Mathematics

Math placement information is in the front of this catalog in the Undergraduate: Applying for Admission section. No student will be permitted to enroll in a course having prerequisites if a grade lower than a C (2.0) is received in the prerequisite course.

A per semester fee to support the Mathematics and Statistics Tutorial Lab will be assessed for one or more of the following courses: MATH F103, F107, F108, F161, F200, F201, F202, F262, F272, STAT F200X. A per semester fee to provide access to computer software and hardware will be assessed for one or more of MATH F310, F460; any STAT course except STAT F200X; and any CS course. Please see the class schedule for details.

MATH F103X Concepts and Contemporary Applications of Mathematics (m)

3 Credits

Applications of mathematics in modern society. Topics include voting systems, probability and statistics and applications of graph theory in management science; uses of probability and statistics in industry, government and science; and applications of geometry to engineering and astronomy. Problem solving emphasized. Also available via Independent Learning. Special fees apply. Prerequisites: DEVM F105 or DEVM F106 or placement; or high school geometry and algebra II. (3+0)

MATH F107X Functions for Calculus (m)

4 Credits

A study of algebraic, logarithmic and exponential functions; sequences and series; conic sections; and as time allows, systems of equations, matrices and counting methods. A brief review of basic algebra in the first week prepares students for the rigor expected. The primary purpose of this course, in conjunction with MATH F108, is to prepare students for calculus. Note: Credit may be earned for taking MATH F107X or MATH F161X, but not for both. Also available via Independent Learning. Special fees apply. Prerequisites: A grade of B (3.0) or better in DEVM F105 or DEVM F106; or two years of high school algebra and MATH F107X placement or higher. (4.5+0)

MATH F108 Trigonometry (m)

2 - 3 Credits

A study of the trigonometric functions. Also available via Independent Learning. Special fees apply. Prerequisites: MATH F107X or placement or concurrent enrollment in MATH F107X. (2 - 3+0)

MATH F161X Algebra for Business and Economics (m)

3 Credits

Functions of one and several variables with attention to linear, polynomial, rational, logarithmic and exponential relationships. Geometric progressions as applied to compound interest and present value. Linear systems of equations and inequalities. Note: Credit may be earned for taking MATH F107X or MATH F161X, but not for both. Special fees apply. Prerequisites: DEVM F105 or DEVM F106 or two years of high school algebra and MATH F161X placement or higher. (3+0)

MATH F200X Calculus I (m)

4 Credits

Limits, including those with indeterminate form, continuity, tangents, derivatives of polynomial, exponential, logarithmic and trigonometric functions, including product, quotient and chain rules, and the mean value theorem. Applications of derivatives including graphing functions and rates of change. Antiderivatives, Newton's method, definite and indefinite integrals, methods for substitution in integrals and the fundamental theorem of calculus. Applications of integrals include areas, distances, and volumes. Note: No credit may be earned for more than one of MATH F200X, MATH F262X or MATH F272X. Also available via Independent Learning. Special fees apply. Prerequisites: MATH F107X and MATH F108 or placement for MATH F200X. (4+1)

MATH F201X Calculus II (m)

4 Credits

Techniques and applications of integration. Integration of trigonometric functions, volumes including those using slicing, arc-length, integration by parts, trigonometric substitutions, partial fractions, hyperbolic functions, and improper integrals. Numeric integration including Simpson's rule, first order differential equations with applications to population dynamics and rates of decay, sequences, series, tests for convergence including comparison and alternating series tests, conditional convergence, power series, Taylor series, polar coordinates including tangent lines and areas, and conic sections. Also available via Independent Learning. Special fees apply. Prerequisites: MATH F200X or placement in MATH F201X. (4+0)

MATH F202X Calculus III (m)

4 Credits

Partial derivatives and multiple integration (double and triple). Vectors, parametric curves, motion in three dimensions, limits, continuity, chain rule, tangent planes, directional derivatives, optimization, Lagrange multipliers, integrals in polar coordinates, parametric surfaces, Jacobians, line integrals, Green's Theorem, surface integrals and Stokes' Theorem. Also available via Independent Learning. Special fees apply. Prerequisites: MATH F201X. (4+0)

MATH F205 Mathematics for Elementary School Teachers I (m)

3 Credits Offered Fall

Elementary set theory, numeration systems, and algorithms of arithmetic, divisors, multiples, integers and introduction to rational numbers. Emphasis on classroom methods. Also available via Independent Learning. Prerequisites: MATH F107X; MATH F161X or placement. Restricted to B.A.S. and B.A. Elementary Education degree students; others by permission of instructor. (3+1)

