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# Mathematics: Courses Offered

**105 - Introduction to Finite Mathematics** - The course provides an introduction to several areas of finite mathematics which have numerous applications, particularly in the social sciences. Topics will include decision theory, discrete probability, linear programming, matrices, and linear systems. Three hours. Staff.

**107 - Introduction to Mathematical Modeling** - An introduction to techniques for mathematical modeling of real world phenomena, including a general introduction to several mathematical concepts. Topics include graph theory (including Eulerian and Hamiltonian circuits, scheduling, and graph coloring); notions of scaling in one, two, and three dimensions; basic functions (linear, power, polynomial, rational, exponential, and logarithmic). Applications include optimization algorithms, uninhibited and inhibited growth models, radioactive decay, and amortization of loans. Computer intensive. Three hours. Staff.

**111 - Introduction to Statistics** - An introduction to statistical inference and sufficient probability theory for such an introduction. Topics include elementary data analysis, elementary probability, discrete and continuous random variables, distributions (including the normal distribution), correlation and regression, sampling distributions, point and interval estimation, confidence levels, and tests of significance. Credit will not be awarded for both 111 and 113. Three hours. Staff.

**113 - Introduction to Statistics** - Computer intensive version of Mathematics 111. Credit will not be awarded for both 111 and 113. Three hours. Staff.

**120 - Introductory Logic** - This course serves as an overview of the basic elements of logic and a deeper treatment of logic as a deductive science. Students are expected to analyze statements and arguments in ordinary language and symbolic form, to use truth tables in the analysis of arguments and the classification of statements, and to use techniques of natural deduction to construct proofs of arguments in propositional and predicate logic. Three hours. Bhattacharya.

**123 - Fundamentals of Mathematics** - This course provides a study of several topics in mathematics essential for those students minoring in education. The topics include number systems, number theory, geometry, algebra, probability, statistics, and the history of mathematics. Prerequisites: Completion of EDUC 220 with a grade of C or better. Three hours. Staff.

**131 - Calculus I** - This is a course in differential calculus. Topics to be covered will include: functions; limits and continuity; the definition of the derivative; techniques of differentiation; and applications of the derivative. Note: A working knowledge of high school algebra, geometry, and trigonometry is required for this course. Credit will not be awarded for both 131 and 141. Four hours. Staff.

**132 - Calculus II** - This course is a continuation of Mathematics 131. Topics to be covered will include: the Fundamental Theorem of calculus; techniques of integration; applications of the definite integral; sequences and series. Credit will not be awarded for both 132 and 142. Prerequisite: MATH 131 or 141, or permission of instructor. Four hours. Staff.

**141 - Calculus with Mathematica I** - This is a course in differential calculus. Topics to be covered will include: functions; limits and continuity; the definition of the derivative; techniques of differentiation; and applications of the derivative. Note: A working knowledge of high school algebra, geometry, and trigonometry is required for this course. Mathematica will be used as an aid in graphing and exploring functions, and as an aid in computation. Credit will not be awarded for both 131 and 141. Satisfies CAR – Computing. Four hours. Staff.

**142 - Calculus with Mathematica II** - This course is a continuation of Mathematics 141. Topics to be covered will include: the Fundamental Theorem of calculus; techniques of integration; applications of the definite integral; and sequences and series. Technology will be used to explain the definition of the definite integral, to obtain numerical approximations of definite integrals, to examine the graphs of functions, and to check computations of integrals and derivatives. Credit will not be awarded for both 132 and 142. Satisfies CAR – Computing. Prerequisite: MATH 131 or 141, or permission of instructor. Four hours. Staff.

**199 - Biostatistics** - An introduction to the design and statistical analysis of experiments in the life sciences. An integrated lecture/lab format directs students on how to pose questions in the form of scientific hypotheses, design valid experiments to investigate the questions, and use appropriate statistical techniques to analyze the data. Students will use computer statistical packages for most analyses. Partially satisfies the collegiate mathematics requirement when not combined with statistics courses offered by the mathematics department. For majors/minors in biology and EVST only. Not open to freshmen. Cross-listed as BIOL 350. Computer intensive. Students may not receive credit for successful completion of both MATH 199 and BIOL 350. They may receive a total of six hours credit for successful completion of a combination of MATH 111 and MATH 119/BIOL 350, or MATH 113 and MATH 199/BIOL 350. However, the two statistics classes may not be used together to satisfy the collegiate requirement in mathematics. Same as BIOL 350. Four hours. Gowan.

