528:  Extended Mathematics Major

Course Descriptions


MATH 136 – CALCULUS I.  (4 semester hours)   GEN ED D-II | QR
Prerequisites:  Four years of high school mathematics, including Algebra II, geometry, and trigonometry, and satisfactory score on Math Placement Exam and Math Placement Trig Exam; or MATH 117 or MATH 118, with grade of C or better.
A course in one-variable calculus including topics from analytic geometry.  Limits, derivatives, integration, and applications of polynomial, rational, trigonometric, and transcendental functions.  Includes lecture and recitation. 

MATH 137 – CALCULUS II.  (4 semester hours)
Prerequisites:  MATH 136 with a grade of C or better. 
A second course in one-variable calculus including topics from analytic geometry.  Methods of integration, sequences and series, polar and parametric functions.  Includes lecture and recitation. 

MATH 237MULTIVARIABLE CALCULUS.  (4 semester hours)
Prerequisite:  MATH 137 with a grade of C or better.
Topics in real-valued functions of several variables including directional derivatives, implicit functions, gradient, Taylor’s Theorem, maxima, minima, and Lagrange multipliers.  Differential calculus of vector-valued functions including chain rule and Inverse Function Theorem.  Multiple integrals, line integrals, surface integrals, Stokes’ and Green’s Theorems. 

MATH 275 – INTRODUCTORY TOPICS IN MATHEMATICS.  (1-3 semester hours)
Prerequisites:  MATH 136 and permission of instructor.
Varied topics selected to give students an early introduction to interesting mathematical problems or applications not found in the foundation sequence.

MATH 305INTRODUCTION TO MATHEMATICAL MODELING.  (3 semester hours)
Prerequisite:  MATH 137 with a grade of C or better.
Theory and computer implementation of mathematical models.  Deterministic, stochastic, discrete, continuous, and matrix models. Introduction to advanced topics such as linear algebra, differential and difference equations, probability, stochastic processes, and dynamical systems. 

MATH 307 – INTRODUCTION TO LINEAR ALGEBRA.  (3 semester hours)
Prerequisites:  MATH 136, and PHIL 215 or EE 180, all with grade of C or better.
Systems of linear equations, matrix algebra, vector spaces, inner product spaces, linear transformations, eigenvectors, quadratic forms.

MATH 310INTRODUCTION TO DISCRETE MATHEMATICS.  (3 semester hours)
Prerequisite:  MATH 137with a grade of C or better.
Introduction to discrete topics.  Development of skills in abstraction and generalization.  Set theory, functions and relations, mathematical induction, elementary propositional logic, quantification, truth tables, validity; counting techniques, pigeonhole principle, permutations and combinations; recurrence relations and generating functions; elementary graph theory, isomorphisms, trees. 

MATH 315 – THEORY OF NUMBERS.  (3 semester hours)
Prerequisite:  MATH 307 with a grade of C or better.
A study of the arithmetic of the integers, divisibility, prime numbers, factorization, diophantine equations, congruences, quadratic residues.

MATH 317INTRODUCTION TO ALGEBRAIC SYSTEMS.  (3 semester hours)
Prerequisites:  MATH 307 and MATH 310 with grades of C or better.
Introduction to groups, rings, polynomial rings, integral domains, and fields.

MATH 323 – GEOMETRY I.  (3 semester hours)
Prerequisite:  MATH 307 with a grade of C or better.
Beginning with a re-examination of elementary Euclidean geometry, the course includes a study of absolute plane geometry and the parallel postulate, which leads to an axiomatic treatment of hyperbolic geometry and related topics.

MATH 331 –  DIFFERENTIAL EQUATIONS.  (3 semester hours)
Prerequisite:  MATH 137 with a grade of C or better.
Methods of solution of differential equations, existence and nature of solutions, sapplications, and numerical solutions. 

MATH 337 – ELEMENTS OF REAL ANALYSIS.  (3 semester hours)
Prerequisites:  MATH 237, MATH 307, MATH 310, all with a grade of C or higher.
Basic concepts and techniques of real analysis, including proofs by induction and contradiction, the number system, functions of real variables, sets, series and sequences, cardinality, continuity, convergence, and elementary topology.

MATH 370 – APPLIED TECHNIQUES IN MATHEMATICS.  (3 semester hours)
Prerequisites:  MATH 237, MATH 331 with grades of C or higher.
Matrices, systems of ordinary differential equations, complex variables, and at least one of the topics from Fourier analysis, numerical analysis, or optimization (linear programming, Lagrange multipliers).

MATH 382 – PROBABILITY AND STATISTICS I.  (3 semester hours)
Prerequisite:  MATH 310 with a grade of C or better.  Prerequisite or corequisite:  MATH 237.
Axioms and laws of probability; discrete and continuous probability distributions; multivariate distributions; random variables; expectation; moment generating functions; Central Limit Theorem. 

MATH 398 – SEMINAR MATHEMATICS.  (1 semester hour; may be repeated for up to a total of 3 hours credit.)
Prerequisite:  MATH 237 with a grade of C or better.
Students will work on a topic of interest under the direction of a mathematics faculty member who will set the requirements for the course.  Mathematics majors could have the opportunity to continue this work in MATH 498.

