## Department of Mathematics

### Courses

- Math 090: Basic Mathematics

A review of intermediate algebra. Topics include arithmetic of natural numbers, integers, and real numbers; operations with algebraic expressions; exponents and radicals; linear equations and inequalities; and quadratic equations and inequalities. Institutional credit only. - Math 100: College Algebra

A course designed to provide the student with the fundamental concepts of algebra, which are essential for all higher mathematics courses. After completing this course, the student should understand the concepts and know how to apply the knowledge of algebraic equations and inequalities; functions and graphs; polynomial and rational functions; exponential and logarithmic functions; and systems of equations and inequalities. Prerequisite: MTH 090 (with a C or better) or mathematics placement. - Math 110: Finite Mathematics

A course designed to provide the non-science/mathematics/engineering/business student an intense introduction to the foundations and fundamentals of mathematics for liberal arts majors. This course introduces many branches of mathematics and concentrates on pertinent and concrete examples and applications. After completing this course, the student should be able to work basic problems and word problems in linear algebra, logic, set theory, counting theory, probability, and statistics. Prerequisite: MTH 100 (with a C or better) or mathematics placement. **Math 120: Precalculus**

Trigonometric functions; exponential and logarithmic functions; analytic geometry; mathematical induction; complex numbers; and the binomial theorem. Prerequisite: MTH 100 (with a C or better) or mathematics placement.- Math 130: Basic Statistics

A course designed to provide the student an intense foundational introduction to the fundamentals of statistics. The course includes an introduction to frequency of distribution and graphs; measures of central tendency; measures of variation; normal distribution; sampling; hypothesis testing; correlation; and linear regression. Also included is the use of some statistical packages (Excel, Minitab, SPSS, SAS, etc.). Prerequisite: MTH 110 (with a C or better) or mathematics placement. - Math 160: Calculus for Business

A course designed to provide the business student a concentrated foundational introduction to the fundamentals of applied calculus. The course includes an introduction to both differential and integral calculus with a concentration in business applications. Prerequisite: MTH 110 or MTH 120 (with a C or better) or mathematics placement. - Math 161: Calculus I

Calculus I is a first course in differential calculus and basic integral calculus. Topics include limits, continuity, elementary transcendental functions, plane analytic geometry, differentiation, implicit differentiation, related rates, maxima and minima, the fundamental theorem of calculus, and introduction to definite integral with applications. Prerequisite: MTH 120 (with a C or better) or mathematics placement. - Math 162: Calculus II

Calculus II is a continuation of Calculus I. Topics include techniques and applications of integration, polar coordinates, parametric equations, infinite sequences and series, numerical integration, differential equations, L’Hôpital’s rule, and improper integration. Prerequisite: MTH 161 (with a C or better) or mathematics placement. - Math 211: Discrete Mathematics

A course designed to provide the student an intense foundational introduction to “discrete” methods of mathematics. Topics include logic; elementary set theory; algebraic structures; combinatorics; Boolean algebra; recurrence relations; and graph theory. This course is primarily designed for students in computer science, but students in other disciplines also benefit from the study of “discrete” methods as a complement to “continuous” methods. Prerequisite: MTH 110 or MTH 120 (with a C or better). - Math 255: Introduction to Set Theory

A course designed to provide the student an introduction to the nature of mathematics and the use of proof. Topics include a review of logic; reading, understanding, and constructing proofs; the first and second principle of mathematical induction, quantification, sets and their properties; axiomatics; product sets; relations; functions; cardinality. Emphasis is placed on sets and their role as one of the foundations of mathematics. Prerequisite: MTH 161 (with a C or better). - Math 263: Calculus III

Calculus III is a continuation of Calculus II. Topics include multivariable calculus; solid analytic geometry; linear approximation and Taylor’s theorems; Lagrange multiples and constrained optimization; multiple integration and vector analysis, including the theorems of Green, Gauss and Stokes; vector functions and curves in space; functions of several variables; and partial derivatives. Prerequisite: MTH 162 (with a C or better). - Math 271: Linear Algebra

Topics include matrices and determinants; simultaneous linear equations; vectors; linear transformations; matrix calculus; canonical forms; special matrices; applications to linear systems; least squares problems; and eigenvalues and eigenvectors. Prerequisite: MTH 161 (with a C or better). - Math 321: Differential Equations

A course designed to provide the student an introduction to the mathematical formulation of physical problems in terms of ordinary differential equations, solutions to these equations, and physical interpretations of these solutions. Topics include first order equations, nth order equations; numerical approximation techniques; Laplace transforms and systems of equations. Prerequisite: MTH 162 (with a C or better). - Math 325: Applied Mathematics I

A course designed to provide the student an introduction to topics selected topics from the following: convergence of infinite series and sequences; second order ordinary differential equations; uniform convergence; regions; Fourier series and integrals; eigenvalues and eigenfunctions; adjointness and boundary-value problems; and Sturm-Liouville Theory. Prerequisites: MTH 263 and MTH 321 (with Cs or better). - Math 327: Applied Mathematics II

A continuation of Applied Mathematics I. Topics include partial differential equations; conformal mappings applications to two-dimension potential problems; classification of second-order partial differential equations; complex variables; integral equations; conformal mappings; Green’s functions; Legendre functions; Bessel functions; integral equations; wave motion; heat conduction; and L2 functions. Prerequisite: MTH 325 (with a C or better). - Math 341: Probability and Statistics I

