## Courses in Mathematics

** 1301. Euclidean and Non-Euclidean Geometries. ** Development of the mathematical way of thinking through firsthand experience. Emphasis
on the students strengthening of his or her imagination, deductive powers, and ability
to use language precisely and efficiently. Study of Euclid's geometry; Hilbert's axioms;
neutral geometry; hyperbolic geometry (non-Euclidean geometry of Gauss, Bolyai, Lobachevsky);
the axiomatic method; and consistency, independence and completeness of axiom systems.
Historical perspective and philosophical implications are included. Students must
prove a significant number of theorems on their own. Fall and Spring.

** 1303. Precalculus. ** Advanced algebra and trigonometry needed for Calculus. Solving equations and inequalities;
polynomials; functions; trigonometry on the unit circle; parametric and polar coordinates;
conic sections; arithmetic and geometric sequences; math induction. Prerequisite:
successful placement in algebra. Fall.

** 1404. Calculus I. ** Limits, derivatives, applications of derivatives, integration, logarithmic and exponential
functions. Prerequisite: Grade of C (2.0) or better in Mathematics 1303, or satisfactory
placement. Fall and Spring.

** 1411. Calculus II. ** L'Hopitals Rule, inverse trigonometric and hyperbolic functions, methods of integration,
analytic geometry, applications of integrals, sequences and series. Prerequisite:
Grade of C (2.0) or better in Mathematics 1404, or satisfactory placement. Fall and
Spring.

** 2107. Mathematics Colloquium. ** A forum for exposing students to the rich and deep areas of mathematics and its applications
not normally seen in the first two years of undergraduate studies. Oral presentations
are selected for their interest and accessibility. Speakers include faculty members,
visiting lecturers, and students. Highly recommended for majors. Visitors are welcome.
Public announcements of speakers will be made. Graded Pass/No Pass. May be repeated.
Fall and Spring.

** 2304. Discrete Mathematics. ** Introduction to the mathematical foundation of computer science with two co-equal
components: a study of combinatorics and graph theory including topics from the theory
of computer science, and a development of the imagination and analytical skills required
in mathematics and computing science. Students are required to do proofs. Prerequisite:
MCS 2410. Offered as needed.

** 2305. Introduction to Statistics. ** Statistics may be broadly defined as the science of making rational decisions in
the face of quantifiable uncertainty. Emphasis on a deep understanding of the fundamental
elements of so-called "statistical thinking", including randomness, uncertainty, modeling,
and decision processes. The superstructure of statistical methodology, including hypothesis
testing, inference, and estimation, using the logical methods of mathematics. A significant
amount of instruction is computer-based. Prerequisite: Successful demonstration of
abilities in algebra. Fall and Spring.

** 2412. Calculus III. ** Vectors, vector calculus, functions of several variables, multiple integrals. Prerequisite:
Grade of C (2.0) or better in Mathematics 1411, or satisfactory placement. Fall.

** 3107. Mathematics Colloquium. ** This course is similar to 2107 except that extra work is required to earn junior-level
credit. Each student is expected to write a paper and present a talk based on it in
addition to fulfilling the other requirements. Graded Pass/No Pass. May be repeated.
Fall and Spring.

**3159. Junior Workshop.** This course is designed to improve the student's ability to "do math at the board"
and to encourage a willingness to engage mathematical problems creatively. Emphasis
is on generating ideas for solving problems and then testing those ideas to see if
they bear fruit. Problems given are often open-ended and may lack a published solution
so as to encourage creative approaches. Fall.

**3190. Problem Solving. **This course presents many problem-solving techniques not typically found in other
mathematics courses. Emphasis is on problems from competitions, but the techniques
have broad application for creatively thinking through many sorts of problems. Problems
are drawn from many different fields of mathematics, yet very accessible to any student
with an interest in math. Prerequisite: MAT 1404 or consent of instructor. Fall. Repeatable
for credit.

** 3310. Linear Algebra. ** Geometry of R^{2} and R^{3} including the dot product and parametric equations of lines and planes. Systems of
linear equations, matrices, determinants, vector spaces, and linear transformations.
Applications to the sciences and economics are included. Prerequisite: Mathematics
1411 or consent of instructor. Fall.

** 3320. Foundations of Geometry. ** A systematic development of topics selected from metric and nonmetric geometries,
comparison of postulate systems. Prerequisite: Mathematics 1411 or consent of instructor.
Offered as needed.

