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MATH 001
**Developmental Mathematics** (6) Arithmetic operations, ratios, proportions, percents; measurement; polynomial and rational expressions; exponents, radicals; equations, inequalities, systems of equations; graphing; applications. Students who have passed MATH 003 may not schedule this course for credit. This course may not be used to satisfy the basic minimum requirements for graduation in any baccalaureate degree program.

Effective: Spring 1994

MATH 002
**Elementary Geometry With Problem Solving** (4) Geometric congruence, similarity, area, surface area, volume, introductory trigonometry; emphasis on logical reasoning skills and the solution of applied problems. This course may not be used to satisfy the basic minimum requirements for graduation in any baccalaureate degree program.

Effective: Summer 2013

Prerequisite:
MATH 001 2 units of high school algebra or satisfactory performance on the mathematics placement examination

MATH 003
**Basic Skills** (3) Natural numbers; integers; rational numbers; decimals; ratio, proportion; percent; graphs; applications. Students who have passed MATH 001 may not schedule this course for credit. This course may not be used to satisfy the basic minimum requirements for graduation in any baccalaureate degree program.

Effective: Spring 1992

MATH 004, 021 GQ, AND 022 GQ form a three-semester sequence in intermediate algebra, college algebra, and analytic geometry. MATH 026 GQ is a one-semester course in plane trigonometry. Students are placed in the appropriate course depending on the results of the mathematics placement examination.

MATH 004
**Intermediate Algebra** (3) Algebraic expressions; linear, absolute value equations and inequalities; lines; systems of linear equations; integral exponents; polynomials; factoring. This course may not be used to satisfy the basic minimum requirements for graduation in any baccalaureate degree program.

Effective: Summer 2013

Prerequisite:
basic arithmetic skills or satisfactory performance on the mathematics placement examination

MATH 010
**Preparation Skills for Success in Mathematics ** (1 per semeseter/maximum of 4) A foundation course that emphasizes study skills and reviews basic mathematical principles.

Effective: Spring 2015

Concurrent:
math 003-201

MATH 017
(GQ)
**Finite Mathematics ** (3) Introduction to logic, sets, probability.

Effective: Summer 1988

Prerequisite:
2 units of high school mathematics

MATH 018
(GQ)
**Elementary Linear Algebra ** (3) Linear functions; systems of equations; matrices; linear programming.

Effective: Fall 1999

Prerequisite:
2 units of high school mathematics

MATH 021
(GQ)
**College Algebra I ** (3) Quadratic equations; equations in quadratic form; word problems; graphing; algebraic fractions; negative and rational exponents; radicals.

Effective: Summer 2013

Prerequisite:
MATH 004 or satisfactory performance on the mathematics placement examination

MATH 022
(GQ)
**College Algebra II and Analytic Geometry ** (3) Relations, functions, graphs; polynomial, rational functions, graphs; word problems; nonlinear inequalities; inverse functions; exponential, logarithmic functions; conic sections; simultaneous equations.

Effective: Summer 2013

Prerequisite:
MATH 021 or satisfactory performance on the mathematics placement examination

MATH 026
(GQ)
**Plane Trigonometry ** (3) Trigonometric functions; solutions of triangles; trigonometric equations; identities.

Effective: Summer 2013

Prerequisite:
MATH 021 or satisfactory performance on the mathematics placement examination; l unit of geometry

MATH 030
(GQ)
**Problem Solving ** (3) Concepts in problem solving; reducing new problems to old ones; techniques for attacking problems; building mathematical models.

Effective: Spring 1994

MATH 033
(GQ)
**Mathematics for Sustainability ** (3) Mathematical analysis of sustainability; measurement, rates of change, risk and probability, networks; examples.

Effective: Spring 2014

Prerequisite:
one unit of algebra orMATH 004

MATH 034
(GQ)
**The Mathematics of Money ** (3) Simple interest, simple discount, compound interest, annuities, investments, retirement plans, taxes, credit cards, and mortgages.

Effective: Summer 2009

Prerequisite:
one unit of algebra orMATH 004

MATH 035
(GQ)
**General View of Mathematics ** (3) Survey of mathematical thought in logic, geometry, combinatorics, and chance.

Effective: Summer 1992

MATH 036
(GQ)
**Insights Into Mathematics ** (3) Examples of mathematical applications in many areas including voting theory, fair division, apportionment, and Euler and Hamilton circuits.

