0015. Prealgebra (3 s.h.) F S SS.

Topics include operations with rational numbers and decimals, problem solving, equations of lines, and graphing linear functions.

Note: Math 0015 is a pass/fail course. It does not count towards the number of credits required for graduation.

0045. Elementary Algebra (3 s.h.) F S SS.

Prerequisite: Mathematics placement or Math 0015.

Topics include algebraic operations, linear and quadratic equations, polynomials, exponentials, systems of linear equations, problem solving, graphing lines, and parabolas.

C055/H090. College Mathematics (3 s.h.) F S SS. Core: QA.

Prerequisite: Mathematics placement or Math 0045.

Mathematical concepts and applications for the non-specialist. Selected topics from areas such as finance, functions and models, exponential growth and decay, counting techniques, and probability and statistics.

C065/H091. Elements of Mathematical Thought (3 s.h.) F S SS. Core: QB.

Prerequisite: Math C055.

Contemporary mathematical applications for the non-specialist. Deals with the general areas of social choice, size, and shape. Specific topics include voting systems, fair division and apportionment, game theory, growth and form, size of populations, measurement, and geometric patterns.

C067. Elements of Statistics (3 s.h.) F S SS. Core: QB.

Prerequisite: Math C055.

This course provides a firm foundation for the study of statistics in other fields. Although no one field is emphasized to the exclusion of others, applications are drawn from psychology, political science, exercise science, and other areas.

C073. College Algebra (3 s.h.) F S SS. Core: QA.

Prerequisite: Mathematics placement or a grade of C or better in Math 0045 or the equivalent.

Bridges the gap in both depth and content between elementary algebra (Mathematics 0045) and pre-calculus (Mathematics C074). Topics include the real number system, operations with algebraic expressions, equations and inequalities, exponents and radicals, factoring, algebraic, exponential, and logarithmic functions.

Note: Mathematics C073 is no longer a preparatory course for Mathematics C075 and it can be followed by any QB Core course except Mathematics C075 or Mathematics C085. Students planning on going on to either Mathematics C075 or Mathematics C085 must take Mathematics C074 after Mathematics C073.

C074. Precalculus (4 s.h.) F S SS. Core: QA.

Prerequisite: Mathematics placement or grade C or better in Math C073 or its equivalent.

A preparatory course for Mathematics C075 and Mathematics C085. Topics include roots of polynomial equations, inequalities, algebraic operations with and graphs of polynomial, rational, exponential and logarithmic functions, triangle trigonometry, and analytic trigonometry.

C075. Calculus with Applications I (4 s.h.) F S SS. Core: QB.

Prerequisite: Mathematics placement or Math C074 with grade C or better or its equivalent.

Mathematics C075 is an intuitive treatment of calculus with emphasis on applications rather than theory. Topics include: functions and function operations, limits and continuity, the derivative, techniques and applications of differentiation.

Note: This course is part of a two semester calculus sequence. Students whose major requires three semesters of calculus should not register for this course. Only one of the following courses may be credited towards the BA or BS degree: Math C075 or Math C085/H095.

0076. Calculus with Applications II (4 s.h.) F S SS.

Prerequisite: Math C075 or C085 with a grade C or better, or equivalent.

Mathematics 0076 is an intuitive treatment of calculus with an emphasis on applications rather than theory. Topics include the definite integral and the Fundamental Theorem of Calculus, techniques and applications of integration, integrals of logarithmic, exponential and trigonometric functions, improper integrals, and application of integration to differential equations and probability.

Note: Only one of the following courses may be credited towards the BA or BS degree: Math 0076 or Math 0086/H096.

0077. Basic Concepts of Calculus (4 s.h.) F S SS.

Prerequisite: Mathematics placement test or grade of C or better in Mathematics C073 or its equivalent.

This is a caculus course in the reform style that will introduce students to the basic concepts of differential and integral calculus. The emphasis of the course will be on understanding the concepts (intuitively rather than rigorously) and on developing analytic ability. However, the course will also cover techniques of differentiation and some techniques of integration.

C085/H095. Calculus I (4 s.h.) F S SS. Core: QB.

