Please refer to SIS or Lou’s list for details about current instructors and current enrollment numbers.

Studies finite probability theory including combinatorics, equiprobable models, conditional probability and Bayes' theorem, expectation and variance, and Markov chains.

The study of the mathematics needed to understand and answer a variety of questions that arise in everyday financial dealings. The emphasis is on applications, including simple and compound interest, valuation of bonds, amortization, sinking funds, and rates of return on investments. A solid understanding of algebra is assumed.

`MATH 1150`

Studies basic concepts, operations, and structures occurring in number systems, number theory, and algebra. Inquiry-based student investigations explore historical developments and conceptual transitions in the development of number and algebraic systems.

A first calculus course for business/biology/social-science students. Topics include college algebra/limits and continuity/differentiation and integration of algebraic and elementary transcendental functions/applications to related-rates & optimization problems as well as to curve sketching & exponential growth. At most one of MATH 1190, MATH 1210, and 1310 may be taken for credit. Prerequisite: No previous exposure to Calculus.

A first calculus course for business/biology/social-science students. Topics include limits and continuity/differentiation & integration of algebraic & elementary transcendental functions/applications to related-rates & optimization problems as well as to curve sketching & exponential growth. At most one of Math 1190, MATH 1210, and 1310 ma1y be taken for credit.

A second calculus course for business/biology/and social-science students. Topics include differential equations/infinite series/analysis of functions of several variables/analysis of probability density functions of continuous random variables. The course begins with a review of basic single-variable calculus. Prerequisite: MATH 1210 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit.

A first calculus course for natural-science majors/students planning further work in mathematics/students intending to pursue graduate work in applied social sciences. Introduces differential & integral calculus for single-variable functions, emphasizing techniques/applications & major theorems, like the fundamental theorem of calculus. Prerequisite: Background in algebra/trigonometry/exponentials/logarithms/analytic geometry.

A second calculus course for natural-science majors, students planning additional work in mathematics, and students intending to pursue graduate work in the applied social sciences. Topics include applications of the integral, techniques of integration, differential equations, infinite series, parametric equations, and polar coordinates. Prerequisite: MATH 1310 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit.

`MATH 1330`

`MATH 1340`

`MATH 1559`

A continuation of Calc I and II, this course is about functions of several variables. Topics include finding maxima and minima of functions of several variables/surfaces and curves in three-dimensional space/integration over these surfaces and curves. Additional topics: conservative vector fields/Stokes' and the divergence theorems/how these concepts relate to real world applications. Prerequisite: MATH 1320 or the equivalent.

`MATH 2315`

`MATH 2559`

`MATH 2700`

Covers basic concepts with an emphasis on writing mathematical proofs. Topics include logic, sets, functions and relations, equivalence relations and partitions, induction, and cardinality. Prerequisite: Math 1320; and students with a grade of B or better in Math 3310, 3354, or any 5000-level Math course are not eligible to enroll in Math 3000.

Introduces fundamental concepts/techniques of probability/the theory of randomness. Focuses on problem solving/understanding key theoretical ideas. Topics include sample spaces combinatorial analysis/discrete and continuous random variables/classical distributions/expectation/Chebyshev's inequality/independence/central limit theorem/conditional probability/generating functions. Prerequisite: MATH 1320. Recommended: knowledge of double integrals.

`MATH 3120`

Introduces the methods, theory, and applications of differential equations. Includes first-order, second and higher-order linear equations, series solutions, linear systems of first-order differential equations, and the associated matrix theory. May include numerical methods, non-linear systems, boundary value problems, and additional applications. Prerequisite: MATH 1320 or its equivalent.

A rigorous development of the properties of the real numbers and the ideas of calculus including theorems on limits/ continuity/differentiability/convergence of infinite series/the construction of the Riemann integral. The focus of students' work will be on getting experience in constructing proofs and developing examples. Prerequisite: MATH 1320.

This course is a continuation of MATH 2315. Covers topics from linear algebra/differential equations/real analysis. Success in this course and MATH 2315 (grades of B- or higher) exempts the student from the math major requirement of taking MATH 3351 and MATH 3250. Students are encouraged to take more advanced courses in these areas. Prerequisite: MATH 2315.

Covers functions of a complex variable that are complex differentiable and the unusual and useful properties of such functions. Some topics: Cauchy's integral formula/power series/the residue theorem/Rouché's theorem. Applications include doing real integrals using complex methods and applications to fluid flow in two dimensions. Prerequisite: MATH 2310.