Effective: Fall 2008

Prerequisite:
one unit of algebra orMATH 004

MATH 040 GQ covers all the topics in MATH 004, 021 GQ, 022 GQ, and 026 GQ in one semester, MATH 041 GQ covers the same topics in trigonometry and analytic geometry as MATH 040 GQ. These courses are designed to prepare students for MATH 140 GQ. Students are placed in the appropriate course depending upon the results of the mathematics placement examinations.

MATH 040
(GQ)
**Algebra, Trigonometry, and Analytic Geometry ** (5) Concepts of algebra; equations; inequalities; functions; graphs; polynomial and rational functions; exponential and logarithmic functions; trigonometry; analytic geometry; complex numbers.

Effective: Summer 2013

Prerequisite:
satisfactory performance on the mathematics placement examination

MATH 041
(GQ)
**Trigonometry and Analytic Geometry ** (3-4) Straight lines; circles; functions and graphs; graphs of polynomial and rational functions; exponential and logarithmic functions; trigonometry; conic sections.

Effective: Summer 2013

Prerequisite:
MATH 021 or satisfactory performance on the mathematics placement examination

MATH 081
(GQ)
**Technical Mathematics I ** (3) Algebraic expressions, equations, systems of equations, trigonometric functions, graphs, solution of triangles, vectors.

Effective: Summer 2013

Prerequisite:
MATH 004 or satisfactory performance on the mathematics placement examination

MATH 082
(GQ)
**Technical Mathematics II ** (3) Exponents, radicals, complex numbers, theory of equations, inequalities, half angle and double angle formulas, inverse trigonometric functions, exponential, logarithm, conic sections.

Effective: Summer 1995

Prerequisite:
MATH 081

MATH 083
(GQ)
**Technical Calculus ** (4) Limits, derivatives of algebraic functions, implicit differentiation, related rates, applied extrema problems, curve sketching, integration, numerical integration, applications of integration, integration techniques, differential equations.

Effective: Summer 1995

Prerequisite:
MATH 082

MATH 097
**Special Topics ** (1-9) Formal courses given infrequently to explore, in depth, a comparatively narrow subject which may be topical or of special interest.

Effective: Fall 1992

MATH 110 GQ and MATH 140 GQ, 141 GQ are two sequences that discuss differential and intergral calculus. They differ in the areas where calculus is applied. The MATH 110 GQ, 111 GQ sequence includes applications from business: the engineering sciences. A student who wants to change from one sequence to another should consult with the chair of the mathematics department.

MATH 110
(GQ)
**Techniques of Calculus I ** (4) Functions, graphs, derivatives, integrals, techniques of differentiation and integration, exponentials, improper integrals, applications. Students may take only one course for credit from MATH 110, 140, 140A, and 140B.

Effective: Summer 2013

Prerequisite:
MATH 022 or satisfactory performance on the mathematics placement examination

MATH 111
(GQ)
**Techniques of Calculus II ** (2) Analytic geometry, partial differentiation, maxima and minima, differential equations.

Effective: Summer 1988

Prerequisite:
MATH 110

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.

Effective: Summer 2013

Prerequisite:
MATH 022, MATH 026 ; orMATH 040 orMATH 041 or satisfactory performance on the mathematics placement examination

MATH 140A
(GQ)
**Calculus, Analytic Geometry, Algebra, and Trigonometry ** (6) Review of algebra and trigonometry; analytic geometry; functions; limits; derivatives, differentials, applications; integrals, applications. Students may take only one course for credit from MATH 110, 140, 140A, and 140B.

Effective: Summer 2013

Prerequisite:
satisfactory performance on the mathematics placement examination

MATH 140B
(GQ)
**Calculus and Biology I ** (4) Functions, limits, analytic geometry; derivatives, differentials, applications from biology; integrals, applications from biology. Students may take only one course for credit from MATH 110, 140, 140A, and 140B.

Effective: Summer 2013

Prerequisite:
MATH 022, MATH 026 ; orMATH 040 orMATH 041 or satisfactory performance on mathematics placement examination

MATH 140E
(GQ)
**Calculus with Engineering Applications I ** (4) Functions; limits; analytic geometry; derivatives; differentials, applications; integrals, applications.

