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Courses in Mathematics

MATH 001 - Elementary College Algebra
Review of fundamental operations and a more extensive study of fractions, exponents, radicals, linear and quadratic equations, ratio, proportion, variation, progressions, and the binomial theorem. Topics normally included in intermediate algebra in high school. Students who have satisfactorily completed two years of high school algebra, or the equivalent, receive no credit for this course. Offered only in Evening Division and Summer Session. Prerequisite: One year of high school algebra.
Credits: 3.
MATH 002 - Plane Trigonometry
Trigonometric functions, their graphs and other properties, solution of triangles, trigonometric equations and identities, and inverse trigonometric functions. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered 20 or above. Prerequisite: 1 or 9. Offered only in Evening Division and Summer Session.
Credits: 3.
MATH 009 - College Algebra
Sets, relations, functions with particular attention to properties of algebraic, exponential, logarithmic functions, their graphs and applications in preparation for 19. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered 19 or above. Pre/co-requisites: Two years of secondary school algebra, one year of secondary school geometry.
Credits: 3.
MATH 010 - Pre-Calculus Mathematics
Skills in working with numerical, algebraic, and trigonometric expressions are developed in preparation for 21. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered 19 or above. Prerequisites: Two years of secondary school algebra, one of secondary school geometry.
Credits: 3.
MATH 011 - Technical Calculus I
Introduction to calculus of functions of one variable, emphasizing techniques and applications of differentiation and integration. Prerequisites: 10, or 9 and 2, or strong background in secondary school algebra and trigonometry and an associates degree in engineering. Dual credit not given for 11 and 21.
Credits: 3.
MATH 012 - Technical Calculus II
Transcendental functions, techniques of integration, polar coordinates, sequences, series and vectors. Prerequisites: 11 or 21; associates degree in engineering. Dual credit not given for 12 and 22.
Credits: 3.
MATH 013 - Calculus via Modeling I
Introduction to mathematical modeling and differential calculus with a graphical, problem-solving approach. Requires graphing calculator. Prerequisite: Three years high school math, or Math. 9. Credit not given for both Math. 13 and 19.
Credits: 3.
MATH 014 - Calculus via Modeling II
Further modeling and an introduction to integral and multivariate calculus with a graphical, problem-solving approach. Requires graphing calculator. Credit not given for both 14 and 20. Prerequisite: 13.
Credits: 3.
MATH 015 - Elementary School Math
Comprehension of operations with real numbers, measurements, and informal geometry provide background for algebra, number theory, statistics, probability, compass and ruler constructions, and problem solving. Prerequisite: 15 for 16. Open only to students in elementary education.
Credits: 3.
MATH 016 - Fund Concepts Elem School Math
Comprehension of operations with real numbers, measurements, and informal geometry provide background for algebra, number theory, statistics, probability, compass and ruler constructions, and problem solving. Prerequisite: 15 for 16. Open only to students in elementary education.
Credits: 3.
MATH 017 - Applications of Finite Math
Introduction to mathematics of finite systems with applications, such as probability, statistics, growth and symmetry, graph theory, fair division and apportionment problems, voting systems. Prerequisite: Two years of secondary school algebra or 9 or 10.
Credits: 0-3.
MATH 018 - Basic Mathematics
Data, statistics, modeling, algebra, word problems, calculus. Students who do well in the algebra section may continue with MATH 19 or MATH 21. Prerequisites: 3 years high school math. No credit for EM students.
Credits: 3.
MATH 019 - Fundamentals of Calculus I
Introduction to limits and differential calculus with a wide variety of applications. Students interested in intensive use of mathematics should take 21. Credit not given for more than one of the courses 19, 21 unless followed by 22. Credit not given for both Math. 13 and 19. Prerequisite: 9, 10, or sufficiently strong background in secondary school algebra and geometry.
Credits: 3.
MATH 020 - Fundamentals of Calculus II
Introduction to integral calculus with a wide variety of applications. A student who completes 20 may be admitted to 22; however 19, 21, 22 is preferable to 19, 20, 22. Credit not given for both MATH 14 and 20. Prerequisite: 19.*
Credits: 3.
MATH 021 - Calculus I
Introduction to calculus of functions of one variable including: limits, continuity, techniques and applications of differentiation and integration. Credit not given for more than one course in the pair 19, 21. Prerequisite: 10; or 9 and 2; or strong background in secondary school algebra and trigonometry
Credits: 4.
