|
Mathematics (MATH)
College of Natural Sciences
MATH 100 Survey of Mathematics (3) Selected
topics designed to acquaint nonspecialists with examples of mathematical
reasoning. May not be taken for credit after 205 or higher. M/L
MATH 111 Introduction to Mathematics (3) Study
of concepts and properties of number systems. Prospective elementary
education majors only; not applicable to arts and sciences requirements.
Pre: two years of high school algebra, one year of geometry, and
placement test. M/L
MATH 140 Trigonometry and Analytic Geometry (3) Functions,
with special attention to polynomial, rational, exponential,
logarithmic, and trigonometric functions, plane trigonometry, polar
coordinates, conic sections. Pre: two years of high school algebra, one
year of plane geometry, and precalculus assessment. M/L
MATH 203 Calculus for Business and Social Sciences
(3) Basic concepts; differentiation and integration; applications to
management, finance, economics, and the social sciences. Pre: two years
high school algebra, one year plane geometry, and precalculus
assessment. M/L
MATH 215 Applied Calculus I (4) Basic concepts;
differentiation, differential equations and integration with
applications directed primarily to the life sciences. Pre: C or better
in 140 or precalculus assessment.
MATH 216 Applied Calculus II (3) Differential
calculus for functions in several variables and curves, systems of
ordinary differential equations, series approximation of functions,
continuous probability, exposure to use of calculus in the literature.
Pre: 215 or consent.
MATH 231 Calculus III (3) Parametric curves,
polar coordinates; vector-oriented study of functions of several
variables; partial derivatives. Pre: a grade of C or better in 206 and
206L (or concurrent).
MATH 232 Calculus IV (3) Multiple integrals;
line integrals, Green’s Theorem, surface integrals; first and second
order ordinary differential equations. Pre: 231 or consent.
MATH 241 Calculus I (4) Basic concepts;
differentiation with applications; integration. Pre: a grade of C or
better in 140 or 215 or precalculus assessment. M/L
MATH 242 Calculus II (3) Integration techniques
and applications, series and approximations. Pre: a grade of C or better
in 241 or 251 or a grade of B or better in 215. Co-requisite: 242L.
MATH 242L Calculus Computer Lab (1) Introduction
to symbolic computer software for solving calculus problems, graphing
functions and experimenting with calculus concepts. No knowledge of
computers required. Co-requisite: 242.
MATH 301 Introduction to Discrete Mathematics (3) Symbolic
logic, sets and relations, algorithms, trees and other graphs.
Additional topics chosen from algebraic systems, networks, automata.
Pre: one semester of calculus from mathematics department and one
semester programming; or consent. Recommended: MATH 197.
MATH 302 Introduction to Differential Equations I
(3) First order ordinary differential equations, constant
coefficient linear equations, oscillations, Laplace transform,
convolution, Green’s function. Recommended: PHYS 170. Pre: 232 or
consent.
MATH 303 Introduction to Differential Equations II
(3) Constant coefficient linear systems, variable coefficient
ordinary differential equations, series solutions and special functions,
Fourier series, partial differential equations. Pre: 302, 311 (or
concurrent); or consent.
MATH 311 Introduction to Linear Algebra (3) Algebra
of matrices, linear equations, real vector spaces and transformations.
Pre: 231 or consent.
MATH 321 Introduction to Advanced Mathematics (3) Formal
introduction to the concepts of logic, finite and infinite sets,
functions, methods of proof and axiomatic systems. Pre: 231 or consent.
MATH 351 Foundation of Euclidean Geometry (3) Axiomatic
Euclidean geometry and introduction to the axiomatic method. Pre: 231
and 321 (or concurrent); or consent.
MATH 352 Non-Euclidean Geometries (3) Hyperbolic,
other non-Euclidean geometries. Pre: 351 or consent.
MATH 371 Elementary Probability Theory (3) Sets,
discrete sample spaces, problems in combinatorial probability, random
variables, mathematical expectations, classical distributions,
applications. Pre: 206 or consent.
MATH 373 Elementary Statistics (3) Estimation,
tests of significance, the concept of power. Pre: 371 or consent.
MATH 402 Partial Differential Equations I (3) Integral
surfaces and characteristics of first and second order partial
differential equations. Applications to the equations of mathematical
physics. Pre: 232 or consent.
MATH 403 Partial Differential Equations II (3) Laplace’s
equation, Fourier transform methods for PDEs, higher dimensional PDEs,
spherical harmonics, Laplace series, special functions and applications.
Pre: 402 or consent.
MATH 405 Ordinary Differential Equations (3) Systems
of linear ordinary differential equations, autonomous systems, and
stability theory applications. Optional topics include series solutions,
Sturm theory, numerical methods. Pre: 232 and 311, or consent.
MATH 407 Numerical Analysis (3) Numerical
solution of equations, interpolation, least-squares approximation,
quadrature, eigenvalue problems, numerical solution of ordinary and
partial differential equations. (These topics are covered in the year
sequence 407-408.) Pre: 232, 311, and one semester programming; or
consent. Recommended: MATH 197.