Effective: Summer 2013

Prerequisite:
MATH 022, MATH 026 ; orMATH 040 orMATH 041 or satisfactory performance in the mathematics placement examination

MATH 140G
(GQ)
**Calculus with Earth and Mineral Sciences Applications I ** (4) Functions, limits, analytic geometry; derivatives, differentials, applications from the earth and mineral sciences; integrals, applications from the earth and mineral sciences. Students may only take one course for credit from MATH 110, 140, 140A, 140B, 140E, and 140G.

Effective: Summer 2013

Prerequisite:
MATH 022, MATH 026 ; orMATH 040 orMATH 041 or satisfactory performance on the mathematics placement examination

MATH 140H
(GQ)
**Honors Calculus with Analytic Geometry I ** (4) Honors course in 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.

Effective: Summer 2013

Prerequisite:
MATH 022, MATH 026 ; orMATH 040 orMATH 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.

Effective: Spring 1996

Prerequisite:
MATH 140, MATH 140A, MATH 140B orMATH 140H

MATH 141B
(GQ)
**Calculus and Biology II ** (4) Derivatives, integrals, applications from biology; sequences and series; analytic geometry; polar coordinates. Students may take only one course for credit from MATH 141 and 141B.

Effective: Spring 1996

Prerequisite:
MATH 140B

MATH 141E
(GQ)
**Calculus with Engineering Applications II ** (4) Integration, applications; sequences and series; parametric equations, application.

Effective: Fall 2001

Prerequisite:
MATH 140, MATH 140A, MATH 140B orMATH 140E

MATH 141G
(GQ)
**Calculus with Earth and Mineral Sciences Applications II ** (4) Derivatives, integrals, applications from the earth and mineral sciences; sequences and series; analytic geometry; polar coordinates. Students may take only one course for credit from MATH 141, 141B, 141E, and 141G.

Effective: Summer 2005

Prerequisite:
MATH 140, MATH 140A, MATH 140B, MATH 140E orMATH 140G

MATH 141H
(GQ)
**Honors Calculus with Analytic Geometry II ** (4) Honors course in derivatives, integrals, applications; sequences and series; analytic geometry; polar coordinates. Students may take only one course for credit from MATH 141, 141B, and 141H.

Effective: Summer 2006

Prerequisite:
MATH 140, MATH 140A, MATH 140B orMATH 140H

MATH 197
**Special Topics ** (1-9) Formal courses given infrequently to explore, in depth, a comparatively narrow subject which may be topical or of special interest.

Effective: Fall 1992

MATH 199
(IL)
**Foreign Studies ** (1-12) Courses offered in foreign countries by individual or group instruction.

Effective: Summer 2005

MATH 200
(GQ)
**Problem Solving in Mathematics ** (3) Fundamental concepts of arithmetic and geometry, including problem solving, number systems, and elementary number theory. For elementary and special education teacher certification candidates only. A student who has passed EDMTH 444 may not take MATH 200 for credit.

Effective: Summer 2009

MATH 201
(GQ)
**Problem Solving in Mathematics II ** (3) A continuation of MATH 200, this course studies the foundations of elementary school mathematics with an emphasis on problem solving.

Effective: Spring 2012

Prerequisite:
completion of MATH 200 is suggested

MATH 210
(GQ)
**Calculus with Engineering Technology Applications ** (3) Topics in calculus with an emphasis on applications in engineering technology.

Effective: Spring 2013

Prerequisite:
trigonometry and an introductory course in calculus

MATH 211
(GQ)
**Intermediate Calculus and Differential Equations with Applications ** (3) Topics in ordinary differential equations, linear algebra, complex numbers, Eigenvalue solutions and Laplace transform methods.

Effective: Spring 2013

Prerequisite:
MATH 210

MATH 220
(GQ)
**Matrices ** (2-3) Systems of linear equations; matrix algebra; eigenvalues and eigenvectors; linear systems of differential equations.

Effective: Spring 2009

Prerequisite:
MATH 110, MATH 140 orMATH 140H

MATH 220H
(GQ)
**Honors Matrices ** (2-3) Honors course in systems of linear equations; matrix algebra; eigenvalues and eigenvectors; linear systems of differential equations.

Effective: Spring 2009

Prerequisite:
MATH 110, MATH 140 orMATH 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.