Prerequisite: Mathematics placement test or Math C074 with a grade of C or better or its equivalent.

Mathematics C085 is a first semester calculus course that involves both theory and applications. Topics include functions, limits and continuity, differentiation of algebraic, trigonometric, exponential and logarithmic functions, curve sketching, optimization and L'Hospital's rule.

Note: Only one of the following courses may be credited towards the BA or BS degree: Math C075, Math C085/H095.

0086/H096. Calculus II (4 s.h.) F S SS.

Prerequisite: Math C085/H095 with a grade of C or better.

This is a second semester calculus course that involves both theory and applications. Topics include the definite integral and the Fundamental Theorem of Calculus, applications of the definite integral, techniques of integration, improper integrals and sequences and series, including power and Taylor series.

Note: Only one of the following courses may be credited towards the BA or BS degree: Math 0076, Math 0086/H096.

H097. Honors-Foundations of Calculus (4 s.h.) F.

Prerequisite: Advanced Placement credit for Calculus I and II.

This is a course for students who have had a year of calculus in high school. Its purpose is two-fold: to present a more theoretical treatment of calculus than is usually seen in an American high school and to prepare students for Math 0127, Calculus III. Topics covered will include some or all of the following: limits and continuity, derivatives and rules of differentiation, the Mean Value Theorem, L'Hospital's rule, optimization, graphing, the definite integral and the Fundamental Theorem of Calculus, u-substitution and integration by parts, limits of sequences, infinite series, convergence tests, power series, and Taylor series.

W115. Mathematical Recreations (3 s.h.) F. Core: WI.

A survey of various mathematical recreations, puzzles, and games. Emphasis on developing problem-solving techniques many of which are applicable in other fields.

0117. Elementary Calculus with Applications III (4 s.h.) F S SS.

Prerequisite: Math 0076 or 0086 with a grade C or better, or equivalent.

Mathematics 0117 is an intuitive treatment of Calculus with an emphasis on applications rather than theory. Topics include; vectors in three-dimensional space, vector valued functions, partial derivatives, multiple integrals, and an introduction to vector analysis.

Note: Only one of the following courses may be credited towards the BA or BS degree: Math 0117, Math 0127.

0127. Calculus III (4 s.h.) F S SS.

Prerequisite: Math 0086 with a grade C or better or equivalent.

This is a third semester calculus course that involves both theory and applications. Topics include vectors in two or three dimensions, lines and planes in space, parametric equations, vector functions and their derivatives, functions of several variables, partial derivatives, multiple integrals, line integrals, and Green's, Divergence and Stoke's Theorems.

Note: Only one of the following courses may be credited towards the BA or BS degree: Math 0117, Math 0127.

0133. Probability and Statistics (3 s.h.) F S SS.

Prerequisite: Math 0077 or two semesters of Calculus with grades of C- or better.

This course presents basic principles of statistical reasoning and the concepts from probability theory that give the student an understanding of the logic behind statistical techniques. Topics covered include rules of probability, discrete probability distributions, normal distribution, sampling distributions, the central limit theorem, point estimation, interval estimation, tests concerning means, tests based on count data, correlation and regression, and nonparametric statistics.

W141. Basic Mathematical Concepts (3 s.h.) F S SS. Core: WI.

Prerequisite: One year of calculus or permission of the instructor.

This is a course designed to introduce students to mathematical abstraction and the language of mathematical proof. Topics include logic, sets, relations, integers, induction and modular arithmetic, functions, and cardinality.

Note: Only one of the following courses may be credited towards the B.A. degree: Mathematics W141; CIS 0066.

0147. Linear Algebra (3 s.h.) F S SS.

Prerequisite: One year of calculus or permission of instructor.

This course covers vectors and vector spaces, matrices, determinants, systems of linear equations, linear transformations, inner products and orthogonality, and eigenvectors and eigenvalues.

Note: Credit is not permitted for both Math 0147 and 0148.

0148. Linear Algebra with Computer Lab (4 s.h.)

Prerequisite: One year of calculus or permission of instructor.

