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**100. Intermediate Algebra (3).** Prerequisite: LS 098 or satisfactory score on ACT/SAT or the departmental placement test. Operations/properties of real numbers, exponents and complex numbers; factoring, solution/application of linear and quadratic equations; operations on polynomials and rational expressions. (Not open to students with credit in MS 125 or higher.) Grades: A, B, C, NC.

**108. Exploring Mathematics (3).** Prerequisite: MS 100 with a "C" or better or satisfactory score on ACT/SAT or the departmental placement test. An introduction to mathematics with topics useable and relevant to any person. Topics include elementary logic, problem solving techniques, use of quantitative techniques, statistical reasoning, and modeling. (Not open to students with credit in MS 133. Department credit not given for mathematics majors or minors.)

**110. Finite Mathematics (3).** Prerequisite: MS 100 with a "C" or better or satisfactory score on ACT/SAT or the departmental placement test. Systems of equations and matrices, linear programming, mathematics of finance, sets and counting, probability, and probability distribution and statistics. Computer applications using Microsoft Excel. (Department credit not given for mathematics majors or minors.)

**111. Honors Finite Mathematics (3).** Prerequisite: Satisfactory score on ACT/SAT or the departmental placement test or by advisement. Advanced study of matrices, linear programming, mathematics of finance, probability, probability distribution, and statistics with emphasis on writing, projects, and technology. Computer application using Microsoft Excel. (Department credit not given for mathematics majors or minors.)

**112. Precalculus Algebra (3).** Prerequisite: MS 100 with a "C" or better or satisfactory score on ACT/SAT or the departmental placement test. First and second degree equations and inequalities; linear and quadratic functions and graphs; polynomial and rational functions; exponential and logarithmic functions; and systems of equations. (Not open to students with credit in MS 125 or higher.)

**113. Precalculus Trigonometry (3).** Prerequisite: MS 112 with a "C" or better or satisfactory score on ACT/SAT or the departmental placement test. Trigonometric functions and inverses, applications, graphs, identities and equations, laws of sines and cosines, vectors and complex numbers.

**115. Precalculus Algebra and Trigonometry (4).** Prerequisites: MS 112 with a "B" or better or MS 113 with a "C "or better or satisfactory score on ACT/SAT or the departmental placement test. The course is an algebra-trigonometry composite providing the student with a mathematical foundation required for calculus or other courses requiring a similar mathematical background.

**117. Advanced Technical Mathematics I (2).** Prerequisite: MS 112 with a "C" or better or satisfactory score on ACT/SAT or the departmental placement test. Selected topics from: unit conversions, geometry, trigonometry, differential and integral calculus. Applications emphasize solving problems in technology. Open only to students in the Technology program, except by instructor permission. Student cannot receive credit for both this course and TEC 302. (Department credit not given for mathematics majors or minors.)

**119. Advanced Technical Mathematics II (2)** Prerequisite: MS 117 with a "C" or better. Selected topics: unit conversions, geometry, trigonometry, differential and integral calculus. Applications emphasize solving problems in technology. Open only to students in the Technology program, except by instructor permission. Student cannot receive credit for both this course and TEC 302. (Department credit not given for mathematics majors or minors.)

**120. Calculus and Its Applications (3).** Prerequisite: MS 112 with a "C" or better or satisfactory score on ACT/SAT or the departmental placement test. Topics in differential and integral calculus with business applications, functions of several variables, partial derivatives with business applications, Lagrange Multipliers, and multiple integration. (Department credit not given for mathematics majors or minors.)

**125. Calculus I (4).** Prerequisite: MS 113 with a "B" or better or MS 115 with a "C" or better or satisfactory score on ACT/SAT or the departmental placement test. Introduction to analytic geometry, functions and limits, differentiation with applications, antiderivatives, definite integrals, numerical integration, calculus of transcendental functions.

**126. Calculus II (4).** Prerequisite: MS 125 with a "C" or better. Applications of integration, techniques of integration, improper integrals, indeterminate forms, infinite series, vectors in the plane and in 3-space.

**133. Mathematical Concepts I (3).** Prerequisite: MS 112. Preparation for implementation of standards set by the NCTM. Problem solving, set theory, number theory, real number operations, historical development and structure of number systems. (Not open to students with credit in MS 108.) (Enrollment by advisement only.) Two hours lecture and two hours lab.

**134. Mathematical Concepts II (3).** Prerequisites: MS 112 and 133. A thorough study of geometry, measurement, and statistics as recommended by the NCTM. Problem solving and application are emphasized. (Enrollment by advisement only.) Two hours lecture and two hours lab.

**135. Mathematical Concepts III (3).** Prerequisites: MS 112 and 133. Further study in NCTM recommended math content to include logic, probability, principles of counting, algebraic reasoning and representation. (Enrollment by advisement only.) Two hours lecture and two hours lab.

