01305/Mathematics

Preparatory Courses

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 Mathematics 0015.

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

Lower Division Courses

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

Mathematical concepts and applications for the non-specialist. Selected topics from areas such as Finance, Linear Programming, Management Science, Counting Techniques, Probability, and Statistics.

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

Prerequisite: Mathematics 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.

C066. Intuitive Calculus (3 s.h.) F S SS. Core: QB.

Prerequisite: Mathematics C055.

This course presents a one-semester overview of the basic topics in calculus, demonstrating their applications in a wide variety of fields. A review of elementary skills will be given during the first week of the semester.

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

Prerequisite: Mathematics 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 Mathematics 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 Mathematics 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 Mathematics 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: the coordinate plane, functions, limits, continuity, differentiation, applications of differentiation, the definite integral, the Fundamental Theorem of Calculus.

Note: 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: Mathematics 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 techniques of integration, integrals of logarithmic, exponential and trigonometric functions, improper integrals, infinite series, 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 (4 s.h.) F S SS. Core: QB.

Prerequisite: Mathematics placement test or Mathematics 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: Mathematics C085 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, polar coordinates, convergence of sequences and series, and 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 course will condense the most important concepts and techniques of differential and integral calculus usually covered in two semesters into one semester. It will be assumed that students in this course already have some facility with techniques of calculus. Consequently, a considerable amount of time will be spent on the concepts of calculus. Upon completing the course students will be able to take Math 0127, Calculus III. Topics include limits and continuity, derivatives and rules of differentiation, the Mean Value Theorem, LíHospitalís rule, optimization, graphing, the definite integral, the Fundamental Theorem of Calculus, u-substitution and integration by parts, limits of sequences, infinite series, convergence tests, power series, and Taylor series.

Upper Division Courses

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: Mathematics 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: Mathematics 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: Mathematics 0077 or two semesters of Calculus.

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.

Sets, relations, functions, logic, ordered fields, induction, cardinality.

Note: Mathematics 0127 may be taken concurrently with this course. 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 eigenvalues.

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.

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

Prerequisite: Mathematics 0077 or two semesters of calculus.

This is a problem-solving course for students of sophomore standing. Topics covered will come from both discrete and continuous mathematics and will generally be left to the instructor's discretion. Suggested topics include bases and base arithmetic, algorithms and complexity, recursion, Newton-Raphson and Taylor polynomial approximations, and numerical integration.

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

Honors section of Mathematics W115.

0203. Theory of Numbers (3 s.h.) F 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, cryptography.

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

Prerequisite: Mathematics 0147 or permission of instructor.

Introduction to the theory of groups, rings, and fields.

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

Prerequisite: Mathematics 0117 or 0127, Mathematics 0147, and CIS C059 or the equivalent.

Mathematical techniques and algorithms which lend themselves to computer implementation and which form a basic repertoire for the mathematician, scientist, or engineer. Extensive computer utilization.

0230. Probability for Applied Sciences (3 s.h.) S.

Prerequisite: Mathematics 0117 or 0127 or permission of instructor.

The axiomatic definition of probability and its properties, combinatorial analysis, random variables, general properties of continuous random variables, normal and exponential distributions, expected values, Markov chains, Law of Large Numbers, Chebyshev's inequality, and stochastic processes. The emphasis is on the use of probability in solving problems rather than detailed development of the theory.

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

Prerequisite: Mathematics 0127 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: Mathematics 0233 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: Mathematics 0127 or permission of instructor.

The real number system, sequences and their limits, the least upper and the greatest lower bounds, the completeness property, point-set topology of the real numbers, open, closed, compact and connected sets, generalizations to the n-dimensional space, continuous functions, differentiation of functions of one variable, the Mean Value Theorem and its applications.

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

Prerequisite: Mathematics 0247 or permission of instructor.

The Riemann integral and the Fundamental Theorem of Calculus, infinite series, convergence tests, power and Taylor series, uniform convergence, operations with power series, partial derivatives, and multiple integrals, transformations of multiple integrals, integrals over curves and surfaces, theorems of Green, Gauss, and Stokes, the divergence theorem.

0251. Differential Equations I (3 to 4 s.h.) F S SS.

Prerequisite: Mathematics 0127 or the equivalent.

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

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

Prerequisite: Mathematics 0251.

Orthogonal polynomials including Legendre and Chebyshev polynomials, Fourier series, partial differential equations, boundary value problems, the phase plane, stability, Liapunov's method, eigenvalue problems, and introduction to functions of a complex variable.

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

0253. Numerical Analysis I (3 to 4 s.h.) F SS.

Prerequisite: Three terms of calculus, linear algebra, and basic knowledge of a high level programming language like FORTRAN, C, or PASCAL.

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.

Note: In sections with 4 credits there is a required lab, where a computing lab is used to demonstrate topics and provide hands-on experience with the ideas encountered. Activities designed to promote understanding are the primary focus. Sections without the laboratory must be taken for 3 credits.

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

Prerequisite: Mathematics 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.

Prerequisite: Mathematics 0147.

A study of the properties of projective, affine, Euclidean and non-Euclidean spaces and their transformation groups.

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.

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: Mathematics 0233.

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: Mathematics 0247 and 0248 or permission of instructor.

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

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

Prerequisite: Mathematics 0147, 0233, and 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: Mathematics 0247 and 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.

0355. Operations Research (3 s.h.) S.

Prerequisite: Mathematics 0147 and 0233.

The theory and applications of various topics, including linear and dynamic programming, game theory, transportation, assignment, and network problems, inventory problems, scheduling and queueing problems.

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

Prerequisite: Mathematics W205 and 0247 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: Mathematics 0247 and 0248.

Topological and metric spaces, continuity, compactness, connectedness, convergence. Introduction to algebraic and combinatorial topology, classification of compact surfaces, fundamental groups.

Note: Offered in even-numbered years only.

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

Prerequisite: Mathematics 0127.

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.

0381. Discrete Algorithms (3 s.h.)

Discrete algorithms such as searching, sorting and backtracking with particular emphasis on applications to artificial intelligence.

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

Prerequisite: Mathematics 0127 and 0147.

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 (3 s.h.) F S SS.

Prerequisite: Approval of the departmental adviser and instructor. Open to seniors only.

Arranged each semester, please consult with the instructor.