Topics in this course include: systems of linear equations; matrix algebra; determinants; fundamental subspaces; linear transformations; eigenvalues and eigenvectors; inner products; orthogonality; and spectral theory. Included is a computational lab component that uses activities and applications designed to promote understanding of the basic concepts from algebraic, symbolic, and geometric viewpoints.

Note: Credit is not permitted for both Math 0147 and 0148.

0163. Sophomore Problem Solving (3 s.h.) F S.

Prerequisite: Math 0077 or permission of the instructor.

This is a course intended primarily for students in the IS&T program. Topics covered come from number theory, cryptology and complexity of algorithms. Other topics can be introduced at instructor's discretion.

Note: This course is for nonmajors only. It cannot be used to fulfill any requirements towards a degree in mathematics.

W195. Honors in Mathematical Recreations (3 s.h.) F. Core: WI.

Honors section of Mathematics W115.

0203. Theory of Numbers (3 s.h.) S SS.

Prerequisite: One year of calculus or permission of instructor.

Divisibility properties of integers, prime factorization, distribution of primes, linear and quadratic congruencies, primitive roots, quadratic residues, quadratic reciprocity, simple Diophantine equations, cryptology.

W205. Modern Algebra (3 s.h.) F. Core: WI.

Prerequisite: Math 0147 or 0148 with a grade of C- or better or permission of instructor.

This is the first semester in a year-long modern algebra sequence Math W205-Math 0305. It is a thorough introduction to the theory of groups and rings.

0227. Mathematical Computer Programming I (3 s.h.) F.

Prerequisite: Math 0127, and Math 0147 or 0148 with grades of C- or better or the equivalent.

Mathematical techniques and algorithms which lend themselves to computer implementation and which form a basic repertoire for the mathematician and computer scientist.

0233. Introduction to Probability Theory (3 s.h.) F S SS.

Prerequisite: Math 0127 with a grade of C- or better or its equivalent.

Counting techniques, axiomatic definition of probability, conditional probability, independence of events, Bayes Theorem, random variables, discrete and continuous probability distributions, expected values, moments and moment generating functions, joint probability distributions, functions of random variables, covariance and correlation.

0234. Introduction to Mathematical Statistics (3 s.h.) S SS.

Prerequisite: Math 0233 with a grade of C- or better or equivalent.

Random sampling, sampling distributions, t, chi-squared and F distributions, unbiasedness, minimum variance unbiased estimators, confidence intervals, tests of hypothesis, Neyman-Pearson Lemma, uniformly most powerful tests.

0247. Advanced Calculus I (3 s.h.) F.

Prerequisite: Math 0127 or permission of instructor.

This is a first semester course in real analysis. Topics include the real number system and the completeness property, sequences and their limits, limits of real-valued functions and continuity and the point-set topology of the real numbers.

0248. Advanced Calculus II (3 s.h.) S.

Prerequisite: Math 0247 or permission of instructor.

This is a second semester course in real analysis. Topics include the derivative and differentiable functions, the Riemann integral, infinite series and convergence tests, power and Taylor series and operations with them, and if time allows topics from calculus of several variables.

0251. Differential Equations I (3 s.h.) F S SS.

Prerequisite: Math 0127 with a grade of C- or better or equivalent.

This is a course in ordinary differential equations. Topics include first order ordinary differential equations, linear second order ordinary differential equations, systems of differential equations, numerical methods and the Laplace transform.

0252. Differential Equations II (4 s.h.) S.

Prerequisite: Math 0251.

This is a second course in differential equations. Topics include orthogonal polynomials, including Legendre and Chebyshev polynomials, Fourier series, partial differential equations, the boundary value problems and other topics of the instructor's choice.

Note: This course is offered only in odd-numbered years.

0253. Numerical Analysis I (4 s.h.) F SS.

Prerequisite: Math 0127, Math 0147 or 0148 with grades of C- or better and a course in computer programming.

Computer arithmetic, pitfalls of computation, iterative methods for the solution of a single nonlinear equation, interpolation, least squares, numerical differentiation, numerical integration, and solutions of linear systems by direct and iterative methods.

0254. Numerical Analysis II (3 s.h.) S.

Prerequisite: Math 0253.