MATH 022 - Calculus II
Techniques and applications of integration. Polar coordinates, Taylor polynomials, sequences and series, power series. Prerequisite: 21.
Credits: 4.
MATH 023 - Transitional Calculus
(Intended to make the transition from a B or better in 19 to 121). Topics are similar to 22 but recognizing different backgrounds of students in 19 versus 21. Credit will not be given for 22 and 23. Pre/co-requisites: MATH 19.
Credits: 4.
MATH 052 - Fundamentals of Mathematics
Fundamental mathematical concepts and techniques, emphasizing proofs and algorithms, are investigated within the context of topics such as number theory and graph theory. Credit not given for both 52 and 54. Corequisite: Math 21.
Credits: 3.
MATH 054 - Fund of Math of Computation
Introduction to mathematical theory and techniques underlying computer science. Corequisite: 19 or 21.
Credits: 3.
MATH 095 - Special Topics
Introductory courses or seminars on topics beyond the scope of existing departmental offerings. See Schedule of Courses for specific titles. Prerequisite: Instructor's consent.
Credits: 1-6.
MATH 111 - Technical Calculus III
Calculus of functions of several variables, partial derivatives, gradient, divergence, curl, multiple integrals. Prerequisites: 12 or 22; associates degree in engineering. Dual credit not given for 111 and 121.
Credits: 3.
MATH 121 - Calculus III
Vectors, vector-valued functions. Calculus of functions of several variables: partial derivatives, gradient, divergence, curl, multiple integrals, line integrals, Stokes' and Green's theorems. Prerequisite: 22.
Credits: 4.
MATH 123 - Calculus III for Engineers
Vectors, vector-valued functions, functions of several variables, partial derivatives, gradient, divergence, curl, multiple integrals, line integrals, Stokes', divergence, Green's theorems. Examples from engineering, physical sciences. Pre/co-requisite: Math 22
Credits: 3.
MATH 124 - Linear Algebra
Matrices, linear dependence, vector spaces, linear transformations, characteristic equations and applications. Prerequisites: 22 or instructor's permission. Corequisite: MATH 121 recommended but not required.
Credits: 3.
MATH 141 - Real Analysis in One Variable
Principles of analysis in one variable. Heine-Borel and Bolzano-Weierstrass theorems; rigorous development of differential and integral calculus; infinite sequences and series of functions. May not be taken concurrently with or after 241. Pre/co-requisites: 52.
Credits: 3.
MATH 151 - Groups and Rings
An introduction to the basic concepts of abstract algebra emphasizing examples, including modular arithmetic, symmetric groups, cyclic groups, polynomial rings, homomorphisms, and isomorphisms. May not be taken concurrently with or after 251. Pre/co-requisites: 52
Credits: 3.
MATH 161 - Development of Mathematics
Historical development of mathematical sciences emphasizing interrelations among them. Individual assignments correspond to background and interests of students. Prerequisite: Nine hours of college mathematics.
Credits: 3.
MATH 162 - Geometry El&Mid School Teacher
An informal, investigative approach to geometry. Extensive use of discovery experiences through inductive procedures as opposed to the traditional emphasis on deductive process found in high school geometry. Credit not given for Math. majors in EM. Prerequisite: 15 or a teaching certificate.
Credits: 3.
MATH 167 - Physical Chemistry Preparation
Review of relevant mathematical and physical concepts as applied to physical chemistry. Credit cannot be obtained for both MATH 167 and MATH 121. Not available for credit for E&M students. Prerequisites: 22; CHEM 32 or 36. (Cross-listing: Chem. 167.)
Credits: 1.
MATH 168 - Mathematics of Biology
Discrete biological processes: nonlinear difference equations. Continuous processes: ordinary differential equations, phase plane methods, quantitative solutions. Applications: population dynamics, epidemiology, Michaelis-Menten kinetics, autocatalysis, muscle contraction. Includes a lab. May not be taken concurrently with or after Math 268. Pre/co-requisites: Math 22 or 23, 124. Cross-listing: Biol 168
Credits: 3.
MATH 173 - Basic Combinatorial Theory
Introduction to basic combinatorial principles emphasizing problem-solving techniques. Enumeration, Generating Functions, Fibonacci Numbers, Pigeonhole Principle, Inclusion-Exclusion, and Graph Theory. Prerequisite: 52 or 54.
