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01305/Mathematics (MATH)

 Unless otherwise noted, all prerequisite courses must be passed with a grade of C- or higher. The prerequisite courses for Math 1021 (C073), 1022 (C074), 1031 (C077), 1041 (C085), 1042 (0086), 1941 (H095), 1942 (H096), 2043 (0127), 3031 (0233) and 3041 (0251) must be passed with a grade of C or higher. Math 1011 (C055) requires only a passing grade in Math 0701 [1001 (0045)] (D- or higher).
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### Preparatory Courses

0701. Elementary Algebra (3 s.h.) F S SS.

(Formerly: MATH 1001 (0045).)

This course covers a basic treatment of algebraic expressions, linear equations and inequalities, polynomial operations, factoring, systems of linear equations, radical and rational expressions, quadratic equations, and various application problems.

Note: This course does not count towards the number of credits required for graduation in the College of Science and Technology.

### Lower Division Courses

0823. Math for a Digital World (3 s.h.) Core: QB.

(Formerly: GE-QUAN 1051 (0060).)

Databases and the Internet present both amazing opportunities and new vulnerabilities to fraud and theft. We will focus on how mathematics is used to digitize information, to compress it, and to transmit it securely. In a term project, students will investigate a socially significant question, using tools and concepts developed in the course. Some of these questions are: Does it make sense to draw for an inside straight? How can polling results differ so much from the election --- or do they? How can the winner of an election in the U.S. get much less than 50% of the vote? How long will the world`s oil last, assuming that we use more each year? How long will a million dollars last you, assuming it earns interest until you spend it? If you bought your text online, could someone tap into the Internet and get your credit card number when it`s transmitted? Why does the VIN on your car have so many digits?

Note: This General Education `Quantitative Literacy` pilot course fulfills the Core Quantitative Reasoning second level (QB) requirement.

0824. Mathematical Patterns (3 s.h.) Core: QB.

(Formerly: GE-QUAN 1052 (0061).)

News stories, everyday situations, and puzzling vignettes will be used to illuminate basic math concepts. Learn probability, for example, by discussing the gambler`s fallacy and gambler`s ruin, the drunkard`s random walks, the Monty Hall problem, the St. Petersburg paradox, the hot hand, monkeys randomly typing on a typewriter, and many others. A similar approach involving estimation problems and puzzles will be taken in the units on basic numeracy and logic. Throughout the course, lectures and readings will examine the mathematical angles of stories in the news, suggesting fresh perspectives, questions, and ideas on current issues from Google searches to the randomness of the iPod shuffle.

Note: This General Education `Quantitative Literacy` pilot course fulfills the Core Quantitative Reasoning second level (QB) requirement.

0923. Honors Math for a Digital World (3 s.h.) Core: QB.

(Formerly: GE-QUAN 1951.)

Databases and the Internet present both amazing opportunities and new vulnerabilities to fraud and theft. In this Honors course, we will focus on how mathematics is used to digitize information, to compress it, and to transmit it securely. In a term project, students will investigate a socially significant question, using tools and concepts developed in the course. Some of these questions are: Does it make sense to draw for an inside straight? How can polling results differ so much from the election --- or do they? How can the winner of an election in the U.S. get much less than 50% of the vote? How long will the world`s oil last, assuming that we use more each year? How long will a million dollars last you, assuming it earns interest until you spend it? If you bought your text online, could someone tap into the Internet and get your credit card number when it`s transmitted? Why does the VIN on your car have so many digits? (This is an Honors course.)

Note: This General Education `Quantitative Literacy` pilot course fulfills the Core Quantitative Reasoning second level (QB) requirement.

0924. Honors Mathematical Patterns (3 s.h.) Core: QB.

(Formerly: GE-QUAN 1952.)

News stories, everyday situations, and puzzling vignettes will be used to illuminate basic math concepts in this Honors course. Learn probability, for example, by discussing the gambler`s fallacy and gambler`s ruin, the drunkard`s random walks, the Monty Hall problem, the St. Petersburg paradox, the hot hand, monkeys randomly typing on a typewriter, and many others. A similar approach involving estimation problems and puzzles will be taken in the units on basic numeracy and logic. Throughout the course, lectures and readings will examine the mathematical angles of stories in the news, suggesting fresh perspectives, questions, and ideas on current issues from Google searches to the randomness of the iPod shuffle. (This is an Honors course.)

Note: This General Education `Quantitative Literacy` pilot course fulfills the Core Quantitative Reasoning second level (QB) requirement.

1011. College Mathematics (3 s.h.) F S SS. Core: QA.

(Formerly: MATH C055.)

Prerequisite: Mathematics placement, a grade of D- or higher in Math 0701 [1001 (0045)], or transfer credit for Math 0701 [1001 (0045)].

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

1012. Elements of Mathematical Thought (3 s.h.) F S SS. Core: QB.

(Formerly: MATH C065.)

Prerequisite: Math 1011 (C055).

Contemporary mathematical applications for a 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.

1013. Elements of Statistics (3 s.h.) F S SS. Core: QB.

(Formerly: MATH C067.)

Prerequisite: Math 1011 (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.