A course designed to provide the student an introduction to the mathematical theory of probability and statistics. Topics include the combinatorial analysis; axioms of probability; conditional probability; random variables; mass functions; distribution functions; discrete and continuous probability functions; marginal distributions; special distributions; joint distributions; and properties of expectation. Prerequisites: MTH 255 or MTH 211; and, MTH 162 (with C or better). - Math 342: Probability and Statistics II

A continuation of Probability and Statistics I. Topics include random processes; the expected value; variance; covariance; correlation; conditional expectation; moment generating funtions; Chebyshev’s Inequality; the Central Limit Theorem; estimation theory; bounding; hypothesis testing; analysis of variance; regression; parametric statistics; and nonparametric statistics. Prerequisite: MTH 341 (with C or better). - Math 361: Real Analysis I

The real numbers, completeness, and elementary topology of Euclidean Spaces; limits, convergence, sequences in Rn; continuity; differentiability and integrability in R. Prerequisites: MTH 255 and MTH 263 (with C or better). - Math 362: Real Analysis II

Real Analysis II is a continuation of Real Analysis I; the theory of multivariable calculus; sequences of functions and series of functions; uniform convergence; transformations; differentiation in Rn; implicit and inverse function theorems; integration in Rn and Jacobian. Prerequisites: MTH 271 and MTH 361 (withCor better). - Math 371: Abstract Algebra I

Topics include groups; subgroups; cyclic groups; permutation groups; normal subgroups and quotient groups; homomorphisms; isomorphisms and the fundamental isomorphism theorems; fundamental theorem of finite abelian groups; rings; integral domains; fields; subrings and ideals; quotient rings; ring homomorphism; and polynomial rings with coefficients in a field. Prerequisites: MTH 255 or MTH 211; and MTH 271 (with C or better). - Math 372: Abstract Algebra II

A continuation of Abstract Algebra I. Topics include Sylow theorems; prime ideals; principal ideals and principal ideal domains; unique factorization domains; Euclidean domains; field extensions; and Galois Theory. Prerequisite: MTH 371 (with C or better). A course designed to be a continuation of Introduction to Linear Algebra. Topics include a review of eigenvalues and eigenvectors, rank of a matrix, the column and null spaces associated with a matrix, the Gram-Schmidt process, diagonalization of a matrix, generalized eigenvectors, Jordan canonical form, Cayley- Hamilton theorem, orthogonal decomposition theorem, symmetric matrices and the spectral theorem, unitary matrices, hermitian matrices, normal matrices, singular value decomposition and Gerschgorin’s circle theorem. Additional topics may include but are not exclusive are group theoretic methods, power and inverse power methods, Rayleigh-Ritz theorem, introduction to the PageRank algorithm, condition number, sparse matrices and Krylov subspaces. Prerequisites : MTH 271 and MTH 255 (with a C or better).**Math 375: Advanced Linear Algebra**-
**Math 391: Special Topics in Mathematics**

Designed to expose the student to areas of mathematics that are not part of the current curriculum, but are recognized as important to the field. Particular attention is paid to recent advances in mathematics. Prerequisites: Dependent on the subject. **Math 463: Real Variables**

Topics include advanced theory of the reals; Lebesgue integration; metric spaces; Lp spaces; Banach spaces; measure theory; and Borel sets. Prerequisite: MTH 362 (with C or better).**Math 465: Complex Variables**

Topics include elementary properties of real and complex numbers; elementary topology in the complex plane; continuity, differentiability, and integrability of a complex variable; the Cauchy Theorem; Cauchy integral formula; elementary complex functions; complex sequences and series; Laurent and Taylor series; residue theory; and contour integration. Prerequisite: MTH 361 (with C or better).**Math 467: Numerical Analysis**

Topics include the basic concepts of numerical analysis; interpolation; finite differences; integration and approximation of orthogonal functions. Trigonometric interpolation; inverse interpolation; least squares; asymptotic representation; differential equations; continued fractions; and linear programming. Prerequisites: MTH 263, MTH 271, and MTH 321 (with Cs or better).**Math 475: Number Theory**

Topics include divisibility; Euclidean algorithm; primes; linear and quadratic congruences; arithmetic functions; primitive roots and indices; diophantine equations; and cryptography. Prerequisite: MTH 371 (with C or better).**Math 485: Topology**

Topics include metric spaces; pseudometrics; topologies; continuous functions; compactness; connectedness; continua; separation axioms; Moore spaces; Tychonoff spaces; and Hausdorff spaces. Prerequisite: MTH 361 (with a C or better).**Math 487: Differential Geometry**

Topics include differential manifolds; tangent spaces; theory curves; torsion; the Frenet frame; directional forms; surfaces; tensor analysis; shape operators; orientation; and intrinsic geometry. Prerequisites: MTH 361 and MTH 271 (with C or better).- Math 497: Senior Seminar

As the capstone course in mathematics, the Senior Seminar will seek to integrate concepts, theories and their applications from the various subfields of mathematics. All students will be required to research, write, and present a substantive paper in their respective areas of concentration. Prerequisites: MTH 361 and MTH 371 (with C or better).