Credits: 3.
MATH 179 - Teaching Secondary School Math
Contemporary secondary school mathematics curricula, their content from an advanced standpoint, unifying mathematical concepts and their implications at various levels, and introduction of selected mathematical topics. Intended only for students with an interest in teaching secondary school mathematics. Not acceptable as part of any mathematics requirement for a degree. Prerequisites: Education 178, acceptance to teacher education, or instructor's permission.
Credits: 3.
MATH 191 - Special Topics
An approved project under guidance of a staff member and culminating in a written report. Involvement with off-campus groups permitted. Prerequisites: Junior or senior standing, approval of department chairperson.
Credits: 1-3.
MATH 192 - Special Topics
An approved project under guidance of a staff member and culminating in a written report. Involvement with off-campus groups permitted. Prerequisites: Junior or senior standing, approval of department chairperson.
Credits: 1-3.
MATH 193 - College Honors
Credits: 1-3.
MATH 194 - College Honors
Credits: 1-3.
MATH 195 - Special Topics
Credits: 1-4.
MATH 207 - Probability Theory
(Cross listed with Statistics 251.) Distributions of random variables and functions of random variables. Expectations, stochastic independence, sampling and limiting distributions (central limit theorems). Concepts of random number generation. Prerequisite: Math 121; Stat 151 or 153 recommended.
Credits: 3.
MATH 221 - Deterministic Modls Oper Rsch
The linear programming problem. Simplex algorithm, dual problem, sensitivity analysis, goal programming. Dynamic programming and network problems. Prerequisites: 124; 121 desirable. Cross-listing: CSYS 221.
Credits: 3.
MATH 222 - Stochastic Models in Oper Rsch
Development and solution of some typical stochastic models. Markov chains, queueing problems, inventory models, and dynamic programming under uncertainty. Prerequisite: 207 or Statistics 151, or instructor's permission.
Credits: 3.
MATH 224 - Algorithm Design & Analysis
(Cross listed with CS 224.) Comprehensive analysis of common algorithmic paradigms including greedy algorithms, divide an conquer, dynamic programming, graph algorithms, and approximation algorithms. Complexity hierarchies. Prerequisites: CS 104 or 124, Math 173 recommended.
Credits: 3.
MATH 230 - Ordinary Differential Equation
Solutions of linear ordinary differential equations, the Laplace transformation, and series solutions of differential equations. Prerequisite: 121. Corequisite: 124 or instructor's permission. Credit not granted for more than one of the courses Math. 230 or 271.
Credits: 3.
MATH 236 - Calculus of Variations
Necessary conditions of Euler, Legendre, Weierstrass, and Jacobi for minimizing integrals. Sufficiency proofs. Variation and eigenvalue problems. Hamilton-Jacobi equations. Prerequisite: 230. Alternate years, 1997-98.
Credits: 3.
MATH 237 - Intro to Numerical Analysis
Error analysis, root-finding, interpolation, least squares, quadrature, linear equations, numerical solution of ordinary differential equations. Prerequisites: 121; 124 or 271; knowledge of computer programming.
Credits: 3.
MATH 238 - Applied Computational Methods
Direct and iterative methods for solving linear systems; numerical solution of ordinary and partial differential equations. Focus will be on application of numerical methods. Prerequisite: MATH 121, either MATH 124 or 271.
Credits: 3.
MATH 240 - Fourier Series&Integral Trans
Fourier series, orthogonal functions, integral transforms and boundary value problems. Prerequisite: 230 or 271.
Credits: 3.
MATH 241 - Anyl in Several Real Vars I
Properties of the real numbers, metric spaces, infinite sequences and series, continuity. Prerequisites: 52, 121, 124 or instructor's permission.
Credits: 3.
MATH 242 - Anyl Several Real Variables II
Differentiation in Rn, Riemann-Stieltjes integral, uniform convergence of functions, Inverse and Implicit Function Theorems. Prerequisite: 241.
Credits: 3.
MATH 243 - Theory of Computation
Introduction to theoretical foundations of computer science. Models of computation. Church's thesis and noncomputable problems. Formal languages and automata. Syntax and semantics. Prerequisite: CS 104 or 124. (Cross listed with Computer Science 243.)
Credits: 3.
MATH 251 - Abstract Algebra I
Basic theory of groups, rings, fields, homomorphisms, and isomorphisms. Prerequisites: 52, 124 or instructor's permission.