**203 - Multivariable Calculus** - This course is a continuation of Mathematics 132/142. Topics to be covered will include: vectors; vector valued functions; functions of two or more variables; partial derivatives; multiple integrals; vector fields; Green's Theorem. We will use *Mathematica* as an aid in graphing and exploring mathematical problems. Prerequisite: MATH 132 or 142. Computer intensive. Four hours. B. Torrence.

**213 - Elementary Linear Algebra** - An introduction to the algebra and geometry of three-dimensional Euclidean space and its extension to n-space. Topics include vector algebra and geometry of R3, systems of linear equations, real vector spaces R^{n}, linear transformations on R^{n}, Euclidean spaces and determinants. Prerequisite: MATH 203, or a minimum grade of C– in MATH 132/142. Three hours. Staff.

**220 - Discrete Mathematics** - Boolean algebra and propositional logic with applications. Elements of the theory of directed and undirected graphs. Permutations, combinations, and related combinatorial concepts. The course provides mathematical topics of particular value to students in computer science. Prerequisite: MATH 132 or 142. Three hours. Staff.

**270 - Indian Mathematics: Ancient and Modern** - A study of mathematics from the ancient Vedic era, early applications of the geometry of the Sulvasutras, the invention of zero and the Hindu-Arabic decimal place-value system, medieval Indian algebra and combinatorics, the development of trigonometric series by the Kerala school and the mathematics of Srinivasa Ramanujan. Prerequisites: MATH 132 or 142. Three hours. Bhattacharya.

**307 - Differential Equations: a Modeling Perspective** - An introduction to the theory and application of differential equations, including the development of mathematical models of scientific phenomena. Qualitative, numerical, and analytic tools will be used to analyze these models, and technology will also play a significant role. Topics include modeling via differential equations, analytic and numeric techniques, existence and uniqueness of solutions, equilibria, bifurcations, changing variables, systems of equations, phase planes, and qualitative analysis. Computer intensive. Prerequisite: MATH 132 or 142. Offered alternate years. Three hours. Staff.

**317 - Number Theory** - An introduction to the theory of numbers. Topics covered will include mathematical induction, the division algorithm, the fundamental theorem of arithmetic, the Euler phi-function, congruence, Diophantine equations, the Chinese Remainder Theorem, quadratic residues, the Law of Quadratic Reciprocity, Waring's Problem, and cryptography. Students are expected to learn definitions and theorems in order to solve problems and prove results. Prerequisite: MATH 220. Offered alternate years. Three hours. Rice.

**321 - Modern Algebra** - A study of the basic properties of abstract algebraic structures, including groups, rings, and fields. The course attempts to develop the student's ability to deal with abstract mathematical ideas and proofs, while providing widely used mathematical language and tools. Prerequisite: MATH 220. MATH 213 is recommended but not required. Three hours. Bhattacharya.

**330 - Graph Theory** - This course is an introduction to the theory of graphs. This mathematical theory deals with points and interconnecting lines, and has wide-ranging applications to computer science, operations research, and chemistry, among many other disciplines. Course topics include degree sequences, trees, Eulerian and Hamiltonian graphs, matching, factoring, coloring, planar graphs, connectivity, Menger's Theorem, and networks. Students are expected to prove theorems and understand applications of the material to practical problems. Prerequisite: MATH 220, or permission of the instructor. Three hours. B. Torrence.

**350 - Game Theory** - This course is a mathematical introduction to the subject of game theory. Its prime objective is to equip the student with sufficient skills to solve applied mathematical problems, taken primarily from the realm of economics. Topics covered will include Zermelo's algorithm, lotteries, utility functions, bimatrix games, bargaining, cooperative and noncooperative games, mixed strategies, zero-sum games, and Nash and subgame-perfect equilibriums. Students will be expected to use mathematical definitions, formulae, and techniques to solve game theoretic problems. Prerequisite: MATH 203, or a minimum grade of B- in MATH 132/142. Offered alternate years. Three hours. Rice.

