Three credits of a MTH elective is required. It can be MTH 215, MTH 244 or any 300 to 500 level mathematics course except MTH 362 or MTH 381. MTH 451 is recommended as a mathematics elective. Below is a list of possible courses.

MTH 215 Introduction to Linear Algebra (3)

Detailed study of finite dimensional vector spaces, linear transformations, matrices, determinants, and systems of linear equations. (Lec. 3) Pre: 131, 141, or equivalent.

MTH 244 Differential Equations (3)

Classification and solution of differential equations involving one independent variable. Applications to the physical sciences. Basic for further study in applied mathematics and for advanced work in physics and engineering. (Lec. 3) Pre: 243.

MTH 307 Introduction to Mathematical Rigor (3)

Introduction to the language of rigorous mathematics: logic, set theory, functions and relations, cardinality, induction, methods of proof. Emphasis on precise written and oral presentation of mathematical arguments. (Lec. 3) Pre: 142.

MTH 316 Algebra (3)

Theory and structure of groups. Topics from ring theory, principal ideal domains, unique factorization domains, polynomial rings, field extensions, and Galois theory. (Lec. 3) Pre: 215 and 307.

MTH 322 Concepts of Geometry (3)

Survey of geometrical systems including non-Euclidean, affine, and projective spaces and finite geometries. A modern view of Euclidean geometry using both synthetic and analytic methods. (Lec. 3) Pre: 215 or permission of instructor. Offered fall semesters.

MTH 382 Number Theory (3)

Some of the arithmetic properties of the integers including number theoretic functions, congruences, diophantine equations, quadratic residues, and classically important problems. (Lec. 3) Pre: 141 or permission of instructor. Offered spring semesters.

MTH 391 Special Problems (1-3)

Advanced work under the supervision of a faculty member and arranged to suit the individual requirements of the student. (Independent Study) Pre: permission of chairperson.

MTH 393 Undergraduate Seminar (1)

Preparation and presentation of selected topics in oral and written form. (Seminar) Pre: permission of chairperson.

MTH 418 Matrix Analysis (3)

Canonical forms, functions of matrices, characteristic roots, applications to problems in physics and engineering. (Lec. 3) Pre: 215 or 362 or permission of instructor. Offered fall semesters.

MTH 420 Re-examining Mathematical Foundations for Teachers (3)

Connects ideas covered in upper level math courses to topics taught in secondary school. Designed for teachers. (Lec. 3) Pre: 316 or permission.

MTH 425 Topology (3)

Abstract topological spaces and continuous functions. Generalizations of some classical theorems of analysis. (Lec. 3) Pre: 243 and 307, or permission of instructor or chairperson. Offered alternate fall semesters.

MTH 435 Introduction to Mathematical Analysis I (3)

Sets and functions, real topology, continuity and uniform continuity, derivatives, the Riemann integral, improper integrals. Detailed proofs emphasized. (Lec. 3) Pre: 243; 307 is strongly recommended. Offered fall semesters.

MTH 436 Introduction to Mathematical Analysis II (3)

Sequences and series of functions, implicit and inverse function theorems, topology of Euclidean space, transformation of multiple integrals. Detailed proofs emphasized. (Lec. 3) Pre: 435. Offered spring semesters

MTH 437, MTH 438 Advanced Calculus and Application I, II (3 each)

Sequences, limits, continuity, differentiability, Riemann integrals, functions of several variables, multiple integrals, space curves, line integrals, surface integrals, Green’s theorem, Stokes’ theorem, series, improper integrals, uniform convergence, Fourier series, Laplace transforms. Applications to physics and engineering emphasized. (Lec. 3) Pre: (for 437) 243 and credit or concurrent enrollment in 215 or 362. Pre: (for 438) 437.

MTH 441 Introduction to Partial Differential Equations (3)

One-dimensional wave equation. Linear second order partial differential equations in two variables. Separation of variables and Fourier series. Nonhomogeneous boundary value problems. Green’s functions. (Lec. 3) Pre: 244 or 442. Offered alternate fall semesters.

MTH 442 Introduction to Difference Equations (3)

Introduction to linear and nonlinear difference equations; basic theory, z-transforms, stability analysis, and applications. (Lec. 3) Pre: 243. Offered spring semesters.

MTH 447 (or CSC 447) Discrete Mathematical Structures (3)

Concepts and techniques in discrete mathematics. Finite and infinite sets, graphs, techniques of counting, Boolean algebra and applied logic, recursion equations. (Lec. 3) Pre: junior standing or better in physical or mathematical sciences, or in engineering, or permission of instructor.

MTH 451 Introduction to Probability and Statistics (3)

Theoretical basis and fundamental tools of probability and statistics. Probability spaces, properties of probability, distributions, expectations, some common distributions, and elementary limit theorems. (Lec. 3) Pre: 243 or equivalent.

MTH 452 Mathematical Statistics (3)

Continuation of 451 in the direction of statistics. Basic principles of statistical testing and estimation, linear regression and correlation. (Lec. 3) Pre: 451. Offered spring semesters.

MTH 455 (445) Introduction to Chaotic Dynamical Systems (3)

Introduction to nonlinear dynamical systems on the real line and/or the plane. (Lec. 3) Pre: 243 or permission of instructor. Offered alternate spring semesters.