1021. College Algebra (4 s.h.) F S SS. Core: QA. \$.

(Formerly: MATH C073.)

Prerequisite: Mathematics placement, a grade of C or better in Math 0701 [1001 (0045)], or transfer credit for Math 0701 [1001 (0045)].

This course covers polynomial, rational and algebraic expressions, equations and inequalities. It also includes some topics in graphing, an introduction to the concept of a function, and a brief introduction to the exponential and logarithmic functions.

1022. Precalculus (4 s.h.) F S SS. Core: QA. \$.

(Formerly: MATH C074.)

Prerequisite: Mathematics placement, grade of C or better in Math 1021 (C073) or transfer credit for Math 1021 (C073).

This course is designed to prepare students for the calculus courses. Topics include functions and function operations, one-to-one and inverse functions, exponential and logarithmic functions, trigonometric functions, inverse trigonometric functions, basic trigonometric identities, and polar coordinates, and an introduction to vectors. The course also contains a brief review of algebraic functions.

1031. Differential and Integral Calculus (4 s.h.) F S SS. Core: QB.

(Formerly: MATH C077.)

Prerequisite: Mathematics placement, grade of C or better in Math 1021 (C073), or transfer credit for Math 1021 (C073).

This is a calculus 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.

Note: This is the course appropriate for those students who are taking calculus in order to fulfill the quantitative core requirements.

1041. Calculus I (4 s.h.) F S SS. Core: QB.

(Formerly: MATH C085.)

Prerequisite: Mathematics placement test, Math 1022 (C074) with a grade of C or better, or transfer credit for Math 1022 (C074).

This 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: This course is not appropriate for students whose sole purpose is to fulfill the quantitative core requirements. They should take Math 1031 (C077) instead.

1042. Calculus II (4 s.h.) F S SS.

(Formerly: MATH 0086.)

Prerequisite: Math 1041 (C085)/1941 (H095) with a grade of C or better or transfer credit for Math 1041 (C085).

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.

1911. Honors College Mathematics (3 s.h.) F S SS. Core: QA.

(Formerly: MATH H090.)

Prerequisite: Mathematics placement, a passing grade in Math 0701 [1001 (0045)], or transfer credit for Math 0701 [1001 (0045)].

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

1912. Honors Elements of Mathematical Thought (3 s.h.) F S SS. Core: QB.

(Formerly: MATH H091.)

Prerequisite: Math 1011 (C055)/1911 (H090).

Contemporary mathematical applications for a 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.

1941. Honors Calculus I (4 s.h.) F S SS. Core: QB.

(Formerly: MATH H095.)

Prerequisite: Mathematics placement test, Math 1022 (C074) with a grade of C or better, or transfer credit for Math 1022 (C074).

This 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: This course is not appropriate for students whose sole purpose is to fulfill the quantitative core requirements. They should take Math 1031 (C077) instead.

1942. Honors Calculus II (4 s.h.) F S SS.

(Formerly: MATH H096.)

Prerequisite: Math 1041 (C085)/1941 (H095) with a grade of C or better or transfer credit for Math 1041 (C085).

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.

1951. Honors Differential & Integral Calculus (4 s.h.) F.

(Formerly: MATH H097.)

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 2043 (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.

### Upper Division Courses

2031. Probability and Statistics (3 s.h.) F S SS.

(Formerly: MATH 0133.)

Prerequisite: Math 1031 (C077) 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.

Note: This course cannot be credited towards graduation if taken after Math 3031 (0233) or C+IN SC 1166 (0066).

2032. Sophomore Problem Solving (3 s.h.) F S.

(Formerly: MATH 0163.)

Prerequisite: Math 1031 (C077) or permission of the instructor.

This is a course intended primarily for students in the IS&T program. It covers various topics from discrete mathematics.

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

2043. Calculus III (4 s.h.) F S SS.

(Formerly: MATH 0127.)

Prerequisite: Math 1042 (0086)/1942 (H096) with a grade C or better or transfer credit for Math 1042 (0086).

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.

2096. Mathematical Recreations (3 s.h.) F. Core: WI.

(Formerly: MATH W115.)

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

2101. Linear Algebra (3 s.h.) F S SS.

(Formerly: MATH 0147.)

Prerequisite: Math 1042 (0086) or equivalent transfer. Co-Requisite: Math 2043 (0127).

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

Note: Only one course, Math 2101 (0147) or Math 2103 (0148), can be credited towards graduation.

2103. Linear Algebra with Computer Lab (4 s.h.)

(Formerly: MATH 0148.)

Prerequisite: Math 1042 (0086) or equivalent transfer. Co-Requisite: Math 2043 (0127).

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: Only one course, Math 2101 (0147) or Math 2103 (0148), can be credited towards graduation.

2196. Basic Mathematical Concepts (3 s.h.) F S SS. Core: WI.

(Formerly: MATH W141.)

Prerequisite: Math 1042 (0086) 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. This course is highly recommended for students who have not been exposed to mathematical proof and intend to take advanced math courses.

Note: Only one of the following courses may be credited towards graduation: Math 2196 (W141); C+IN SC 1166 (0066).