**204. Basic Statistics (3).** Prerequisite: MS 108 or 110 or 112 or satisfactory score on ACT/SAT or the departmental placement test. Numerical descriptive methods, axioms of probability, random variables, statistical inference, point and interval estimation of mean, and hypothesis testing. (Department credit not given for mathematics majors or minors.)

**227. Calculus III (4).** Prerequisite: MS 126 with a "C" or better. Polar coordinates, parametric equations, vector-valued functions, multivariate functions, multiple integrals, vector analysis.

**250. Introduction to Linear Algebra (3).** Prerequisite: MS 113 or 115. Basic theory of linear equations, matrices, real vector spaces, bases, dimension, linear transformations, determinants, eigenvalues, eigenvectors, inner product spaces, and the diagonalization of symmetric matrices.

**300. Introduction to Advanced Mathematics (3).** Prerequisites: MS 126 with a "C" or better. Mathematical writing, including methods of proof, and fundamentals of sets and functions. May also include selected topics in algebra, analysis, number theory, or discrete mathematics.

**302. Applied probability and Statistics (3).** Prerequisite: MS 120 with a "C" or better or MS 125 with a "C" or better. Provides a summary of introductory probability and statistics centered around data analysis examples and computer simulations. Includes discrete and continuous probability distributions, estimation, and hypothesis testing.

**304. Mathematical Statistics I (3).** Prerequisite: MS 126 with a "C" or better. Probability, discrete random variables and their probability distributions, continuous random variables and their probability distributions, estimation and confidence intervals, hypothesis testing, and analysis of enumerative data.

**305. Number Theory (3).** Prerequisite: MS 126 with a "C" or better. An introduction to the principal topics of elementary number theory, including divisibility, linear Diophantine equations, distribution of primes, congruences, Fermat's Theorem, and number theoretic functions.

**309. Combinatorics (3).** Prerequisite: MS 126 with a "C" or better. An introduction to counting techniques such as permutations and combinations, the inclusion-exclusion principle, recurrence relations, and generating functions. May also include topics from graph theory, combinatorial design, and discrete probability.

**322. Selected Survey of Secondary School Mathematics (3).** Prerequisites: MS 112 and 113 or equivalents. For students pursuing certification in mathematics. Overview of secondary school mathematics for prospective and in-service teachers of mathematics. (Department credit not given for mathematics majors or minors.)

**323. College Geometry (3).** Prerequisite: MS 300. Euclidean geometry including synthetic and analytic proofs, geometric constructions, properties of the triangle and circle; an introduction to non-Euclidean geometry.

**331. Peer Educator (1).** Academic credit given to advanced undergraduate students that provide tutorial assistance in the mathematics department. Students will work under the guidance of an experienced mathematics instructor. Permission of department head required. (Department credit not given for mathematics majors or minors. Course graded Pass/Fail.)

**332. Peer Educator (2).** Academic credit given to advanced undergraduate students that provide tutorial assistance in the mathematics department. Students will work under the guidance of an experienced mathematics instructor. Permission of department head required. (Department credit not given for mathematics majors or minors. Course graded Pass/Fail.)

**344. Differential Equations (3**). Prerequisite: MS 126 with a "C" or better. The methods of solving differential equations of first or second order and higher order linear equations, including series solutions and selected applications.

**352. Linear Algebra (3).** Prerequisite: MS 126 with a "C" or better. Matrices, linear systems, vector spaces with emphasis on algebraic structures.

**390. Numerical Analysis (3).** Prerequisites: MS 352 and CS 231 with a "C" or better in both. Numerical analysis and computing with emphasis on methods adaptable to electronic computing machinery.

**399. Study Tour (3).** Topics, excursions, and requirements determined by department. May be duplicated for credit; however, only three (3) credits may be applied toward any major or minor. Infrequently scheduled and subject to minimum and maximum numbers. Advanced deposit required.

**403. Vector Analysis (3).** Prerequisite: MS 227. The algebra and calculus of vectors; applications to geometry, electricity, harmonic functions, and potentials.

**404. Mathematical Statistics II (3).** Prerequisites: MS 227 and 304. A continuation of MS 304. Selected topics from multivariate probability distributions, functions of random variables, approximations to probability distributions, methods of estimation, linear models and least squares estimators, analysis of variance, and non-parametric statistics.

**415. Advanced Calculus I (3).** Prerequisites: MS 227 and 300. Real number system, elementary point set theory, limits, theory of continuous functions, differentiable functions.

**416. Advanced Calculus II (3).** Prerequisite: MS 415. Selected topics from advanced calculus. Elements of partial differentiation including the general theorems, Jacobians. Topics on the theory of integration.