Topics will include systems of linear equations, matrix operations and inverses, vector spaces and subspaces, determinants, eigenvalues and eigenvectors, matrix factorizations, inner products and orthogonality, and linear transformations. Emphasis will be on applications, with computer software integrated throughout the course. The target audience for MATH 3350 is non-math majors from disciplines that apply tools from linear algebra. Credit is not given for both MATH 3350 and 3351.

Includes matrices, elementary row operations, inverses, vector spaces and bases, inner products and Gram-Schmidt orthogonalization, orthogonal matrices, linear transformations and change of basis, eigenvalues, eigenvectors, and symmetric matrices. Credit is not given for both MATH 3350 and 3351. Prerequisite: MATH 1320.

Surveys major topics of modern algebra: groups, rings, and fields. Presents applications to areas such as geometry and number theory; explores rational, real, and complex number systems, and the algebra of polynomials. Prerequisite: MATH 1320 or equivalent.

`MATH 3559`

`MATH 4040`

`MATH 4080`

Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory. Prerequisite: MATH 3100 or APMA 3100; and a knowledge of matrix algebra

This class introduces students to the mathematics used in pricing derivative securities. Topics include a review of the relevant probability theory of conditional expectation and martingales/the elements of financial markets and derivatives/pricing contingent claims in the binomial & the finite market model/(time permitting) the Black-Scholes model. Prerequisites: MATH 3100 or APMA 3100. Students should have a knowledge of matrix algebra.

This course covers linear algebra/complex analysis/vector differential & integral calculus. Thus it is a compressed version of MATH 3351 & MATH 3340 and a review of some of the material in MATH 2310. Emphasis is on the physical interpretation. [This course does not count as a Mathematics elective for Mathematics majors if both MATH 3351 and MATH 3340 are to be counted.] Prerequisite: MATH 2310.

`MATH 4220`

A second course in ordinary differential equations, from the dynamical systems point of view. Topics include: existence and uniqueness theorems; linear systems; qualitative study of equilibria and attractors; bifurcation theory; introduction to chaotic systems. Further topics as chosen by the instructor. Applications drawn from physics, biology, and engineering. Prerequisites: MATH 3351 or APMA 3080 and MATH 3310 or MATH 4310.

`MATH 4300`

`MATH 4310`

Differential and integral calculus in Euclidean spaces. Implicit and inverse function theorems, differential forms and Stokes' theorem. Prerequisites: MATH 2310 or MATH 2315; MATH 3351 or MATH 4651 or APMA 3080; and MATH 3310 or MATH 4310

`MATH 4452`

`MATH 4559`

`MATH 4595`

Review of topics from Math 3351 including vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth with emphasis on theoretical aspects. The course continues with more advanced topics including Jordan and rational canonical forms of matrices and introduction to bilinear forms. Additional topics such as modules and tensor products may be included. Prerequisite: MATH 3351

Structural properties of basic algebraic systems such as groups, rings, and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization, and symmetric polynomials. Time permitting such topics as group representations or algebras over a field may be included. Prerequisites: MATH 3351 or 4651 and MATH 3354 or permission of the instructor.

`MATH 4653`

`MATH 4657`

`MATH 4658`

`MATH 4660`

Geometric study of curves/surfaces/their higher-dimensional analogues. Topics vary and may include curvature/vector fields and the Euler characteristic/the Frenet theory of curves in 3-space/geodesics/the Gauss-Bonnet theorem/and/or an introduction to Riemannian geometry on manifolds. Prerequisites: MATH 2310 and MATH 3351 or instructor permission.

Examines the knotting and linking of curves in space. Studies equivalence of knots via knot diagrams and Reidemeister moves in order to define certain invariants for distinguishing among knots. Also considers knots as boundaries of surfaces and via algebraic structures arising from knots. Prerequisite: MATH 3354 or instructor permission.

`MATH 4770`

`MATH 4830`

This course will introduce students to the techniques and methods of mathematical research. Students will independently work with mathematical literature on a topic assigned by the instructor and present their findings in various formats (presentation, paper etc.).

`MATH 4900`

`MATH 4901`

Reading and study programs in areas of interest to individual students. For third- and fourth-years interested in topics not covered in regular courses. Students must obtain a faculty advisor to approve and direct the program.

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