MATH 408 Numerical Analysis (3) Continuation
of 407. This is the second course of a year sequence and should be taken
in the same academic year as 407. Pre: 407 or consent.
MATH 411 Linear Algebra (3) Vector spaces over
arbitrary fields, minimal polynomials, invariant subspaces, canonical
forms of matrices; unitary and Hermitian matrices, quadratic forms. Pre:
a grade of B or better in 311 or consent.
MATH 412 Introduction to Abstract Algebra (3) Introduction
to basic algebraic structures. Groups, finite groups, abelian groups,
rings, integral domains, fields, factorization, polynomial rings, field
extensions, quotient fields. (These topics are covered in the year
sequence 412-413.) Pre: 311 or consent.
MATH 413 Introduction to Abstract Algebra (3) Continuation
of 412. This is the second course of a year sequence and should be taken
in the same academic year as 412. Pre: 412 or consent.
MATH 414 Operations Research: Discrete Models (3) Techniques
of mathematical programming. Topics may include linear programming,
integer programming, network analysis, dynamic programming, and game
theory. Pre: 311 or consent.
MATH 416 Operations Research: Probabilistic Models
(3) Queuing theory, inventory theory, Markov chains, simulation.
Pre: 311 and 371, or consent.
MATH 420 Introduction to the Theory of Numbers (3) Congruences,
quadratic residues, arithmetic functions, distribution of primes. Pre:
311 or consent.
MATH 421 Topology (3) Geometric and
combinatorial topology. Surfaces, homology, Euler characteristics,
winding numbers. Jordan curve theorem. Pre: two courses from 311, 321,
351, 411, 412, or 420; or consent.
MATH 431 Advanced Calculus (3) Topology of Rn,
continuous functions, Riemann integration, sequences and series, uniform
convergence, implicit function theorems, differentials and Jacobians.
(These topics are covered in the year sequence 431-432.) Pre: three
courses from 311, 321, 412, 413, 420, 455, 471, or consent.
MATH 432 Advanced Calculus (3) Continuation of
431. This is the second course of a year sequence and should be taken in
the same academic year as 431. Pre: 431 or consent.
MATH 442 Vector Analysis (3) Vector operations,
wedge product, differential forms, and smooth mappings. Theorems of
Green, Stokes, and Gauss, both classically and in terms of forms.
Applications to electromagnetism and mechanics. Pre: 232 and 311, or
consent.
MATH 443 Differential Geometry (3) Properties
and fundamental geometric invariants of curves and surfaces in space;
applications to the physical sciences. Pre: 232 (or concurrent) and 311;
or consent.
MATH 444 Complex Variable (3) Analytic
functions, complex integration, introduction to conformal mapping. Pre:
232 and 311; or consent.
MATH 449 (Alpha) Topics in Undergraduate
Mathematics (3) Advanced topics from various areas: algebra, number
theory, analysis, and geometry. Repeatable. Pre: consent.
MATH 454 Axiomatic Set Theory (3) Sets,
relations, ordinal arithmetic, cardinal arithmetic, axiomatic set
theory, axiom of choice and the continuum hypothesis. Pre: 321 or
graduate standing in a related field or consent. Not open to mathematics
graduate students.
MATH 455 Mathematical Logic (3) A
system of first order logic. Formal notions of well-formed formula,
proof, and derivability. Semantic notions of model, truth, and validity.
Completeness theorem. Pre: 454 or consent.
MATH 471 Probability (3) Probability spaces,
random variables, distributions, expectations, moment-generating and
characteristic functions, limit theorems. Continuous probability
emphasized. Pre: 232 (or concurrent) and 371, or consent.
MATH 472 Statistical Inference (3) Sampling
and parameter estimation, tests of hypotheses, correlation, regression,
analysis of variance, sequential analysis, rank order statistics. Pre:
471 or consent.
MATH 475 Combinatorial Mathematics (3) Finite
configurations. Topics may include counting methods, generating
functions, graph theory, map coloring, block design, network flows,
analysis of discrete algorithms. Pre: 311 or consent.
MATH 499 Directed Reading (V) Limited to
advanced students who must arrange with an instructor before enrolling.
Repeatable once for a maximum of 3 credits each.
MATH 500 Master’s Plan B/C Studies (1) Enrollment
for degree completion. Pre: master’s Plan B or C candidate and
consent.
MATH 511 Writing and Problem Solving (2) Exploration
of topics in algebra, analysis, and geometry, with emphasis on writing
skills, experimentation, mathematical thinking, and problem solving.
Enrollment limited to mathematics teachers.
MATH 602 Ordinary and Partial Differential
Equations (3) Classical existence and uniqueness theory for ODEs and
PDEs, qualitative properties, classification, boundary value and initial
value problems, fundamental solutions, other topics. (These topics are
covered in the year sequence 602-603.) Pre: 402, 431, 432, 442, or
consent.
MATH 603 Ordinary and Partial Differential
Equations (3) Continuation of 602. This is the second course of a
year sequence and should be taken in the same academic year as 602. Pre:
602.