Credits: 3.
MATH 252 - Abstract Algebra II
Modules, vector spaces, linear transformations, rational and Jordan canonical forms. Finite fields, field extensions, and Galois theory leading to the insolvability of quintic equations. Prerequisite: 251.
Credits: 3.
MATH 255 - Elementary Number Theory
Divisibility, prime numbers, Diophantine equations, congruence of numbers, and methods of solving congruences. Prerequisite: 52 or 54.
Credits: 3.
MATH 257 - Topics in Group Theory
Topics may include abstract group theory, representation theory, classical groups, Lie groups. Prerequisite: 251. Alternate years, 2000-01.
Credits: 3.
MATH 260 - Foundations of Geometry
Geometry as an axiomatic science; various non-Euclidean geometries; relationships existing between Euclidean plane geometry and other geometries; invariant properties. Prerequisite: 52 or 54.
Credits: 3.
MATH 264 - Vector Analysis
Gradient, curl and divergence, Green, Gauss, and Stokes Theorems, applications to physics, tensor analysis. Prerequisite: 121, 124 or 271.
Credits: 3.
MATH 266 - Chaos,Fractals&Dynamical Syst
Discrete and continuous dynamical systems, Julia sets, the Mandelbrot set, period doubling, renormalization, Henon map, phase plane analysis and Lorenz equations. Corequisite: 271 or 230 or instructor's permission. Cross-listing: CSYS 266.
Credits: 3.
MATH 268 - Mathematical Biology&Ecology
Mathematical modeling in the life sciences. Topics include population modeling, dynamics of infectious diseases, reaction kinetics, wave phenomena in biology, and biological pattern formation. Prerequisites: 124, 230; or instructor's permission. Cross-listing: CSYS 268.
Credits: 3.
MATH 271 - Adv Engineering Mathematics
Differential equations and linear algebra, including linear ordinary differential equations, Laplace transforms, matrix theory, and systems of differential equations. Examples from engineering and physical sciences. Pre/co-requisites: Math 121 or Math 123.
Credits: 3.
MATH 272 - Applied Analysis
Partial Differential Equations of Mathematical Physics, Calculus of Variations, Functions of a Complex Variable, Cauchy's Theorem, integral formula. Conformal mapping. Prerequisite: 230 or 271.
Credits: 3.
MATH 273 - Combinatorial Graph Theory
Paths and trees, connectivity, Eulerian and Hamiltonian cycles, matchings, edge and vertex colorings, planar graphs, Euler's formula and the Four Color Theorem, networks. Prerequisite: 52 or 54 or instructor's permission.
Credits: 3.
MATH 274 - Numerical Linear Algebra
Direct and iterative methods for solving linear equations, least square factorization methods, eigenvalue computations, ill-conditioning and stability. Prerequisite: 237.
Credits: 3.
MATH 275 - Advanced Engineer Analysis I
(Cross listed with Mechanical Engineering 304; Civil Engineering 304.) Prerequisites: 271 or 230; 275 for 276
Credits: 3.
MATH 276 - Adv Engineering Analysis II
(Cross listed with Mechanical Engineering 305; Civil Engineering 305.) Prerequisites: 271 or 230; 275 for 276.
Credits: 3.
MATH 278 - Intro Wavelets & Filter Banks
Continuous and discrete-time signal processing. Continuous wavelet transform. Series expansion of continuous and discrete-time signals. Perfect reconstruction, orthogonal and biorthogonal filter banks. Wavelets from filter. Pre/co-requisites: 171, or instructor permission. Cross-listing: EE 274.
Credits: 3.
MATH 283 - Junior-Senior Seminar
Students required to give presentations on selected topics. Prerequisite: Instructor's permission.
Credits: 1.
MATH 293 - Undergraduate Honors Thesis
Program of reading and research culminating in written thesis and oral presentation. Honors notation appears on transcript and Commencement Program. Contact department chairperson for procedures.
Credits: 3-4.
MATH 294 - Undergraduate Honors Thesis
Program of reading and research culminating in written thesis and oral presentation. Honors notation appears on transcript and Commencement Program. Contact department chairperson for procedures.
Credits: 3-4.
MATH 295 - Special Topics
For advanced students in the indicated fields. Lectures, reports, and directed readings on advanced topics. Prerequisite: Instructor's permission. Credit as arranged. Offered as occasion warrants.