**353 - Complex Analysis** - An introduction to the calculus of analytic functions. The principal topics are complex arithmetic, elementary functions of a complex variable, analyticity, contour integrals, Cauchy's theorem and its applications, and power series. Prerequisite: MATH 203. Offered alternate years. Three hours. Staff.

**360 - Mathematical Logic** - A course intended to introduce students to the concepts of truth, proof, and computability. Major topics of this course include the completeness theorem for first order logic, which shows that the concept of provability (from axioms) can be established; the Gödel incompleteness theorem, which shows there is an inherent gap between what is true (about the whole numbers, for example) and what can be proved about an axiomatic system; and the insolvability of the halting problem, which shows that computers can't do everything. Prerequisite: MATH 120 and MATH 220, or consent of the instructor. Offered on demand. Three hours. Mr. Torrence.

**371 - Probability** - An introduction to combinatorial theory, sample spaces, random variables, and mathematical expectation and probability distributions, including their properties for both the discrete and continuous cases. Prerequisite: MATH 203 or 220. Offered alternate years. Three hours. Sutton.

**372 - Statistical Inference** - The theory and practice of statistical inference. Experimental and statistical design, point estimation, regression and correlation, confidence intervals, and significance tests. Mathematical foundations including the Central Limit Theorem. Prerequisite: MATH 203 (or concurrently). Offered alternate years. Three hours. Sutton.

**391-92 - Independent Study** - An independent exploration of a specialized area in mathematics under the guidance of a member of the department. Prerequisites: permission of the instructor, a cumulative grade point average of 3.25 or greater, and approval of the Committee on the Curriculum. Three hours each. Staff.

**415 - Mathematics Seminar** - This course serves to present mathematics and the mathematician in a variety of contexts. Students will read selections from current mathematical literature. Lectures given by students and guest speakers will present mathematical ideas and lead to discussions. Students will gain experience making presentations, and critiquing mathematical arguments presented by others. Prerequisites: MATH 220 and Senior status. One hour. Staff.

**421 - Real Analysis I** - A first course in the theory of functions of real variables. Topics include axiomatic description of the real number system, topology of Euclidean and metric spaces, limits and continuity, and differentiation. Students are expected not only to learn the material presented but also to construct proofs independently. Prerequisite: MATH 220. Three hours. Staff.

**422 - Real Analysis II** - A continuation of MATH 421. Topics include sequences and series of functions. Riemann-Stieltjes and Lebesgue integration. Prerequisite: MATH 421. Offered as needed. Three hours. Staff.

**435 - Higher Geometry** - The axiomatic method will be used to develop a geometric system. Topics will be chosen from Euclidean geometry, plane hyperbolic geometry, and real projective geometry. This course is of particular value to students who anticipate entering secondary teaching. Prerequisite: MATH 203. Offered alternate years. Three hours. E. Torrence.

**442 - Numerical Analysis** - The mathematical foundations of scientific computing. Numerical methods for the approximation of roots of equations, integrals, and solutions of differential equations. Also included are interpolation and error estimation. Prerequisite: MATH 203. Computer intensive. Offered alternate years. Three hours. Sutton.

**450 - Mathematics Internship** - Students in this course are placed in an appropriate organization (typically a commercial, industrial, government, nonprofit, or research facility) and follow an arranged set of readings relevant to their internship experience. Students will be expected to demonstrate through a written report upon completion of the internship an understanding of the mathematics used and of its utility in context. An application is required. Three hours. Staff.

**451 - Topology** - An introduction to point-set topology. Topics will include topological spaces, metric spaces, continuous mappings, and homeomorphisms. Students are expected to learn basic definitions and theorems, and to construct proofs on their own. Prerequisite: MATH 220. Offered alternate years. Three hours. Clark.

**470 - History of Mathematics** - A study of the historical development of various branches of mathematics, from antiquity to the twentieth century. Topics will include: mathematics in ancient Greece, Islamic mathematics, the development of symbolic algebra, the invention of calculus, and the liberation of algebra and geometry. Students are expected to construct cogent mathematical and historical arguments in essay form. Travel course to Britain. Prerequisite: MATH 203 and ENGL 112, 123, 180, or 185. Offered alternate years. Three hours. Rice.

**487-488 - Departmental Honors I and II** - Offered on demand. Three hours each. Staff.