MATH F206 Mathematics for Elementary School Teachers II (m)

3 Credits Offered Spring

A continuation of MATH F205. Real number systems and subsystems, logic, informal geometry, metric system, probability and statistics. Emphasis on classroom methods. Also available via Independent Learning. Prerequisites: MATH F205. (3+1)

MATH F215 Introduction to Mathematical Proofs (m)

2 Credits Offered Spring

Emphasis on proof techniques with topics including logic, sets, relations, equivalence, induction, number theory, graph theory and congruence classes. In addition, a rigorous treatment of topics from calculus may be included. Prerequisites: MATH F200X, MATH F201X or concurrent with MATH F201X or permission of instructor. (2+0)

MATH F262X Calculus for Business and Economics (m)

4 Credits

Ordinary and partial derivatives. Maxima and minima problems, including the use of Lagrange multipliers. Introduction to the integral of a function of one variable. Applications include marginal cost, productivity, revenue, point elasticity of demand, competitive/complementary products, consumer's surplus, etc. Note: No credit may be earned for more than one of MATH F200X, MATH F262X or MATH F272X. Special fees apply. Prerequisites: MATH F161X or placement. (4+0)

MATH F272X Calculus for Life Sciences (m)

3 Credits Offered Fall

Differentiation and integration with applications to the life sciences. Note: No credit may be earned for more than one of MATH F200X, MATH F262X or MATH F272X. Special fees apply. Prerequisites: MATH F107X and MATH F108 or placement. (3+0)

MATH F302 Differential Equations

3 Credits

Nature and origin of differential equations, first order equations and solutions, linear differential equations with constant coefficients, systems of equations, power series solutions, operational methods, and applications. Prerequisites: MATH F202X. (3+0)

MATH F305 Geometry

3 Credits Offered Spring Even-numbered Years

Topics selected from such fields as Euclidean and non-Euclidean plane geometry, affine geometry, projective geometry, and topology. Prerequisites: MATH F202X and MATH F215 or permission of instructor. (3+0)

MATH F306 Introduction to the History and Philosophy of Mathematics

3 Credits Offered Spring Odd-numbered Years

Important periods of history as exemplified by such thinkers as Plato, B. Russell, D. Hilbert, L.E.J. Brouwer and K. Godel. For students of mathematics, science, history history and philosophy. Prerequisites: MATH F202X or permission of instructor. (3+0)

MATH F307 Discrete Mathematics

3 Credits

Logic, counting, sets and functions, recurrence relations, graphs and trees. Additional topics chosen from probability theory. Prerequisites: MATH F201X or permission of instructor. (Cross-listed with CS F307.) (3+0)

MATH F310 Numerical Analysis

3 Credits Offered Fall

Direct and iterative solutions of systems of equations, interpolation, numerical differentiation and integration, numerical solutions of ordinary differential equations, and error analysis. Special fees apply. Prerequisites: MATH F302 or MATH F314 or permission of instructor. Recommended: Knowledge of programming. (3+0)

MATH F314 Linear Algebra

3 Credits

Linear equations, finite dimensional vector spaces, matrices, determinants, linear transformations and characteristic values. Inner product spaces. Prerequisites: MATH F201X. (3+0)

MATH F371 Probability

3 Credits Offered Fall Even-numbered Years

Probability spaces, conditional probability, random variables, continuous and discrete distributions, expectation, moments, moment generating functions, and characteristic functions. Prerequisites: MATH F202X. (3+0)

MATH F401W Advanced Calculus

3 Credits Offered Fall

One and several dimensional calculus. Includes mappings from n-space and their continuity, differentiability and integrability properties as well as sequences and series. Prerequisites: ENGL F111X; ENGL F211X or ENGL F213X or permission of instructor; MATH F202X; MATH F215. (3+0)

MATH F402 Advanced Calculus

3 Credits Offered Spring

One and several dimensional calculus. Includes mappings from n-space and their continuity, differentiability and integrability properties as well as sequences and series. Prerequisites: MATH F401. (3+0)

MATH F404 Topology

3 Credits Offered Fall Even-numbered Years

Introduction to topology, set theory, open sets, compactness, connectedness, product spaces, metric spaces and continua. Prerequisites: MATH F202X; MATH F215. Recommended: MATH F314 and/or MATH F308. (3+0)