MATH 607 Numerical Analysis (3) Perron-Frobenius
theory, nonnegative matrices, matrix numerical analysis, iterative
methods, discrete approximation to partial differential equations. Pre:
402, 407, 408, or consent.
MATH 611 Modern Algebra (3) Modules, Sylow
theorems, Jordan-Holder theorem, unique factorization domains, Galois
theory, algebraic closures, transcendence bases. (These topics are
covered in the year sequence 611- 612.) Pre: consent.
MATH 612 Modern Algebra (3) Continuation of
611. This is the second course of a year sequence and should be taken in
the same academic year as 611. Pre: 611.
MATH 613 Group Theory (3) Sylow theorems,
solvable groups, nilpotent groups, extension theory, representation
theory, additional topics. Pre: consent.
MATH 615 Ring Theory (3) Ideal theory in
Noetherian rings, localization, Dedekind domains, the Jacobson radical,
the Wedderburn-Artin theorem, additional topics. Pre: consent.
MATH 618 Lattice Theory (3) Introduction with
applications to general algebra. Partially ordered sets, decomposition
theory, representations of lattices, varieties and free lattices,
coordinatization of modular lattices. Pre: 612 or consent.
MATH 619 Universal Algebra (3) Introduction to
basic techniques, including subalgebras, congruences, automorphisms and
endomorphisms, varieties of algebras, Mal’cev conditions. Pre: 612 or
consent.
MATH 621 Topology (3) Properties of topological
spaces; separation axioms, compactness, connectedness; metrizability;
convergence and continuity. Additional topics from general and algebraic
topology. (These topics are covered in the year sequence 621- 622.) Pre:
consent.
MATH 622 Topology (3) Continuation of 621. This
is the second course of a year sequence and should be taken in the same
academic year as 621. Pre: 621.
MATH 625 Differentiable Manifolds I (3) Differentiable
structures on manifolds, tensor fields, Frobenius theorem, exterior
algebra, integration of forms, Poincare Lemma, Stoke’s theorem. Pre:
411, 432, and 622; or consent.
MATH 631 Theory of Functions of a Real Variable (3)
Lebesgue measure and integral, convergence of integrals, functions
of bounded variation, Lebesgue-Stieltjes integral and more general
theory of measure and integration. (These topics are covered in the year
sequence 631-632.) Pre: consent.
MATH 632 Theory of Functions of a Real Variable (3)
Continuation of 632. This is the second course of a year sequence
and should be taken in the same academic year as 631. Pre: 631.
MATH 633 Functional Analysis (3) Linear
topological spaces, normed spaces, Hilbert spaces, function spaces,
function algebras, operator theory. Pre: consent.
MATH 635 Potential Theory (3) Primary classical
and modern analysis pertaining to Dirichlet’s problem. Integral
equations, extremum problems, Brownian motion. Pre: 632 or consent.
MATH 637 Calculus of Variations (3) Simple
variational problems, first and second variation formulas. Euler-Lagrange
equation, direct methods, optimal control. Pre: 432 or consent.
MATH 644 Analytic Function Theory (3) Conformal
mapping, residue theory, series and product developments, analytic
continuation, special functions. (These topics are covered in the year
sequence 644-645.) Pre: consent.
MATH 645 Analytic Function Theory (3) Continuation
of 644. This is the second course of a year sequence and should be taken
in the same academic year as 644. Pre: 644.
MATH 649 (Alpha) Topics in Mathematics (3) Commutative
rings, function theory, geometric topology, transformation groups, etc.
Repeatable. Pre: consent.
MATH 655 Set Theory (3) Axiomatic development,
ordinal and cardinal numbers, recursion theorems, axiom of choice,
continuum hypothesis, consistency and independence results. Pre:
consent.
MATH 657 Recursive Functions and Complexity (3) Recursive,
r.e., Ptime, and Logspace classes. Nondeterminism, parallelism,
alternation, and Boolean circuits. Reducibility and completeness. Pre:
455, ICS 441, or consent.
MATH 671 Advanced Probability (3) Independence
and conditioning, martingales, ergodic theory, Markov chains, central
limit theorem. Pre: 631 or consent.
MATH 672 Stochastic Processes (3) Stationary,
Gaussian, and Markov processes. Pre: 671 or consent.
MATH 681 Graph Theory (3) Connected graphs and
digraphs. Graph embeddings. Connectivity and networks. Factors and
factorizations. Coverings. Coloring. Applications. Pre: 311 or consent.
MATH 699 Directed Reading and Research (V) Maximum
of 3 credit hours. Repeatable three times. Pre: graduate standing and
consent.
MATH 700 Thesis Research (V) Research for
master’s thesis. Pre: consent.
MATH 799 Apprenticeship in Teaching (V) An
experience-based introduction to college-level teaching; students serve
as student teachers to professors; responsibilities include supervised
teaching and participation in planning and evaluation. Open to graduate
students in mathematics only. Repeatable once. CR/NC only. Pre: graduate
standing in mathematics and consent.
MATH 800 Dissertation Research (V) Research
for doctoral dissertation.
For key to symbols and abbreviations, see the first
page of this section. |