Effective: Spring 1996

Prerequisite:
MATH 141 orMATH 141H

MATH 230H
**Honors Calculus and Vector Analysis ** (4) Honors course in 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.

Effective: Spring 2006

Prerequisite:
MATH 141 orMATH 141H

MATH 231
**Calculus of Several Variables ** (2) Analytic geometry in space; partial differentiation and applications. Students who have passed MATH 230 or MATH 230H may not schedule this course.

Effective: Spring 1996

Prerequisite:
MATH 141 orMATH 141H

MATH 231H
**Honors Calculus of Several Variables ** (2) Honors course in analytic geometry in space; partial differentiation and applications. Students who have passed MATH 230 or MATH 230H may not schedule this course.

Effective: Summer 2006

Prerequisite:
MATH 141 orMATH 141H

MATH 232
**Integral Vector Calculus ** (2) Multidimensional analytic geometry, double and triple integrals; potential fields; flux; Green's, divergence and Stokes' theorems. Students who have passed MATH 230 may not schedule this course for credit.

Effective: Spring 1996

Prerequisite:
MATH 231

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.

Effective: Fall 1988

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.

Effective: Fall 1988

Prerequisite:
MATH 141 orMATH 141H

MATH 251H
**Honors Ordinary and Partial Differential Equations ** (4) Honors course in first- and second-order equations; special functions; Laplace transform solutions; higher order equations; Fourier series; partial differential equations.

Effective: Summer 2006

Prerequisite:
MATH 141 orMATH 141H

MATH 294
**Research Project ** (1-12) Supervised student activities on research projects identified on an individual or small-group basis.

Effective: Spring 1995

MATH 296
**Independent Studies ** (1-18) Creative projects, including nonthesis research, which are supervised on an individual basis and which fall outside the scope of formal courses.

Effective: Fall 1983

MATH 297
**Special Topics ** (1-9) Formal courses given infrequently to explore, in depth, a comparatively narrow subject which may be topical or of special interest.

Effective: Fall 1983

MATH 310
**Elementary Combinatorics ** (3) Fundamental techniques of enumeration and construction of combinatorial structures, permutations, recurrences, inclusion-exclusion, permanents, 0, 1- matrices, Latin squares, combinatorial designs.

Effective: Spring 1985

Prerequisite:
MATH 220

MATH 310A
**Concepts in Combinatorics - Recitation ** (1) Recitation for MATH 310H - Concepts in Combinatorics.

Effective: Spring 2013

Prerequisite:
MATH 220
Concurrent:
MATH 310H

MATH 310H
**Honors Concepts of Combinatorics ** (3) Honors version of elementary and enumerative combinatorics.

Effective: Spring 2012

Prerequisite:
MATH 220

MATH 311M
**Honors Concepts of Discrete Mathematics ** (3) Basic methods of mathematical thinking and fundamental mathematical structures, primarily in the context of numbers, groups, and symmetries.

Effective: Spring 2006

Prerequisite:
MATH 141

MATH 311W
**Concepts of Discrete Mathematics ** (3-4) Introduction to mathematical proofs; elementary number theory and group theory. Students who have passed CMPSC 360 may not schedule this course for credit.

Effective: Spring 2007

Prerequisite:
MATH 141

MATH 312
**Concepts of Real Analysis ** (3) An introduction to rigorous analytic proofs involving properties of real numbers, continuity, differentiation, integration, and infinite sequences and series.

Effective: Spring 1994

Prerequisite:
MATH 141

MATH 312A
**Honors Concepts of Real Analysis - Recitation ** (1) A recitation component to MATH 312H, practice in problem solving.

Effective: Fall 2012

Prerequisite:
MATH 140H, MATH 311M
Concurrent:
MATH 312H

MATH 312H
**Honors Concepts of Real Analysis ** (3) Basic methods of mathematical thinking and fundamental structures, primarily in the context of infinite sets, real numbers, and metric spaces.

Effective: Summer 2006

Prerequisite:
MATH 141

MATH 313A
**Concepts of Geometry - Recitation** (1) A recitation component to Math 313H, practice in problem solving.

Effective: Fall 2012

Prerequisite:
MATH 140H, MATH 311M
Concurrent:
MATH 313H

MATH 313H
**Concepts of Geometry ** (3) Development thorough understanding and technical mastery of foundations of modern geometry.