MTH 456 Introduction to Random Processes (3)

Conditional probability and expectation. Mean and covariance functions. Calculus of random processes. Introduction to Gaussian processes, Poisson processes, stationary processes, and Markov chains with applications. (Lec. 3) Pre: 451 or equivalent.

MTH 462 Functions of a Complex Variable (3)

First course in the theory of functions of a single complex variable, including analytic functions, power series, residues and poles, complex integration, conformal mapping, and applications. (Lec. 3) Pre: 243 or equivalent. Offered alternate fall semesters.

MTH 471 Introduction to Numerical Analysis (3)

Computer arithmetic, interpolation, numerical approximation of derivatives, integral numerical ODE, and other topics. (Lec. 3). Pre: 243 or permission of instructor. Offered alternate fall semesters.

MTH 492 Special Problems (1-3)

Advanced work under the supervision of a faculty member arranged to suit the individual requirements of the student. (Independent Study) Pre: permission of chairperson.

MTH 513 Linear Algebra (3)

Linear spaces and transformations, linear functionals, adjoints, projections, diagonalization, Jordan form of matrices, inner products; positive, normal, self-adjoint, and unitary operators; spectral theorem, bilinear and quadratic forms. (Lec. 3) Offered spring semesters.

MTH 515, MTH 516 Algebra I, II (3 each)

Groups, rings, modules, commutative algebra. (Lec. 3) Pre: 316 for 515; 515 for 516. In alternate years.

MTH 525 Topology (3)

Topological spaces, separation properties, connectedness, compactness, uniformities. Function spaces, spaces of continuous functions, and complete spaces. (Lec. 3) Pre: 435. In alternate years.

MTH 535, MTH 536 Measure Theory and Integration (3 each)

Elements of topology and linear analysis. Lebesgue measure and integration in R, in Rn, and in abstract spaces. Convergence theorems. Bounded variation, absolute continuity, and differentiation. Lebesgue-Stieltjes integral. Fubini and Tonelli theorems. The classical Banach spaces. (Lec. 3) Pre: 435 for 535; 535 for 536.

MTH 542, MTH 543 Global Character of Difference Equations I, II (3 each)

Global character, periodic behavior, and asymptotic nature of solutions of difference equations and systems of difference equations with applications. Recent topics on rational equations and rational systems in higher dimensions. (Lec. 3) Pre: 435 and 436.

MTH 545, MTH 546 Ordinary Differential Equations I, II (3 each)

Existence and uniqueness theorems. Continuous dependence on parameters and initial conditions. Singularities of the first and second kinds, self-adjoint eigenvalue problems on a finite interval. Oscillation and comparison theorems. Introduction to delay and difference equations. Elements of stability theory of Lyapunov’s second method. (Lec. 3) Pre: 435 for 545; 545 for 546. In alternate years.

MTH 547 (or CSC 547) Combinatorics (3)

Enumeration: generation functions, recurrence relations, classical counting numbers, inclusion-exclusion, finite set systems and designs. Polya theory, coding theory, and Ramsey theory. Finite fields and algebraic methods. (Lec. 3) Pre: 316. Offered alternate fall semesters.

MTH 548 (or CSC 548) Graph Theory (3)

Basic concepts and techniques of graph theory as well as some of their applications. Topics include: connectivity, matchings, colorings, extremal problems, Ramsey theory, planar graphs, algebraic techniques.(Lec. 3) Pre: 316. Offered alternate fall semesters.

MTH 550 Probability and Stochastic Processes (3)

Review of probability theory. Generating functions, renewal theory, Markov chains and processes, Brownian motions, stationary processes. (Lec. 3) Pre: (435 or437) and 451. Offered alternate fall semesters.

MTH 551 Mathematical Statistics (3)

Theory of estimation and hypothesis testing. Large sample methods. Regression and analysis of variance. (Lec. 3) Pre: 550. Offered alternate spring semesters.

MTH 562 Complex Function Theory (3)

Rigorous development of theory of functions. Topology of plane, complex integration, singularities, conformal mapping. (Lec. 3) Pre: (435 and 436) or (437 and 438). Offered alternate spring semesters.

MTH 571 Numerical Analysis (3)

Computer arithmetic, interpolation, numerical approximation of derivatives and integrals, numerical ODE, and other topics. (Lec. 3) Pre: 243. Offered alternate fall semesters.

MTH 572 Numerical Partial Differential Equations (3)

Further numerical methods of solution of simultaneous equations, partial differential equations, integral equations. Error analysis. (Lec. 3) Offered alternate spring semesters.

MTH 575 Approximation Theory and Applications to Signal Processing

See Electrical Engineering 575.

MTH 591, MTH 592 Special Problems (1-3 each)

Advanced work under the supervision of a member of the department arranged to suit the individual requirements of the student. (Independent Study) Pre: permission of chairperson.

MTH 599 Master’s Thesis Research

Number of credits is determined each semester in consultation with the major professor or program committee. (Independent Study) S/U credit.

Write us at: 4 East Alumni Ave, Kingston, RI 02881-0805, USA.
Phone: 401-874-2505, Fax: 401-782-6422.
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Page last updated: Monday, November 15, 2004