MATH 405 – NUMERICAL ANALYSIS I.  (3 semester hours)
Prerequisites:  MATH 237 or 307 or 310, and CS 180 or CS 146, all with grades of C or better.
Computer arithmetic, roots of equations, polynomial approximation and interpolation, numerical differentiation and integration.  Computer solutions of problems will be required.

MATH 406 – NUMERICAL ANALYSIS II.  (3 semester hours)
Prerequisites:  MATH 237, 307, 331, and either MATH 405 or CS 405, all with grades of C or better.
The solution of linear systems by direct and iterative methods, matrix inversion, the calculation of eigenvalues and eigenvectors of matrices.  Initial and boundary value problems in ordinary differential equations.  Computer solution of problems will be required.

MATH 409 – HISTORY OF MATHEMATICS.  (3 semester hours)
Prerequisite:  Six hours of approved mathematics courses at the 300 and/or 400 level, or permission of instructor.
History of mathematics from ancient times through the development of calculus, with emphasis on famous problems.  Provides knowledge and appreciation useful in the classroom.  Term papers will be required.

MATH 415 – ALGEBRA AND NUMBER THEORY.   (3 semester hours)
Prerequisite:  MATH 315 or 317 with a grade of C or better.
An integrated survey of modern algebra and number theory.  Topics include number systems,theory. 

MATH 417 – ALGEBRAIC SYSTEMS.  (3 semester hours)
Prerequisite:  MATH 317 with a grade of C or better.
Theory of groups.

MATH 423 – GEOMETRY II.  (3 semester hours)
Prerequisite:  MATH 323 with a grade of C or better, or permission of instructor.
An axiomatic development of hyperbolic geometry based on the hyperbolic parallel postulate and the absolute geometry developed in MATH 323, including an emphasis on contrasts with Euclidean geometry. 

MATH 431 – INTERMEDIATE ANALYSIS.  (3 semester hours)
Prerequisite:  MATH 337 with a grade of C or better.
Topics in analysis chosen from inverse and implicit function theorems, differentiation, integration, infinite series, series of functions, and introductory functional analysis.

MATH 432 – INTRODUCTION TO MEASURE THEORY.  (3 semester hours)
Prerequisite:  MATH 431 with a grade of C or better.
Algebra of sets, axiom of choice, axioms for the real numbers, continuous functions, Borel sets, Lebesgue measure, Lebesgue integral. 

MATH 435 – PARTIAL DIFFERENTIAL EQUATIONS.  (3 semester hours)
Prerequisites:  MATH 237, 307, and 331, all with grades of C or better.
Equations of first and second order; elliptic, hyperbolic and parabolic equations; Sturm-Liouville theory; applications to equations of mathematical physics using separation of variables and Fourier series.

MATH 439 – TOPOLOGY I.  (3 semester hours)
Prerequisite:  MATH 317 with a grade of C or better, or permission of instructor.
Introduction to topology including topics selected from: topological spaces, mappings, homeomorphisms, metric spaces, surfaces, knots, manifolds, separation properties, compactness and connectedness.

MATH 450 – COMPLEX VARIABLES.   (3 semester hours)
Prerequisite:  MATH 237 with grade of C or better.
Complex number plane, analytic functions of a complex variable, integration, power series, calculus of residues, conformal representation, applications of analytic function theory.

MATH 470 – INTRODUCTION TO OPERATIONS RESEARCH.  (3 semester hours)
Prerequisites:  MATH 237 and 307 with grades of C or better.
Principles and techniques of operations research including linear programming, integer programming, quality theory, sensitivity analysis, and dynamic programming.

MATH 473 – INTRODUCTION TO GRAPH THEORY.  (3 semester hours)
Prerequisites:  MATH 307 and MATH 310 with grades of C or better, or permission of instructor.
Fundamental concepts, key ideas and tools in graph theory, with an emphasis on proof methods, algorithms and applications.  Techniques and tools are applied to practical optimization problems and other areas of mathematics and computer science.  This course is equivalent to CS 473.

MATH 475 – SELECTED TOPICS IN MATHEMATICS.  (1-3 semester hours)
Prerequisite:  Permission of instructor.
A consideration of special topics to acquaint the advanced undergraduate student with significant problems and developments of current interest in mathematics.  Topics may vary each semester offered.

MATH 482 – PROBABILITY AND STATISTICS II.  (3 semester hours)
Prerequisites:  MATH 237 and MATH 382 with grades of C or better.
Multivariate probability distributions; sampling distributions, statistical inference; point and interval estimation, properties of estimators; hypothesis testing; regression and correlation; analysis of variance; non-parametric methods.

MATH 498 – SENIOR SEMINAR.  (1-3 semester hours)
Prerequisites: MATH 237 and MATH 317 with grades of C or better and senior standing, or permission of instructor. 
Students will study articles in current mathematical journals or undertake independent investigations in mathematics.  Written and oral presentations will be required.

STAT 301 – INTRODUCTORY PROBABILITY AND APPLIED STATISTICS.  (3 semester hours)
Prerequisite:  MATH 136 or MATH 142, with a grade of C or higher.
A calculus-based introduction to applied statistics, with emphasis on analysis of real data.  Curve fitting, probability models, estimation and testing for means and proportions, quality control; use of computers for data analysis and simulation.


Dr. David K. Neal, Lead Academic Advisor
Department of Mathematics
COHH 4108
Western Kentucky University
Bowling Green, KY 42101
270.745.6213