (1-18)
Creative projects, including research and design, which are supervised on an individual basis and which fall outside the scope of formal courses.

MATH 497 — Special Topics (1-9)
Formal courses given infrequently to explore, in depth, a comparatively narow subject which may be topical or of special interest.

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