300 level course descriptions

Math 300 Computational Problem Solving (4)
Prerequisite: Math 121 or approval of instructor. This course will utilize a Scheme programming environment to teach student how to solve a broad range of Mathematical problems.

Math 305/605 Real Analysis I (3)
Prerequisite: Math 221. Introduction to analysis. Real numbers, limits, continuity, uniform continuity, sequences and series, compactness, convergence, Riemann integration. An in-depth treatment of the concepts underlying calculus.

Math 307 Introduction to Probability (3)
Prerequisite: Math 221 or equivalent. An introduction to probability theory. Counting methods, conditional probability and independence. Discrete and continuous distributions, expected value, joint distributions and limit theorems. Prepares student for future work in probability and statistics.

Math 308 Introduction to Statistical Inference (3)
Prerequisite: Math 221, Math 307. Basics of Statistical inference. Sampling distributions, parameter estimation, hypothesis testing, optimal estimates and tests. Maximum likelihood estimates and likelihood ratio tests. Data summary methods, categorical data analysis. Analysis of variance and introduction to linear regression.

Math 309/609 Linear Algebra (4)
Prerequisite: Math 221. An introduction to linear algebra emphasizing matrices and their applications. Gaussian elimination, determinants, vector spaces and linear transformations, orthogonality and projections, eigenvector problems, diagonalizability, Spectral Theorem, quadratic forms, applications. MATLAB is used as a computational tool.

Math 311/611 Abstract Algebra I (3)
Prerequisite: Math 221. An introduction to abstract algebra. Elementary number theory and congruences. Basic group theory: groups, subgroups, normality, quotient groups, permutation groups. Ring theory: polynomial rings, unique factorization domains, elementary ideal theory. Introduction to field theory.

Math 314 Experimental Mathematics(3)

Prerequisites: The class will be made available to any student that has completed the Calculus sequence: Math121,122, 221. The exploration of Mathematical tools in Symbolic Languages. Examples are taken from Calculus, Differential Equations and Linear Algebra.

Math 320 Combinatorics (3)
Prerequisites: Math 121, 122, and either 221 or 309 or approval of instructor. Basics of combinatorics with emphasis on problem solving. Provability, pigeonhole principle, Mathematical induction. Counting techniques, generating functions, recurrence relations, Polya’s counting formula, a theorem of Ramsey.

Prerequisites: Math 217 or equivalent. Introduction to the theory of computation: Formal languages, finite automata and regular languages, deterministic and nondeterministic computation, context-free grammars, languages, and pushdown automata. Turing machines, undecidable problems, recursion theorem, computational complexity, NP-completeness..

Prerequisites: Math 305 or Math 311 or Math 320. Also, students who have taken neither Math 217 or Math 320 should talk with the instructor before registering for the course. A study of important algorithms (including searching and sorting, graph/network algorithms, and algorithms in number theory) and algorithm design techniques (including greedy, recursive, and probabilistic algorithms). Covers the analysis of algorithms (including worst- and average-case analysis) and discussion of complexity classes for decision and enumeration problems (including P, NP, #P, PSPACE).

Prerequisites: Math 221, 224, and Computer Science 101 or equivalent. Errors. Curve fitting and function approximation, least squares approximation, orthogonal polynomials, trigonometric polynomial approximation. Direct methods for linear equations. Iterative methods for nonlinear equations and systems of nonlinear equations. Interpolation by polynomials and piecewise polynomials. Numerical integration. Single-step and multi-step methods for initial-value problems for ordinary differential equations, variable step size. Current algorithms and software.

Math 365 Number Theory and Applications (3)
The subject of number theory is one of the oldest in Mathematics. The course will cover some basic material and describe interesting applications. One of the recurrent themes is the realization that Mathematics that was developed usually for its own sake, has found applications in many unexpected problems. Some of the topics covered in the class are Pythagorean triples, prime numbers, divisibility and the highest common divisor, linear diophantine equations, congruences, round-robin tournaments and perpetual calendars, multiple functions, perfect numbers, primitive roots, pseudo-random numbers, decimal fractions and continued fractions, quadratic reciprocity.

Math 398-399 Seminar in Mathematics (1, 3)
Prerequisites: Math 305, 309, and two additional courses at the 300-level or above. Under faculty guidance, students will select a topic in current Mathematical research, write an expository article on that topic, and give an oral presentation. This seminar is required of all Mathematics majors who are not doing an Honors Project within the department. Completion of 398 and 399 fulfills the college writing requirement.

300 level courses