Credits: 1-9.
MATH 300 - Principles of Complex Systems
Introduction to fundamental concepts of complex systems. Topics include: emergence, scaling phenomena, and mechanisms, multi-scale systems, failure, robustness, collective social phenomena, complex networks. Students from all disciplines welcomed. Pre/co-requisites: Calculus and statistics required. Linear Algebra, Differential Equations, and Computer programming recommended but not required. Cross-listing: CSYS 300.
Credits: 3.
MATH 303 - Complex Networks
Detailed exploration of distribution, transportation, small-world, scale-free, social, biological, organizational networks; generative mechanisms; measurement and statistics of network properties; network dynamics; contagion processes. Students from all disciplines welcomed. Pre/co-requisites: Math 301/CSYS 301, Calculus, and Statistics required. Cross-listing: CSYS 303.
Credits: 3.
MATH 330 - Adv Ordinary Diff Equations
Linear and nonlinear systems, approximate solutions, existence, uniqueness, dependence on initial conditions, stability, asymptotic behavior, singularities, self-adjoint problems. Prerequisite: 230.
Credits: 3.
MATH 331 - Theory of Func of Complex Var
Differentiation, integration, Cauchy-Riemann equations, infinite series, properties of analytic continuation, Laurent series, calculus of residues, contour integration, meromorphic functions, conformal mappings, Riemann surfaces. Prerequisite: 242.
Credits: 4.
MATH 332 - Approximation Theory
Interpolation and approximation by interpolation, uniform approximation in normed linear spaces, spline functions, orthogonal polynomials. Least square, and Chebychev approximations, rational functions. Prerequisites: 124, 237.
Credits: 3.
MATH 333 - Thry Functions Real Variables
The theory of Lebesgue integration, Lebesgue measure, sequences of functions, absolute continuity, properties of LP-spaces. Prerequisite: 242.
Credits: 4.
MATH 335 - Advanced Real Analysis
L2-spaces, LP-spaces; Hilbert, Banach spaces; linear functionals, linear operators; completely continuous operators (including symmetric); Fredholm alternative; Hilbert-Schmidt theory; unitary operators; Bochner's Theorem; Fourier-Plancherel, Watson transforms. Prerequisites: 333; 335 for 336.
Credits: 3.
MATH 336 - Advanced Real Analysis
L2-spaces, LP-spaces; Hilbert, Banach spaces; linear functionals, linear operators; completely continuous operators (including symmetric); Fredholm alternative; Hilbert-Schmidt theory; unitary operators; Bochner's Theorem; Fourier-Plancherel, Watson transforms. Prerequisites: 333; 335 for 336.
Credits: 3.
MATH 337 - Numerical Diff Equations
Numerical solution and analysis of differential equations: initial-value and boundary-value problems; finite difference and finite element methods. Prerequisites: MATH 237, either MATH 230 or 271 recommended.
Credits: 3.
MATH 339 - Partial Differential Equations
Classification of equations, linear equations, first order equations, second order elliptic, parabolic, and hyperbolic equations, uniqueness and existence of solutions. Prerequisites: 230, 242.
Credits: 3.
MATH 351 - Topics in Algebra
Topics will vary each semester and may include algebraic number theory, algebraic geometry, and the arithmetic of elliptic curves. Repeatable for credit with permission. Prerequisite: 252.
Credits: 3.
MATH 353 - Point-Set Topology
Topological spaces, closed and open sets, closure operators, separation axioms, continuity, connectedness, compactness, metrization, uniform spaces. Prerequisite: 241.
Credits: 3.
MATH 354 - Algebraic Topology
Homotopy, Seifert-van Kampen Theorem; simplicial, singular, and Cech homology. Prerequisite: 353.
Credits: 3.
MATH 373 - Topics in Combinatorics
Topics will vary each semester and may include combinatorial designs, coding theory, topological graph theory, cryptography. Prerequisites: 251 or 273 or permission.
Credits: 3.
MATH 382 - Seminar
Topical discussions with assigned reading. Required of M.S. degree candidates.
Credits: 1.
MATH 391 - Master's Thesis Research
Credits: 1-18.
MATH 395 - Special Topics
Subject will vary from year to year. May be repeated for credit. Prerequisite: Permission.
Credits: 1-6.
MATH 491 - Doctoral Dissertation Research
Credits: 1-18.
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