Effective: Summer 2011

Prerequisite:
MATH 140H, MATH 311M
Concurrent:
MATH 312H
MATH 312R
MATH 313R

MATH 314H
**PMASS Problem Solving Seminar ** (1) Group work on challenging problems, discussions and project presentations.

Effective: Summer 2011

Prerequisite:
MATH 140H, MATH 311M
Concurrent:
MATH 312H
MATH 312R
MATH 313R
MATH 313H
MATH 315H

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.

Effective: Spring 2007

Prerequisite:
MATH 141

MATH 315H
**PMASS Colloquium ** (1) Bi-weekly lecture series with multiple invite speakers.

Effective: Summer 2011

Prerequisite:
MATH 140H, MATH 311M
Concurrent:
MATH 312H
MATH 313R
MATH 313H
MATH 312R
MATH 314H

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.

Effective: Spring 1989

Prerequisite:
MATH 141

MATH 319
(STAT 319)
**Applied Statistics in Science ** (3) Statistical inference: principles and methods, estimation and testing hypotheses, regression and correlation analysis, analysis of variance, computer analysis. Students who have passed MATH(STAT) 415 may not schedule this course for credit.

Effective: Spring 1989

Prerequisite:
MATH 318 or knowledge of basic probability

MATH 397
**Special Topics ** (1-9) Formal courses given infrequently to explore, in depth, a comparatively narrow subject which may be topical or of special interest.

Effective: Fall 1992

MATH 399
(IL)
**Foreign Studies ** (1-12) Courses offered in foreign countries by individual or group instruction.

Effective: Summer 2005

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.

Effective: Fall 1983

Prerequisite:
MATH 230 orMATH 231

MATH 403
**Classical Analysis I ** (3) Topology of Rn, compactness, continuity of functions, uniform convergence, Arzela-Ascoli theorem in the plane, Stone-Wierstrass theorem.

Effective: Spring 1996

Prerequisite:
MATH 312

MATH 403H
**Honors Classical Analysis I ** (3) Development of a thorough understanding and technical mastery of foundations of classical analysis in the framework of metric spaces.

Effective: Spring 2010

Prerequisite:
MATH 311M, MATH 312H

MATH 404
**Classical Analysis II ** (3) Differentiation of functions from Rn to Rm, implicit function theorem, Riemann integration, Fubini's theorem, Fourier analysis.

Effective: Fall 1985

Prerequisite:
MATH 403

MATH 405
**Advanced Calculus for Engineers and Scientists I ** (3) Vector calculus, linear algebra, ordinary and partial differential equatinos. Students who have passed MATH 411 or 412 may not take this course for credit.

Effective: Spring 1994

Prerequisite:
MATH 231;MATH 250 orMATH 251

MATH 406
**Advanced Calculus for Engineers and Scientists II ** (3) Complex analytic functions, sequences and series, residues, Fourier and Laplace transforms. Students who have passed MATH 421 may not take this course for credit.

Effective: Spring 1994

Prerequisite:
MATH 405

MATH 408
**Advanced Calculus ** (3) Differential and integral calculus of functions of several variables, line and surface integrals, infinite series, series of functions, power series.

Effective: Spring 2007

Prerequisite:
MATH 141

MATH 410
**Complex Analysis for Mathematics and Engineering ** (3) Complex analytic functions; Cauchy-Riemann equations; complex contour integrals; Cauchy's integral formula; Taylor and Laurent series; residue theory; applications in engineering.

Effective: Summer 2014

Prerequisite:
MATH 230 orMATH 232

MATH 411
**Ordinary Differential Equations ** (3) Linear ordinary differential equations; existence and uniqueness questions; series solutions; special functions; eigenvalue problems; Laplace transforms; additional topics and applications.

Effective: Fall 1983

Prerequisite:
MATH 230 orMATH 231;MATH 250 orMATH 251

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.

Effective: Spring 2009

Prerequisite:
MATH 230;MATH 250 orMATH 251

MATH 414
(STAT 414)
**Introduction to Probability Theory ** (3) Probability spaces, discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central limit theorems. Students may take only one course from MATH(STAT) 414 and 418 for credit.

Effective: Fall 2001

Prerequisite:
MATH 230 orMATH 231

MATH 415
(STAT 415)
**Introduction to Mathematical Statistics ** (3) A theoretical treatment of statistical inference, including sufficiency, estimation, testing, regression, analysis of variance, and chi-square tests.