3003. Theory of Numbers (3 s.h.) F SS.

(Formerly: MATH 0203.)

Prerequisite: Math 1042 (0086) 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.

3031. Introduction to Probability Theory (3 s.h.) F S SS.

(Formerly: MATH 0233.)

Prerequisite: Math 1042 (0086) with a grade of C or better or transfer credit for Math 1042 (0086). Co-Requisite: Math 2043 (0127).

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.

3032. Introduction to Mathematical Statistics (3 s.h.) F S SS.

(Formerly: MATH 0234.)

Prerequisite: Math 3031 (0233) or an equivalent transfer.

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

3041. Differential Equations I (3 s.h.) F S SS.

(Formerly: MATH 0251.)

Prerequisite: Math 1042 (0086) with a grade of C or better or transfer credit for Math 1042 (0086). Co-Requisite: Math 2043 (0127).

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.

3042. Differential Equations II (4 s.h.) S.

(Formerly: MATH 0252.)

Prerequisite: Math 3041 (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.

3043. Numerical Analysis I (3 to 4 s.h.) F SS.

(Formerly: MATH 0253.)

Prerequisite: Math 2043 (0127), Math 2101 (0147) or Math 2103 (0148), and one of C+IN SC 1053 (C061), C+IN SC 1057 (C071), C+IN SC 1068 (0067), or Physics 2501 (0161).

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.

3044. Numerical Analysis II (3 s.h.) S.

(Formerly: MATH 0254.)

Prerequisite: Math 3043 (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.

3061. Modern Geometry I (3 s.h.) F SS.

(Formerly: MATH 0271.)

Prerequisite: Math 2101 (0147) or Math 2103 (0148) or their equivalents.

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.

3082. Junior Individual Study (1 to 4 s.h.) F S SS.

(Formerly: MATH 0297.)

Prerequisite: Approval of the department advisor and the instructor.

Intensive study in a specific area.

Note: May be taken in either semester.

3083. Junior Directed Reading (1 to 4 s.h.) F S SS.

(Formerly: MATH 0298.)

Prerequisite: Approval of the department advisor and the instructor.

Intensive study in a specific area.

Note: May be taken in either semester.

3098. Modern Algebra (3 s.h.) F. Core: WI.

(Formerly: MATH W205.)

Prerequisite: Math 2101 (0147) or 2103 (0148).

This is the first semester in a year-long modern algebra sequence Math 3098 (W205)- Math 3101 (0305). It is a thorough introduction to the theory of groups and rings.

Note: Students who have had limited exposure to proofs should consider taking Math 2196 (W141) first.

3101. Topics in Modern Algebra (3 s.h.) S.

(Formerly: MATH 0305.)

Prerequisite: Math 3098 (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.

3141. Advanced Calculus I (3 s.h.) F.

(Formerly: MATH 0247.)

Prerequisite: Math 2043 (0127) and Math 2101 (0147) or 2103 (0148) or equivalent transfers.

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 point-set topology of Euclidean spaces.

Note: Students who have had limited exposure to proofs should consider taking Math 2196 (W141) first.

3142. Advanced Calculus II (3 s.h.) S.

(Formerly: MATH 0248.)

Prerequisite: Math 3141 (0247).

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 topics from calculus of several variables.

4001. History of Mathematics (3 s.h.) S.

(Formerly: MATH 0313.)

Prerequisite: At least one mathematics course numbered above 3000.

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.

4003. Combiniatorics (3 s.h.) F.

(Formerly: MATH 0382.)

Prerequisite: Math 2043 (0127) and Math 2101 (0147) or 2103 (0148) or equivalent transfer.

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.

4033. Introduction to Probability Models (3 s.h.) S.

(Formerly: MATH 0333.)

Prerequisite: Math 3031 (0233) or equivalent.

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

4041. Partial Differential Equations (3 s.h.) S.

(Formerly: MATH 0351.)

Prerequisite: Math 3041 (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.

4043. Applied Mathematics (3 s.h.) F.

(Formerly: MATH 0350.)

Prerequisite: Math 2101 (0147) or 2103 (0148), and Math 3041 (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.

4051. Introduction to Functions of a Complex Variable (3 s.h.) F.

(Formerly: MATH 0347.)

Prerequisite: Math 3142 (0248).

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

4061. Differential Geometry (3 s.h.) S.

(Formerly: MATH 0377.)

Prerequisite: Math 2043 (0127) or equivalent.

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.

4063. Topology I (3 s.h.) S.

(Formerly: MATH 0365.)

Prerequisite: Math 3141 (0247) and Math 3098 (W205).

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.

4082. Senior Individual Study (1 to 4 s.h.) F S SS.

(Formerly: MATH 0397.)

Prerequisite: Approval of the departmental advisor 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.

4083. Senior Directed Reading (1 to 4 s.h.) F S SS.

(Formerly: MATH 0398.)

Prerequisite: Approval of the departmental advisor 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.

4096. Senior Problem Solving (3 s.h.) S. Core: WI.

(Formerly: MATH W363.)

Prerequisite: Math 3098 (W205) and Math 3142 (0248).

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.)

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