Wilkes University

Mathematics

MTH-411. Real Analysis

Credits: 4

A rigorous treatment of fundamental concepts in analysis, with emphasis on careful reasoning and proofs. Topics covered include the completeness and order properties of real numbers; limits and continuity; conditions for integrability and differentiability; infinite sequences and series of functions. Basic notions of the topology of the real line are also introduced.

Pre-Requisites
MTH-302 (Introduction to Higher Mathematics) or consent of instructor

MTH-413. Functions of Several Variables

Credits: 3

A modern treatment of calculus of functions of several real variables. Topics include: Euclidean spaces, differentiation, integration and manifolds leading to the classical theorems of Green and Stokes.

Pre-Requisites
MTH-214 (Linear Algebra) and MTH-411 (Real Analysis) or consent of instructor.

MTH-414. Complex Analysis

Credits: 3

Complex functions, limit, continuity, analytic functions, power series, contour integration, Laurent expansion, singularities and residues.

Pre-Requisites
MTH-212 (Multivariable Calculus) or consent of instructor.

MTH-431. Abstract Algebra I

Credits: 4

A rigorous treatment of fundamental concepts in algebra, with emphasis on careful reasoning and proofs. Topics covered include equivalence relations, binary operations. Integers: divisibility, factorization, integers modulo n, elementary group theory, subgroups, cyclic groups, permutation groups, quotient groups. Homomorphisms and isomorphisms. Introductory topics in ring theory as time permits.

Pre-Requisites
MTH-302 (Introduction to Higher Mathematics) or consent of instructor

MTH-432. Abstract Algebra II

Credits: 3

A continuation of MTH-431. Includes the study of polynomial rings, ideals, field extensions and Galois Theory.

Pre-Requisites
MTH-431 (Abstract Algebra).

MTH-442. Topology

Credits: 3

An introduction to point-set topology, including a study of metric spaces, topological spaces, countability and separation axioms, compactness, connectedness, product spaces.

Pre-Requisites
MTH-411 (Real Analysis) or consent of instructor.

MTH-443. Geometry

Credits: 3

A study of selected topics from Euclidean and non-Euclidean geometry.

Pre-Requisites
MTH-302 (Introduction to Higher Mathematics) or consent of instructor

MTH-451. Probability and Mathematical Statistics I

Credits: 3

Random variables, probability distributions, expectation and limit theorems, confidence intervals.

Pre-Requisites
A one-year calculus sequence or consent of instructor.

MTH-452. Probability and Mathematical Statistics II

Credits: 3

Hypothesis testing, non-parametric methods, multivariate distributions, introduction to linear models.

Pre-Requisites
MTH-451 or consent of instructor.

MTH-454. Statistical Methodology

Credits: 3

This course emphasizes applications, using statistical computer packages (R, SPSS) and real data sets from a variety of fields. Topics include estimation and testing; stepwise regression; analysis of variance and covariance; design of experiments; contingency tables; and multivariate techniques, including logistic regression.

Pre-Requisites
MTH-451 or consent of instructor.

MTH-461. Partial Differential Equations

Credits: 3
Fees: $40

Partial differential equations and boundary value problems, inner product spaces, orthogonal functions, eigen value problems, Sturm-Liouville equations, Fourier series, Fourier transforms, Green’s functions, and classical equations of engineering and physics. 

Offered fall of odd years.

Pre-Requisites

MTH-462. Advanced Calculus

Credits: 3
Fees: $40

Topics from advanced calculus, including matrix representation of differentials and the multivariable chain rule, vector calculus, curvilinear coordinates, tensors, change of variables in higher dimensions, improper multiple integrals, applications of line and surface integrals, differential forms and the general Stokes’ theorem, potential theory, and Taylor’s formula for functions of several variables.

Offered fall of even years

Pre-Requisites
MTH-212 (Multivariable Calculus)

MTH-463. Operations Research

Credits: 3

A survey of operations research topics such as decision analysis, inventory models, queuing models, dynamic programming, network models,  and linear programming. Cross-listed with CS-463. Offered in the spring semester of odd-numbered years when demand warrants.

Pre-Requisites
Programming experience in a high-level language and completion of a one-year calculus sequence.

MTH-464. Numerical Analysis

Credits: 3

An introduction to numerical algorithms as tools to providing solutions to common problems formulated in mathematics, science, and engineering. Focus is given to developing the basic understanding of the construction of numerical algorithms, their applicability, and their limitations. (Cross-listed with CS-464)

Pre-Requisites
Programming experience in a high-level language and completion of a one-year calculus sequence.

MTH-465. Numerical Linear Algebra

Credits: 3

Direct and iterative methods for the solution of systems of linear equations, matrix decompositions, computation of eigenvalues and eigenvectors, and relaxation techniques. The theoretical basis for error analysis including vector and matrix norms. Applications such as least squares and finite difference methods. Offered spring semester of even-numbered years. 

Pre-Requisites
MTH 214 and CS 125 (or equivalent programming experience)

MTH-470. Readings In Mathematics

Credits: 3
Pre-Requisites
Consent of Mathematics Department Chairperson May be repeated for credit if a different topic is selected.

MTH-511. Measure and Integration

Credits: 3

Measures, measurable functions, integration, convergence theorems, product measures, signed measures.

Pre-Requisites
MTH-442 or consent of instructor.

MTH-513. Functional Analysis

Credits: 3

Topics include: Banach spaces, Lp-spaces, Hilbert spaces, topological vector spaces, and Banach algebra.

Pre-Requisites
MTH-411 and a course in linear algebra.

MTH-532. Modern Algebra

Credits: 3

A study of group theory (including the Sylow Theorems and solvable groups); ring theory (including the Noetherian rings and UFDs); modules, tensor algebra, and semi-simple rings.

Pre-Requisites
MTH-431, and a course in linear algebra or consent of instructor.

MTH-542. Algebraic Topology

Credits: 3

Polyhedra, simplicial homology theory, cohomology rings, and homotopy groups.

Pre-Requisites

MTH-590. Thesis Writing

Credits: up-6
Pre-Requisites
Consent of Department Chairperson

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