Course Descriptions

74 Transition to College Mathematics
Arithmetic and Algebraic operations; number systems and notations; unit conversion; creating and interpreting graphs; basic geometry; other topics requisite for college level mathematics. (Not open to those who have had 75, 76, 80, 81, 85, 139A, or 141A.) One semester, 3 credits.

75 Quantitative Reasoning
This course is designed to help students develop their ability to create, analyze, and communicate quantitative and scientific arguments. It will emphasize critical thinking and problem-solving skills while also giving students practice in computation and symbolic manipulation. Topics to be covered include elementary linear equations, polynomial modeling, working with and understanding graphs and graphical presentations, and elementary probability and statistics. These topics will be presented in the context of applications and models from various disciplines. (Not open to those who have had 81, 85, 139A, or 141A.) Prerequisite: Math 74 or suffi cient score on Math Placement Exam. One semester, 3 credits.

76 College Algebra
Basic properties of real numbers, linear equations and inequalities, quadratic equations,graphs of linear equations, and inequalities, systems of linear equations, conic sections. (Not open to those who have had 81, 85, 139A or 141A.) One semester, 3 credits.

80 Elementary Statistics
Descriptive Statistics: descriptive measures, probability concepts, discrete random variables, normal distribution. Inferential Statistics: sampling distributions, confi dence intervals, hypothesis testing, Chi-square procedures, linear regression. Emphasis on methodology rather than theory. ( Not open to those who have had 315.) Prerequisite: Math 74 or sufficient score on Math Placement Exam. One semester, 3 credits.

81 Mathematics for the Management Sciences
Functions, matrices, linear systems, linear programming, logarithmic and exponential functions, limits, differential calculus. Prerequisite: Math 76 or suffi cient score on math placement exam. (Not open to those who have had 85, 139A or 141A) One semester, 3 credits.

85 Precalculus Mathematics
Solutions of algebraic equations and inequalities; functions and graphs; exponential, logarithmic and trigonometric functions; plane analytic geometry. Recommended for those who plan to take the Calculus sequence but who did not score sufficiently high on the Math Placement Exam. (Not open to those who have had 81, 139A or 141A.) Prerequisite: Math 76 or suffi cient score on Math Placement Exam. One semester, 3 credits.

139 A, B Integrated Precalculus/Calculus
Calculus I with a review of Precalculus. Topics include: functions of one real variable and their graphs, various types of functions (polynomials, rational functions, exponential, logarithmic, trigonometric, and discrete functions) derivatives of these functions, applications of derivatives, introduction to integrals of functions, Riemann Sums. Prerequisite: 85 or suffi cient score on Math Placement Exam. Fall, 4 credits, January, 3
credits.

141 A, B Calculus and Analytic Geometry I-II
Unified course in analytic geometry and calculus: progresses from functions of one real variable, their derivatives and integrals, through multivariate calculus; topics from infi nite series and differential equations. Prerequisite: 85 or suffi cient score on Math Placement Exam. One semester, 4 credits each.

220* Discrete Mathematics
Sequences; recursion and recurrence relations; finite-state automata; elementary set theory; graphs and trees; elementary probability and combinatorics. Prerequisite: Suffi cient score on
Math Placement Exam. One semester, 3 credits.

241 Calculus and Analytic Geometry III
Continuation of 141 A, B. Unifi ed course in analytic geometry and calculus: progresses from functions of one real variable, their derivatives and integrals, through multivariate calculus; topics from infi nite series and differential equations. Prerequisite: 141 B. One
semester, 4 credits.

280 Abstract Thinking
Designed to bridge the gap between lower-and upper-division mathematics courses. Deals with sets, applications of logic, propositional and predicate calculus, techniques of mathematical proofs, relations, functions, number systems, mathematical induction, algebraic structures. Prerequisite: 141A,B. One semester, 3 credits.

305* Number Theory
Euclidean algorithm; fundamental theorem of arithmetic; multiplicative functions; congruences; Chinese remainder theorem; Euler, Fermat, Wilson, and Lagrange's theorems; diophantine equations. Prerequisites: 141B, 280. One semester, 3 credits.