MATH F405W Abstract Algebra

3 Credits Offered Spring

Theory of groups, rings and fields. Prerequisites: ENGL F111X; ENGL F211X or ENGL F213X; MATH F215; or permission of instructor. Recommended: MATH F307 and/or MATH F314. (3+0)

MATH F408 Mathematical Statistics

3 Credits Offered Spring Odd-numbered Years

Distribution of random variables and functions of random variables, interval estimation, point estimation, sufficient statistics, order statistics, and test of hypotheses including various criteria for tests. Prerequisites: MATH F371; STAT F200X. (3+0)

MATH F412 Differential Geometry

3 Credits Offered Spring Odd-numbered Years

Introduction to the differential geometry of curves, surfaces, and Riemannian manifolds. Basic concepts covered include the Frenet-Serret apparatus, surfaces, first and second fundamental forms, geodesics, Gauss curvature and the Gauss-Bonnet Theorem. Time permitting, topics such as minimal surfaces, theory of hypersurfaces and/or tensor analysis may be included. Prerequisites: MATH F314 and MATH F401; or permission of instructor. (3+0)

MATH F421 Applied Analysis

4 Credits Offered Fall

Vector calculus, including gradient, divergence, and curl in orthogonal curvilinear coordinates, ordinary and partial differential equations and boundary value problems, and Fourier series and integrals. Prerequisites: MATH 302. (4+0)

MATH F422 Introduction to Complex Analysis

3 Credits Offered Spring

Complex functions including series, integrals, residues, conformal mapping and applications. May be taken independently of MATH F421. Prerequisites: MATH F302. (3+0)

MATH F460 Mathematical Modeling

3 Credits Offered Fall Odd-numbered Years

Introduction to mathematical modeling using differential or difference equations. Emphasis is on formulating models and interpreting qualitative behavior such models predict. Examples will be taken from a variety of fields, depending on the interest of the instructor. Students develop a modeling project. Special fees apply. Prerequisites: COMM F131X or COMM F141X; ENGL F111X; ENGL F211X or ENGL F213X; MATH F201X; or permission of instructor. Recommended: One or more of MATH F302; MATH F314; MATH F314; MATH F401; STAT F300; some programming experience. (3+0)

MATH F490O Senior Seminar

1 Credit Offered Spring

Advanced topics selected from areas outside the usual undergraduate offerings. A substantial level of mathematical maturity is assumed. Prerequisites: COMM F131X or COMM F141X, at least one of MATH F308 or MATH F401. (1+0)

MATH F600 Teaching Seminar

1 Credit

Fundamentals of teaching mathematics in a university setting. Topics may include any aspect of teaching: university regulations, class and lecture organization, testing, book selection, teaching evaluations, etc. Specific topics will vary on the basis of student and instructor interest. Individual classroom visits will also be used for class discussion. May be repeated for credit. Graded Pass/Fail. Prerequisites: Graduate standing. (1+0)

MATH F608 Partial Differential Equations

3 Credits Offered As Demand Warrants

First and second order differential equations, boundary value problems, and existence and uniqueness theorems. Green's functions, and principal equations of mathematical physics. Prerequisites: MATH F422 or permission of instructor. (3+0)

MATH F611 Mathematical Physics

3 Credits Offered Fall

Mathematical tools and theory for classical and modern physics. Core topics: Linear algebra including eigenvalues, eigenvectors and inner products in finite dimensional spaces. Infinite series. Hilbert spaces and generalized functions. Complex analysis, including Laurent series and contour methods. Applications to problems arising in physics. Selected additional topics, which may include operator and spectral theory, groups, tensor fields, hypercomplex numbers. Prerequisites: MATH F302; MATH F314; MATH F421; MATH F422; or permission of instructor. (Cross-listed with PHYS F611.) (3+0)

MATH F612 Mathematical Physics

3 Credits Offered Spring

Continuation of Mathematical Physics I; mathematical tools and theory for classical and modern physics. Core topics: classical solutions to the principal linear partial differential equations of electromagnetism, classical and quantum mechanics. Boundary value problems and Sturm-Liouville theory. Green's functions and eigenfunction expansions. Integral transforms. Orthogonal polynomials and special functions. Applications to problems arising in physics. Selected additional topics, which may include integral equations and Hilbert-Schmidt theory, perturbation methods, probability theory. Prerequisites: PHYS/MATH F611 or equivalent; or permission of instructor. (Cross-listed with PHYS F612.) (3+0)