Effective: Fall 1989

Prerequisite:
MATH 414

MATH 416
(STAT 416)
**Stochastic Modeling ** (3) Review of distribution models, probability generating functions, transforms, convolutions, Markov chains, equilibrium distributions, Poisson process, birth and death processes, estimation.

Effective: Spring 1984

Prerequisite:
MATH 318 orMATH 414;MATH 230

MATH 417
**Qualitative Theory of Differential Equations ** (3) Linear differential equations, stability of stationary solutions, ordinary bifurcation, exchange of stability, Hopf bifurcation, stability of periodic solutions, applications.

Effective: Spring 2009

Prerequisite:
MATH 220;MATH 250 orMATH 251

MATH 418
(STAT 418)
**Introduction to Probability and Stochastic Processes for Engineering ** (3) Introduction to probability axioms, combinatorics, random variables, limit laws, and stochastic processes. Students may take only one course from MATH(STAT) 414 and 418 for credit.

Effective: Fall 2011

Prerequisite:
MATH 230 orMATH 231

MATH 419
(PHYS 419)
**Theoretical Mechanics ** (3) Principles of Newtonian, Lagrangian, and Hamiltonian mechanics of particles with applications to vibrations, rotations, orbital motion, and collisions.

Effective: Spring 2007

Prerequisite:
MATH 230 orMATH 231;MATH 250 orMATH 251;PHYS 212, PHYS 213 andPHYS 214

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.

Effective: Summer 1993

Prerequisite:
MATH 230, MATH 232 orMATH 405;MATH 401 orMATH 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 problem, inventory problems.

Effective: Spring 2012

Prerequisite:
MATH 141 andMATH 220

MATH 426
**Introduction to Modern Geometry ** (3) Plane and space curves; space surfaces; curvature; intrinsic geometry of surfaces; Gauss-Bonnet theorem; covariant differentiation; tensor analysis.

Effective: Spring 1994

Prerequisite:
MATH 401 orMATH 403

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.

Effective: Spring 1994

Prerequisite:
MATH 230 orMATH 231

MATH 428
**Geometry for Teachers ** (1) Research in mathematics education using ideas from Euclidean and non-Euclidean geometry. Students who have passed MATH 471 may not schedule MATH 427.

Effective: Spring 2007

Prerequisite:
MATH 311W . Prerequisite or concurrent:MATH 427

MATH 429
**Introduction to Topology ** (3) Metric spaces, topological spaces, separation axioms, product spaces, identificaiton spaces, compactness, connectedness, fundamental group.

Effective: Spring 1994

Prerequisite:
MATH 311W

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.

Effective: Spring 2010

Prerequisite:
MATH 220

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

Effective: Spring 2007

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.

Effective: Spring 2010

Prerequisite:
MATH 311W orMATH 315

MATH 436
**Linear Algebra ** (3) Vector spaces and linear transformations, canonical forms of matrices, elementary divisors, invariant factors; applications. Students who have passed MATH 436 may not schedule MATH 441.

Effective: Fall 1983

Prerequisite:
MATH 311W

MATH 437
**Algebraic Geometry ** (3) Study of curves in the plane defined by polynomial equations p(x,y)= 0. Projective equivalence, singular points, classification of cubics.

Effective: Spring 2009

Prerequisite:
MATH 230 orMATH 231;MATH 311W

MATH 441
**Matrix Algebra ** (3) Determinants, matrices, linear equations, characteristic roots, quadratic forms, vector spaces. Students who have passed Math 436 may not schedule this course.

Effective: Fall 1985

Prerequisite:
MATH 220

MATH 444
**Mathematical Statistics and Applications I ** (3) Distributions of random variables, special distributions, limiting distributions, sampling, statistical inference, point and interval estimation, orthogonal polynomials, and least squares.

Effective: Spring 2007

Prerequisite:
MATH 141

MATH 445
**Mathematical Statistics and Applications II ** (3) Further topics in point estimation, statistical hypotheses, other statistical tests, nonparametric methods.

Effective: Spring 2007

Prerequisite:
MATH 444

MATH 446
**Introduction to Applied Statistics I ** (3) Descriptive statistics, probability theory, discrete and continuous probability distributions, statistical inferences for means and proportions.