315* Probability and Statistics
Continuous random variables and their probability distributions, marginal and conditional probability distributions, functions of random variables, the Central Limit theorem, stimations; the method of maximum likelihood; hypothesis testing, power of tests, The Neyman - Pearson lemma, regression, linear statistical models, method of least squares.
Prerequisite: 241. One semester, 3 credits.

320* Advanced Geometry
Hilbert's axioms for Euclidean geometry; non-Euclidean geometries; finite geometries; isometries in the Euclidean plane. Prerequisite: 141B, 280. One semester, 3 credits.

344* Complex Variables
Algebra of complex numbers, theory and applications of functions of complex variables, contour integrals, conformal mappings, and boundary value problems. Prerequisite: 241. One semester, 3 credits.

345* A, B Differential Equations I, II
The theory of fi rst-and second-order ordinary differential equations including their series solutions, introduction to Laplace Transforms with applications, including the solutions of differential equations, systems of ordinary linear differential equations, introduction to Fourier Series and integrals with applications, difference equations, partial differential equations with applications, introduction to the boundary and initial value problems and their applications. Also other selected topics in ordinary and partial differential equations depending on the particular emphases of the students in the class. Prerequisite: 241 or concurrent enrollment. One semester, 3 credits each.

350* Numerical Analysis
Numerical solutions of non-linear equations; interpolation; curve fi tting; and estimation of error. Prerequisites: 141B. One semester, 3 credits.

354* Mathematical Modeling
Formulation and evaluation of models; continuous and stochastic models; sources of error; accuracy, precision and robustness; mathematical techniques used in modeling; analytical and numeric solutions; optimization. Prerequisites: 141B. One semester, 3 credits.

360* Point Set Topology
Metric spaces, sequences, continuity, connectedness, product spaces, separation axioms, compactness, topological spaces. Prerequisite: 241, 280. One semester, 3 credits.

380* Linear Algebra
Vector spaces, linear transformations, similarity, eigenvectors, diagonalization, quadratic forms. Prerequisites: 141B, 280. One semester, 3 credits.

400* History of Mathematics
Selected topics in the development of mathematics will be discussed. A good background in mathematics is needed. Prerequisite: 141B. One semester, 3 credits.

440* A, B Introduction to Analysis I, II
Topology of the Reals and Euclidean n-space; compact sets; Heine-Borel and Bolzano-Weierstrass Theorems; connected sets; mappings; continuity and uniform continuity; differentiability; uniform convergence; power series; Inverse Function Theorem; Implicit Function Theorem; Integration. Prerequisite: 241, 280. One semester, 3 credits each.

480* A,B Modern Algebra I,II
Sets, mappings, relations, operations, algebraic structures (groups, rings, fields, modules), homomorphisms, substructures, quotient structures, finite fields, field extensions, proof of impossibility of some geometric constructions using only compass and ruler, Galois Correspondence. Prerequisite: 141B and 280. One semester, 3 credits each.

491 A,B Senior Seminar
Develops the student's ability to learn mathematics independently and to write for a mathematical audience. Includes a signifi cant expository or research paper and a public presentation. Must be taken in the fall semester of the senior year. Permission required. Fall 1 credit, January 3 credits.

190, 290, 390, 490* Selected Topics in Mathematics
Subject of current importance in mathematics. May be repeated for credit. Variable time and
credit.

295, 395, 495 Independent Studies
Credit and time arranged. Permission. May be repeated for credit. Variable credit.

COMPUTER SCIENCE COURSE DESCRIPTIONS (COSC)


120 Computer Science I
Introduction to computer programming in a high-level language such as C, C++ or Java, emphasizing structured programming techniques, procedural methods and simple userdefined data structures. One semester, 3 credits.

220 Computer Science II
Computer programming emphasizing data structures, algorithms, pointers and low-level interface. Prerequisite: 120. One semester, 3 credits.

190, 290, 390, 490 Selected Topics in Computer Science
Variable credits. Permission. May be repeated for credit.

295, 395, 495 Independent Studies
Credit and time arranged. Permission. May be repeated for credit.

*Not offered every year.