MATH F615 Applied Numerical Analysis

3 Credits Offered Spring Odd-numbered Years

Review of numerical differentiation and integration, and the numerical solution of ordinary differential equations. Main topics to include the numerical solution of partial differential equations, curve fitting, splines, and the approximation of functions. Supplementary topics such as the numerical method of lines, the fast Fourier transform, and finite elements may be included as time permits and interest warrants. Prerequisites: CS F201, MATH F310, MATH F314, MATH F421, MATH F422 or permission of instructor. (3+0)

MATH F617 Functional Analysis

3 Credits Offered Spring Even-numbered Years

Study of Banach and Hilbert spaces, and continuous linear maps between them. Linear functionals and the Hahn-Banach theorem. Applications of the Baire Category theorem. Compact operators, self adjoint operators, and their spectral properties. Weak topology and its applications. Recommended: MATH F422; MATH F641 or equivalent. Prerequisites: MATH F314; MATH F401 or equivalent. (3+0)

MATH F630 Advanced Linear Algebra

3 Credits Offered As Demand Warrants

Vector spaces over arbitrary fields rational and Jordan canonical forms, invariant subspace decompositions and multilinear algebra. Prerequisites: MATH F405; MATH F314. (3+0)

MATH F631 Theory of Modern Algebra I

4 Credits Offered Fall Even-numbered Years

Rigorous development of groups, rings and fields. Introduction to category theory, module theory, homological algebra and Galois Theory. Prerequisites: MATH F405; graduate standing; or permission of instructor. (4+0)

MATH F632 Theory of Modern Algebra II

3 Credits Offered Fall Odd-numbered Years

Advanced topics taken from group theory, category theory, ring theory, homological algebra and field theory. Prerequisites: MATH F631. (3+0)

MATH F641 Real Analysis

4 Credits

General theory of Lebesgue measure and Lebesgue integration on the real line. Convergence properties of the integral. Introduction to the general theory of measures and integration. Differentiation, the product measures and an introduction to LP spaces. Prerequisites: MATH F401-F402 or permission of instructor. (4+0)

MATH F645 Complex Analysis

4 Credits Offered Spring Even-numbered Years

Analytic functions, power series, Cauchy integral theory, residue theorem. Basic topology of the complex plane and the structure theory of analytic functions. The Riemann mapping theorem. Infinite products. Prerequisites: Math F641 or permission of instructor. (4+0)

MATH F651 Topology

4 Credits Offered Spring Odd-numbered Years

Treatment of the fundamental topics of point-set topology. Separation axioms, product and quotient spaces, convergence via nets and filters, compactness and compactifications, paracompactness, metrization theorems, countability properties, and connectedness. Set theory as needed for examples and proof techniques. Prerequisites: MATH F401-F402 or MATH F404 or permission of instructor. (4+0)

MATH F655 Algebraic Topology

3 Credits

Fundamentals of algebraic topology with applications to topology and geometry. The fundamental group, covering spaces, axiomatic homology and singular homology. Prerequisites: MATH F405; MATH F401-F402; MATH F404; or permission of instructor. (3+0)

MATH F660 Advanced Mathematical Modeling

3 Credits Offered Spring Even-numbered Years

The mathematical formulation and analysis of problems arising in the physical, biological, or social sciences. The focus area of the course may vary, but emphasis will be given to modeling assumptions, derivation of model equations, methods of analysis, and interpretation of results for the particular applications. Examples include heat conduction problems, random walk processes, molecular evolution, perturbation theory. Students will develop a modeling project as part of the course requirements. Special fees apply. Prerequisites: Permission of instructor. (3+0)

MATH F661 Optimization

3 Credits Offered Fall Even-numbered Years

Linear and nonlinear programming, simplex method, duality and dual simplex method, post-optimal analysis, constrained and unconstrained nonlinear programming, Kuhn-Tucker conditions. Applications to management, physical and life sciences. Computational work with the computer. Prerequisites: Knowledge of calculus, linear algebra, and computer programming. (Cross-listed with CS F661.) (3+0)

MATH F663 Applied Combinatorics and Graph Theory

3 Credits Offered Spring Even-numbered Years

A study of combinatorial and graphical techniques for complexity analysis including generating functions, recurrence relations, theory of counting, planar directed and undirected graphs, and applications to NP complete problems. Prerequisites: MATH F307 and MATH F314. (3+0)