Effective: Spring 2007

Prerequisite:
MATH 022 orMATH 040

MATH 447
**Introduction to Applied Statistics II ** (3) Regression, correlation, analysis of variance, contingency tables, nonparametric methods, time series, index numbers.

Effective: Spring 2007

MATH 449
**Applied Ordinary Differential Equations ** (3) Differential and difference equations and their application to biology, chemistry, and physics; techniques in dynamical systems theory.

Effective: Spring 2007

Prerequisite:
MATH 250 orMATH 251

MATH 450
**Mathematical Modeling ** (3) Constructing mathematical models of physical phenomena; topics include pendulum motion, polymer fluids, chemical reactions, waves, flight, and chaos.

Effective: Spring 2007

Prerequisite:
MATH 315 andMATH 430 orMATH 405 orMATH 412

MATH 451
(CMPSC 451)
**Numerical Computations ** (3) Algorithms for interpolation, approximation, integration, nonlinear equations, linear systems, fast FOURIER transform, and differential equations emphasizing computational properties and implementation. Students may take only one course for credit from MATH 451 and 455.

Effective: Spring 2008

Prerequisite:
3 credits of programming;MATH 230 orMATH 231

MATH 455
(CMPSC 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.

Effective: Spring 2008

Prerequisite:
CMPSC 201, CMPSC 202 orCMPSC 121;MATH 220;MATH 230 orMATH 231

MATH 456
(CMPSC 456)
**Introduction to Numerical Analysis II ** (3) Polynomial and piecewise polynomial approximation, matrix least squares problems, numerical solution of eigenvalue problems, numerical solution of ordinary differential equations.

Effective: Spring 2008

Prerequisite:
MATH 455

MATH 457
**Introduction to Mathematical Logic ** (3) Propositional logic, first-order predicate logic, axioms and rules of inference, structures, models, definability, completeness, compactness.

Effective: Summer 2011

Prerequisite:
MATH 311W ; 3 additional credits in philosophy

MATH 461
(PHYS 461)
**Theoretical Mechanics ** (3) Continuation of Math.(Phys.) 419. Theoretical treatment of dynamics of a rigid body, theory of elasticity, aggregates of particles, wave motion, mechanics of fluids.

Effective: Fall 1986

Prerequisite:
MATH 419

MATH 465
**Number Theory ** (3) Elements, divisibility of numbers, congruences, residues, and forms.

Effective: Spring 2009

Prerequisite:
MATH 311W

MATH 467
(CMPSC 467)
**Factorization and Primality Testing ** (3) Prime sieves, factoring, computer numeration systems, congruences, multiplicative functions, primitive roots, cryptography, quadratic residues. Students who have passed MATH 465 may not schedule this course.

Effective: Spring 1995

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.

Effective: Fall 1983

Prerequisite:
MATH 311W ; advanced calculus

MATH 470
**Algebra for Teachers ** (3) An introduction to algebraic structures and to the axiomatic approach, including the elements of linear algebra. Designed for teachers and prospective teachers. Students who have passed Math 435 may not schedule this course.

Effective: Fall 1988

Prerequisite:
MATH 311W

MATH 471
**Geometry for Teachers ** (4) Problem solving oriented introduction to Euclidean and non-Euclidean geometries; construction problems and geometrical transformations via "Geometer's Sketchpad" software. Intended primarily for those seeking teacher certification in secondary mathematics. Students who have passed MATH 427 may not schedule this course.

Effective: Spring 1996

Prerequisite:
MATH 311W

MATH 475W
(US;IL)
**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.

Effective: Spring 2012

Prerequisite:
MATH 315 orMATH 311W

MATH 479
(PHYS 479)
**Special and General Relativity ** (3) Mathematical description, physical concepts, and experimental tests of special and general relativity.

Effective: Spring 2007

Prerequisite:
PHYS 237, PHYS 400, PHYS 419;MATH 250 orMATH 251;MATH 230 orMATH 231

MATH 482
**Mathematical Methods of Operations Research ** (3) Survey of linear and nonlinear programming; mathematics of optimization; queues; simulation.

Effective: Spring 2007

Prerequisite:
MATH 220, MATH 230, STAT 301

MATH 484
**Linear Programs and Related Problems ** (3) Introduction to theory and applications of linear programming; the simplex algorithm and newer methods of solution; duality theory.