**423. A Survey of Geometries (3).** Prerequisite: MS 323. Selected topics from advanced Euclidean geometry, finite geometries, Non-Euclidean geometry, and other related topics.

**441. Abstract Algebra I (3).** Prerequisites: MS 300 and 352. Algebraic structures, rings, and fields. The axiomatic approach.

**442. Abstract Algebra II (3).** Prerequisite: MS 441. Introduction to group theory and related topics.

**451. Functions of a Complex Variable (3).** Prerequisites: MS 227 and 300 and 415. Fundamental operations with complex numbers, differentiation and integration theorems, mappings, series, and residues.

**475. Senior Seminar in Mathematics (3).** Prerequisite or corequisite: MS 415 or 441 or 451, and senior standing. A capstone course in advanced mathematics. Goals include examining deeply the fundamental ideas of mathematics and connections among various branches of mathematics, exploring the historical development of major concepts, and further developing the habits of mind that define mathematical approaches to problems.

**480. Introductory Topology (3).** Prerequisite: MS 415. Basic topological concepts to include topological spaces, mapping, compactness, connectedness, and separation axioms.

**484. Partial Differential Equations (3).** Prerequisites: MS 227 and 344. Standard methods of solution: separation of variables, Fourier Series, Laplace Transforms. Selected applications.

**499. Undergraduate Research in Mathematics (3).** Prerequisites: MS 302 or 304 or 415 or 441, senior standing, and permission of instructor. A guided independent investigation of a topic outside the department's normal course offerings, to culminate in a written paper and oral presentation to the faculty.

NOTE: Prerequisite for all graduate mathematics courses:

Graduate courses in mathematics are open only to students who

(1) are admitted to a graduate program of study in mathematics, or

(2) are admitted to a graduate program of study in secondary education with a teaching field of mathematics, and with all undergraduate deficiencies in mathematics removed, or

(3) have completed 32 semester hours in mathematics with at least 19 upper division hours. Some individual courses have further prerequisites; see the course descriptions below. Exemptions from course prerequisites require permission of the department head.

**403G. Vector Analysis (3).** Prerequisite: MS 227 and see "Prerequisite for all Mathematics Courses." Algebra and calculus of vectors, Stokes theorem, and divergence theorem; applications to geometry, mass potential functions, electricity, and fluid flow.

**404G. Mathematical Statistics II (3).** Prerequisites: MS 227 and MS 304, and see "Prerequisite for all Mathematics Courses." Continuation of MS 304; selected topics from multivariate probability distributions, functions of random variables, approximations to probability distributions, methods of estimation, linear models and least squares estimators, analysis of variance, and nonparametric statistics.

**416G. Advanced Calculus II (3**). Prerequisite: MS 415 and see "Prerequisite for all Mathematics Courses." Selected topics from advanced calculus; elements of partial differentiation including the general theorems, Jacobians; topics on theory of integration.

**423G. Survey of Geometries (3).** Prerequisite: MS 323 and see "Prerequisite for all Mathematics Courses." Selected topics from advanced Euclidean geometry, finite geometries, non‐Euclidean geometry, and other geometries.

**451G. Functions of a Complex Variable (3).** Prerequisites: MS 227 and MS 300 and MS 415, and see "Prerequisite for all Mathematics Courses." Fundamental operations with complex numbers, differentiation and integration theorems, mapping, series, and residues.

**480G. Introductory Topology (3).** Prerequisite: MS 415 and see "Prerequisite for all Mathematics Courses." Basic topological concepts to include topological spaces, mapping, compactness, connectedness, and separation axioms.

**484G. Partial Differential Equations (3).** Prerequisites: MS 227 and MS 344, and see "Prerequisite for all Mathematics Courses." Standard methods of solution; separation of variables, Fourier Series, Laplace Transforms; selected applications.

**504. Applied Statistical Methods (3).** Prerequisite: See "Prerequisite for all Mathematics Courses." Fundamental concepts of descriptive and inferential statistics, probability distributions, estimation, and hypothesis testing; statistical software packages are used to facilitate valid analysis and interpretation of results; emphasis is on method and selection of proper statistical techniques for analyzing real situations.

**505. Basic Logic and Set Theory (3).** Prerequisite: MS 415 or MS 441, and see "Prerequisite for all Mathematics Courses." Basic topics in symbolic logic and naive set theory, including sets and set operations, symbolic logic, the language of set theory, and applications of set theory.

**515. Real Variables I (3).** Prerequisite: MS 416 or permission of the instructor, and see "Prerequisite for all Mathematics Courses." Selected topics from real analysis with emphasis on functions of one and several variables, measure, and the Riemann and/or Darboux integral.

