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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.