Effective: Spring 1987

Prerequisite:
MATH 220;MATH 230 orMATH 231

MATH 485
**Graph Theory ** (3) Introduction to the theory and applications of graphs and directed graphs. Emphasis on the fundamental theorems and their proofs.

Effective: Spring 1987

Prerequisite:
MATH 311W

MATH 486
**Mathematical Theory of Games ** (3) Basic theorems, concepts, and methods in the mathematical study of games of strategy; determination of optimal play when possible.

Effective: Spring 2006

Prerequisite:
MATH 220

MATH 494
**Research Project ** (1-12) Supervised student activities on research projects identified on an individual or small-group basis.

Effective: Spring 1995

MATH 494H
**Research Project ** (1-12) Supervised student activities on research projects identified on an individual or small-group basis.

Effective: Fall 2007

MATH 495
**Internship ** (1-18) Supervised off-campus, nongroup instruction including field experiences, practica, or internships. Written and oral critique of activity required.

Effective: Spring 2007

Prerequisite:
prior approval of proposed assignment by instructor

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.

Effective: Fall 1983

MATH 496A
**Lattice Structures of Topologies ** (1-6) Study of lattice theory and point free topology will be the main focus of this course. Along with this, examples of lattices will be considered from ring theory and group theory. Grade for the course will be based on presentations by student and take-home exams.

Effective: Fall 2015 Ending: Fall 2015

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.

Effective: Fall 1983

MATH 497A
**Introduction to Applied Algebraic Geometry ** (4) Fundamentals of algebraic geometry. Polynomial rings, ideals, varieties. Affine and projective space, Segre varieites, secant varieties, and tensor rank. Group actions on varieties. Techniques for application including identifying algebraic varieties in nature, computational methods, and solving systems of polynomial equations. Applications to statistics, quantum information, and computational complexity.

Effective: Fall 2015 Ending: Fall 2015

Prerequisite:
acceptance into the MASS Program

MATH 497B
**Classical Mechanics and Calculus of Variations ** (4) Classical mechanics and calculus of variations lie at the foundation of the modern theory of dynamical systems. This is the field where geometry, differential equations and number theory interact with each other and with physics. I will describe examples of this interaction, along with the fundamental concepts and ideas of the subject, with numerous special examples and with many entertaining problems.

Effective: Fall 2015 Ending: Fall 2015

MATH 497C
**Lie Groups in Two, Three and Four Dimensions ** (4) Lie groups arise from the continous symmetries that are seen in the nature and mathematics. Sometimes the symmetries are easy to appreciate (such as the continuous rotational symmetries of circle, as opposed to the discrete, 3-fold rotational symmetries of an equilateral triangle) and sometimes they are not. This course will give an introduction to the theory of Lie groups, with an emphasis on examples in low dimensions, where many of the most interesting applications to mathematics and physics are to be found. Topics will include the basic properties of matrix Lie groups, Lie groups, Lie algebras and the exponential map; examples from real Euclidean space, complex Hermitian space, the quaternions and the octonions; the mechanics of rotating bodies; complexification; representations; applications to spin, the eightfold way, Lorentz transformations, and other things.

Effective: Fall 2015 Ending: Fall 2015

MATH 497D
**MASS Interdisciplinary Seminar ** (3) This seminar is designed to focus on selected interdisciplinary topics in Algebra, Analysis, and Geometry to coordinate core courses and to prepare students to MASS Colloquium.

Effective: Fall 2015 Ending: Fall 2015

MATH 497E
**MASS Colloquium ** (1) Cover selected topics in Mathematics with varies speakers.

Effective: Fall 2015 Ending: Fall 2015

MATH 497G
**MASS Research Option ** (4) Individual or small-group research projects supervised by a faculty member.

Effective: Fall 2015 Ending: Fall 2015

Prerequisite:
acceptance into the MASS Program

MATH 498
**Special Topics ** (1-9) Formal courses given infrequently to explore, in depth, a comparatively narrow subject which may be topical or of special interest.

Effective: Fall 1992

MATH 499
(IL)
**Foreign Studies ** (1-12) Courses offered in foreign countries by individual or group instruction.

Effective: Summer 2005

NOTE: Courses in computer science and statistics are listed separately.

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