**516. Real Variables II (3).** Prerequisite: MS 515 and see "Prerequisite for all Mathematics Courses." Selected topics from real analysis emphasizing Lebesgue integration, sequences and series of functions.

**517. Introduction to Functional Analysis (3).** Prerequisites: MS 352 and MS 415 and see "Prerequisite for all Mathematics Courses." Introduction to the fundamental topics of functional analysis. Topics include metric spaces, completeness, linear operators, normed spaces and Banach spaces, inner product spaces, and Hilbert spaces. Objectives include the Riesz Representation Theorem, the Hahn‐Banach Theorem, and the Contraction Mapping Theorem.

**523. Topics in Geometry for Teachers (3).** Prerequisite: See "Prerequisite for all Mathematics Courses." Classical theorems, ideas, and constructions of Euclidean and non‐Euclidean geometry in theorems of Ceva, Menalaus, Pappus, and Feuerbach; homothetic transformations, inversion, harmonic sets of points, and cevians.

**526. Topics in Analytic Geometry for Teachers (3).** Prerequisite: See "Prerequisite for all Mathematics Courses." Applications of Euclidean and homogeneous coordinates, geometric transformations, trigonometric, and vector techniques to geometric problems.

**528. Theory of Equations and Functions for Teachers (3).** Prerequisite: See "Prerequisite for all Mathematics Courses." Topics in the theory of polynomial and other equations, and in the properties of transcendental functions. (The goal is the development of a deeper understanding of the equations and functions commonly encountered in precalculus mathematics.) May require the use of computer software.

**530. Foundations in Calculus for Teachers (3).** Prerequisite: See "Prerequisite for all Mathematics Courses." Theory, problem‐solving techniques, and applications of differential and integral calculus, including the use of graphing calculators and computer software. (Recommended for students that are teaching or planning to teach Advanced Placement Calculus.)

**533. Topics in Modern Analysis for Teachers (3).** Prerequisite: See "Prerequisite for all Mathematics Courses." Logic and set theory, functions and sequences, structure and development of the real number system including completeness.

**535. Topics in Finite Mathematics for Teachers (3).** Prerequisite: See "Prerequisite for all Mathematics Courses." Elementary combinatorial analysis, probability, vectors and matrices, game theory, linear programming, and model building in the social and physical sciences.

**537. Foundations in Algebra for the Secondary Teacher (3**). Prerequisite: MS 441 and see "Prerequisite for all Mathematics Courses." Concepts of high school algebra from the perspective of ring theory.

**541. Abstract Algebra I (3).** Prerequisite: MS 441 and see "Prerequisite for all Mathematics Courses." General group theory including cyclic groups and permutation groups, homomorphism and isomorphism theorems.

**542. Abstract Algebra II (3).** Prerequisite: MS 441 and see "Prerequisite for all Mathematics Courses." Theory of rings, ideals, fields, and integral domains.

**549. Selected Topics in Mathematics for the Secondary Teacher (3).** Prerequisite: See "Prerequisite for all Mathematics Courses." Selected topics suitable for the secondary teacher; problem solving; secondary school mathematics from an advanced standpoint.

**552. Linear Algebra (3).** Prerequisites: MS 352 and MS 441 and see "Prerequisite for all Mathematics Courses." Abstract treatment of finite dimensional vector spaces. Linear transformations, determinants, eigenvalues and eigenvectors, invariant subspaces, Rational and Jordan Canonical Forms, inner product spaces, unitary and normal operators, bilinear forms.

**591. Seminar in Algebra (3) (3).** Prerequisites: MS 541 and MS 542 or permission of instructor and see "Prerequisite for all Mathematics Courses." Selected topics in modern algebra beyond the scope of the graduate algebra sequence. Topics may be chosen from the theory of groups, rings, fields, or modules; linear algebra; homological algebra; or other topics, depending on student and instructor interests.

**595. Seminar in Analysis (3) (3).** Prerequisites: MS 515 and MS 516 or permission of instructor and see "Prerequisite for all Mathematics Courses." Selected topics in modern analysis beyond the scope of the graduate analysis sequence. Topics may be chosen from the fields of real analysis (measure theory and integration, special functions, finite differences, functional equations, sequences and series), complex variables, Fourier and harmonic analysis, integral transforms, operator theory, or other topics, depending on student and instructor interests.

**598. Directed Readings (3) (3).** Prerequisites: Students must have two courses in the topical area chosen and approval by the faculty advisor in mathematics and the instructor and see "Prerequisite for all Mathematics Courses." Algebra, analysis, geometry, and topology.

**599. Thesis (3) (3).** (Grade of Pass or Fail only.) Prerequisite: Approval of Application for Thesis Option. See "Thesis Options and Procedures" in the graduate bulletin.