** 3321. Linear Point Set Theory. ** Limit points, convergent sequences, compact sets, connected sets, dense sets, nowhere
dense sets, separable sets. Prerequisite: Mathematics 1411 or consent of instructor.
Fall and Spring.

** 3322. History and Philosophy of Mathematics. ** The history of the development of mathematics, the lives and ideas of noted mathematicians.
Prerequisite: Consent of instructor. Offered as needed.

** 3324. Differential Equations. ** First order equations, existence and uniqueness of solutions, differential equations
of higher order, Laplace transforms, systems of differential equations. Prerequisite:
Mathematics 1411 or consent of instructor. Fall, even years.

**3325. Complex Analysis.** An analysis of functions defined on complex numbers. Topics include holomorphic
functions, contour integrals and Cauchy's theorem, power and Laurent series, residues
and poles, and conformal mapping. Applications to physics are included. Prerequisite:
Mathematics 2421. Offered as needed.

3326. **Probability. ** Axioms and basic properties, random variables, univariate probability functions and
density functions, moments, standard distributions, law of large numbers, and central
limit theorem. Prerequisite: Mathematics 1411. Fall, odd years.

** 3327. Statistics. ** Sampling, tests of hypotheses, estimation, linear models, and regression. Prerequisite:
Mathematics 3326. Spring, even years.

**3331. Number Theory. **A study of the properties of the integers. Topics include divisibility and primes,
congruences, Euler's theorem, primitive roots, and quadratic reciprocity. Prerequisite:
Mathematics 3321 or consent of instructor. Spring, even years.

** 3338. Numerical Analysis. ** Zeros of polynomials, difference equations, systems of equations, numerical differentiation
and integration, numerical solution of differential equations, eigenvalues and eigenvectors.
Prerequisite: Mathematics 3310 and knowledge of a programming language. Offered as
needed.

** 3V50. Special Topics. ** Gives the student an opportunity to pursue special studies not otherwise offered.
Topics have included chaos, fractals, combinatorics, differential geometry, surreal
numbers and dynamical systems. May be repeated for credit. Prerequisite: consent
of instructor.

**4095. Mathematics Senior Comps. **A comprehensive exam is required of all majors in their final year. It is administered
by the mathematics faculty and covers all required courses for the B.A. or B.S. degree.
The exam is offered once in the Fall semester and twice in the Spring semester.

**4314**. **Advanced Multivariable Analysis. ** Continuous and differential functions from R^{m} into R^{n}, integration, differential forms, Stokes' theorem. Prerequisite: Mathematics 2412
and 3310, or consent of instructor. Offered as needed.

**4315. Applied Mathematics. **Symmetric linear systems, equilibrium equations of the discrete and continuous cases,
Fourier series, the heat and wave equations and boundary value problems. Prerequisite: Math 2412. Spring, odd years.

** 4332. Abstract Algebra I. **Group theory, including homomorphisms, normal subgroups, quotient groups, direct products,
and symmetric groups; and an introduction ring theory including integral domains,
fields, ideals, and polynomial rings. Prerequisite: Mathematics 3310, 3321, and
junior standing, or consent of instructor. Fall, even years.

**4333. Abstract Algebra II. ** A continuation of MAT 4332. Topics are chosen by the instructor and may include
vector spaces, field theory including Galois theory, field extensions and splitting
fields, group actions and the Sylow theorems, and module theory. Prerequisite: Mathematics
4332 and junior standing, or consent of instructor. Spring, odd years.

** 4334. Topology. ** Topological spaces, connectedness, compactness, continuity, separation, metric spaces,
complete metric spaces, product spaces. Prerequisite: Mathematics 3321 or consent
of instructor. Spring, odd years.

**4341.Analysis I. **The real and complex number systems, topology of the real line, convergent sequences
and series, and continuity. Prerequisite: Mathematics 1411 and 3321, or consent
of instructor. Fall, odd years.

**4342. Analysis II. **A continuation of MAT 4341. Differentiation, the Stieltjes integral, sequences of
functions and uniform convergence and series of functions, including power and Taylor
series. Prerequisite: Mathematics 4341 or consent of instructor. Spring, even years.

** 4V43-4V44. Research. ** Under the supervision of a member of the faculty, the student involves himself or
herself in the investigation and/or creation of some areas of mathematics. The research
should be original to the student. A paper is required. Prerequisite: junior or senior
standing.

** 4V61. Independent Studies. ** An opportunity for the student to examine in depth any topic within the field under
the guidance of the instructor. For advanced students.