2004 - 2005 Mathematics Course Descriptions

MATH

085

Prealgebra

(3)

Operations with fractions, decimals, and signed numbers; percents; introduction to algebraic expressions, solving equations, and graphing; geometry and measures. No prerequisite.

MATH

095

Elementary Algebra

(3)

Properties of real numbers, variables, exponents, equations, and operations with algebraic expressions, including factoring, solving linear equations and inequalities, graphing. Prerequisite: MATH 085 or placement test.

MATH

105

Intermediate Algebra

(3)

The real numbers, algebraic expressions and functions, polynomial operations and factoring, complex numbers, solutions of equations and inequalities including the quadratic formula, systems of equations, and graphs. Prerequisite: MATH 095 or placement test.

MATH

120

Quantitative Reasoning

(4)

An introduction to contemporary mathematics through a survey of several practical and interesting uses of mathematics in society, including topics in logic, geometry, probability and statistics, with some attention given to historical background. Prerequisite: MATH 105 or placement test.

MATH

141

College Algebra

(4)

A study of equations and inequalities, graphs and functions including polynomials, rational functions, exponential and logarithmic functions; conic sections, systems of equations and matrices. Prerequisite: MATH 105 or placement test.

MATH

142

Trigonometry

(2)

The study of trigonometric functions, their graphs, and applications: navigation and surveying problems, modeling cyclic behavior, complex numbers, polar coordinates, and vectors. Prerequisite: MATH 141 or placement test.

MATH

150

Elementary Statistics

(4)

An introduction to the use of statistics as a valuable tool for analyzing data in a variety of fields. Includes topics in elementary descriptive and inferential statistics, including the normal distribution, correlation, regression, and testing hypotheses. Prerequisite: MATH 105 or placement test.

MATH

200/300

Special Topics

(1-4)

Prerequisite: consent of mathematics faculty. Offered on sufficient demand.

MATH

201-202

Calculus I and II

(4,4)

Processes of differentiation and integration of algebraic, trigonometric, exponential, and logarithmic functions; applications to geometry, physical and life sciences, and economics; limits; sequences and series. Prerequisite: MATH 142 or placement test. MATH 201 is a prerequisite for MATH 202.

MATH

204

Linear Algebra and Differential Equations

(4)

Topics from both fields, emphasizing geometric and qualitative properties; includes an introduction to vectors, dot products, orthogonality, matrix operations, existence and uniqueness of solutions to differential equations. Prerequisite: MATH 202. Offered every Fall Semester.

MATH

210

Discrete Mathematics

(3)

Topics in sets, logic, elementary counting including permutations and combinations, finite probability, sequences and mathematical induction. Prerequisite: MATH 201. Offered every semester.

MATH

303

Multivariate Calculus

(4)

Topics include vector functions, partial derivatives, multiple integrals, the gradient, divergence, and curl of vector functions, and theorems from vector calculus. Prerequisite: MATH 204. Offered every Spring Semester.

MATH

308

Putnam Seminar

(1)

Preparation for taking the national Putnam exam, given each December. Students will practice solving problems from previous exams and making presentations to the class. Prerequisites: MATH 204, 210, junior or senior standing or consent of instructor. Offered every fall semester.

MATH

310

Probability and Statistics

(4)

Mathematical treatment of selected topics from statistics, including introduction to theory of probability, binomial and normal distributions, sampling theory, correlation, and regression analysis. Prerequisites: MATH 202, 210. Offered Fall Semester 2007.

MATH

311

Linear Algebra II

(4)

Vector spaces, basis, dimension; theory of matrices, rank, systems of equations, determinants; linear transformations, change of basis, characteristic value problems, quadratic forms. Prerequisites: MATH 204, 210, 303. Offered Fall Semester 2004.

MATH

312

Abstract Algebra

(4)

Sets, relations, and functions. Introduction to theory of groups, rings, and fields. Prerequisites: MATH 202; 210, or the equivalent. Offered every Spring Semester.

MATH

314

Foundations of Geometry

(4)

Modern axiomatic development of plane geometry and related systems. Includes investigation of finite geometry and hyperbolic geometry. Prerequisites: MATH 202, 210. Offered Fall Semester 2004.

MATH

321

Advanced Calculus

(4)

Topics include the theory of limits, properties of real numbers, properties of continuous functions, uniform convergence, completeness of metric spaces, the Riemann integral, implicit and inverse function theorems, calculus of several variables, geometry of curves and surfaces, and vector calculus. Prerequisites: MATH 210, 303 and junior or senior status. Offered every Fall Semester.

MATH

323

Real and Complex Analysis

(3)

Topics include integration theory, sequences and series (complex and real), contour integration, analytic functions, and conformal mappings, with some applications to partial differential equations. Prerequisite: MATH 321. Offered Spring Semester 2006.

MATH

340

History of Mathematics

(3)

A survey of the history of mathematics, from antiquity to the modern period. Prerequisites: MATH 204, 210. Offered every Spring Semester.

MATH

350

Methods of Teaching Secondary School Mathematics

(2)

Credit does not apply towards academic major or minor. Prerequisite: Admittance into Elementary or Secondary Education Program; junior or senior standing. Offered every Fall Semester.

MATH

360

Discrete Mathematics II

(4)

Further study of topics introduced in MATH 210, including recurrence relations, combinatories, algorithm analysis, and graph theory. Additional topics are finite automata theory, stochastic processes, neural networks, Boolean algebras, and formal languages. Prerequisite: MATH 210, CMPT 201. Offered Spring Semester 2005.

MATH

362

Numerical Analysis

(4)

Solution of nonlinear equations and linear systems, interpolation and approximation, and numerical differentiation and integration. Students will be expected to program some problems for computer solutions. Prerequisites: MATH 210, 303; CMPT 201. Same as CMPT 362. Offered Spring Semester 2006.

MATH

363

Differential Equations II

(4)

Topics include a review of methods for solving linear systems; non-linear systems, Laplace transform cd power series methods of solving equations; topics from partial differential equations; heat equation, Laplace's equation, wave equation, and Fourier series methods. Prerequisites: MATH 204, 210, 303. Offered Fall Semester 2005.

MATH

387

Undergraduate Teaching

(1-1)

For teaching assistants in lower division mathematics problem-solving courses. A maximum of two credit hours of MATH 387 may be applied toward the major or minor. Prerequisite: consent of program director.

MATH

401

Directed Studies

(1-4)

A tutorial-based course used only for student-initiated proposals for intensive individual study of topics not otherwise offered in the Mathematics Program. Prerequisites: junior or senior standing and consent of instructor and school dean.

MATH

440

Internship

(1-8)

Offers students the opportunity to integrate classroom knowledge with practical experience. Prerequisites: junior or senior standing (for transfer students, at least 15 hours completed at Westminster), minimum 2.5 GPA, completion of the Career Resource Center Internship Workshop, and consent of program director and Career Center Internship Coordinator.