Solution of systems of nonlinear equations, solution of initial value problems, matrix norms and the analysis of iterative solutions, numerical solution of boundary value problems and partial differential equations, and introduction to the finite element method.

Note: Offered in even-numbered years only.

0271. Modern Geometry I (3 s.h.) F SS.

Prerequisite: Math 0147.

An introduction to Euclidean and Noneuclidean geometries with a particular emphasis on theory and proofs.

Note: This course is primarily intended for math education majors.

0297-0298. Junior Individual Study (1 to 4 s.h. each) F S SS.

Prerequisite: Approval of the department adviser and the instructor.

Intensive study in a specific area.

Note: May be taken in either semester.

0305. Topics in Modern Algebra (3 s.h.) S.

Prerequisite: Math W205 or equivalent.

This is the second semester of a year-long modern algebra course. Topics come from theory of rings, fields and modules and from Galois theory.

0313. History of Mathematics (3 s.h.) S.

Prerequisite: At least one mathematics course numbered above 0200.

The development of the major mathematical concepts from ancient times to the present , emphasizing topics in the standard undergraduate curriculum. Special attention will be paid to the history of mathematics and mathematics education in the United States.

Note: Offered in even-numbered years only.

0333. Introduction to Probability Models (3 s.h.) S.

Prerequisite: Math 0233 with a grade of C- or better.

Markov chains, exponential distribution, Poisson process, continuous time Markov chains, Brownian motion, stationary processes.

0347. Introduction to Functions of a Complex Variable (3 s.h.) F.

Prerequisite: Math 0248 or permission of instructor.

Complex numbers, analytic functions, harmonic functions, power and Laurent series, Cauchy's theorem, calculus of residues, and conformal mappings.

0350. Applied Mathematics (3 s.h.) F.

Prerequisite: Math 0147 or 0148, and Math 0251 or permission of instructor.

The construction and study of mathematical models for physical, economic, and social processes.

Note: Offered in odd-numbered years only.

0351. Partial Differential Equations (3 s.h.) S.

Prerequisite: Math 0251.

The solution and properties of first and second order equations; heat and wave equation. Elliptic boundary value problems and Green's functions. Hyperbolic problems and the theory of characteristics. Finite difference methods. The equations of mathematical physics.

Note: Offered in odd-numbered years only.

W363. Senior Problem Solving (3 s.h.) S. Core: WI.

Prerequisite: Math W141 or W205 and Math 0248 or permission of instructor.

This is a course in mathematical discovery through problem solving. Students will be expected to develop two or three areas of mathematics by solving problems, assigned by the instructor. Problems will be solved both individually and in groups. (Capstone W course.)

0365. Topology I (3 s.h.) S.

Prerequisite: Math 0248.

Topological and metric spaces. Continuity, compactness, connectedness, convergence. Introduction to algebraic and combinatorial topology. Classification of compact surfaces, fundamental groups and covering spaces.

Note: Offered in even-numbered years only.

0377. Differential Geometry (3 s.h.) S.

Prerequisite: Math 0127 with a grade of C- or better.

This course is an introduction to differential geometry starting with concepts learned in Calculus III. A particular emphasis will be placed on the study of curves and surfaces in 3-space and their generalizations. The course will revolve around Riemannian geometry, but, time permitting, it will also include a brief introduction to one or more of the following: symplectic geometry and its relation to classical mechanics, general connections and their relation with field theory and pseudoriemannian manifolds, and general relativity.

Note: Offered in odd-numbered years only.

0382. Combiniatorics (3 s.h.) F.

Prerequisite: Math 0127 and Math 0147 or 0148 with grades of C- or better.

Basic theorems and applications of combinatorial analysis, including generating functions, difference equations, Polya's theory of counting, graph theory, matching, and block diagrams.

Note: Offered in odd-numbered years only.

0397-0398. Senior Individual Study (1-4 s.h.) F S SS.

Prerequisite: Approval of the departmental adviser and instructor.

Intensive individual study at a senior or graduate level. Arranged each semester. Please consult with the instructor.

Note: Can be taken in either semester.
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