Mathematics

Kenneth Wiggins, Chair; Jonathan Duncan, Heidi Haynal, Thomas Thompson, Timothy Tiffin.

The Department of Mathematics offers programs leading to the Bachelor of Arts and Bachelor of Science degrees. It is highly recommended that mathematics majors have four years of high school mathematics.

MATHEMATICS MAJOR (Bachelor of Arts)

A student majoring in mathematics must complete 46 quarter hours in the major. In addition, the student must complete the required cognates, the general studies program, and all baccalaureate degree requirements as outlined in this bulletin. Senior students are required to take the Major Field Test (MFT) in mathematics.

Major Requirements:

*Electives must be chosen in consultation with and approved by the academic adviser assigned by the department chair. Credit will not be given toward the major for mathematics courses with numbers below 181. Students seeking a teaching endorsement should consult with the certification officer in the School of Education and Psychology.

Cognate:

MATHEMATICS MAJOR (Bachelor of Science)

A student majoring in mathematics must complete 57 quarter hours in the major, consisting of the core requirements and one of four options. In addition, the student must complete the required cognates, the general studies program, and all baccalaureate degree requirements as outlined in this bulletin. A student contemplating graduate work is encouraged to take a foreign language sequence. Senior students are required to take the Major Field Test (MFT) in mathematics.

Core Requirements:

Cognates:

Actuarial Studies Option

This option prepares the student to take the first actuarial examination. Students preparing for the second examination should consult with their advisers.

Mathematics Preparation for Graduate Study Option

Mathematics Preparation for Secondary Teaching Option

Applied Mathematics Option

*Electives must be chosen in consultation with and approved by the academic adviser assigned by the department chair. Credit will not be given for mathematics courses with numbers below 181. Students seeking a teaching endorsement should consult with the certification officer in the School of Education and Psychology.

MATHEMATICS MINOR

A student minoring in mathematics must complete 28 quarter hours:

Credit will not be given toward the minor for MATH 206, MEDU 395 or for mathematics courses numbered below 181 .

*Electives must be chosen in consultation with and approved by the academic adviser assigned by the department chair.

Because of the unique nature of the professional curriculum of the engineering degree, any mathematics course taken to meet any requirement for the BSE degree is considered a cognate and therefore can be simultaneously counted toward the credit requirements for a mathematics minor.

MINOR IN MATHEMATICS FOR MIDDLE SCHOOL TEACHERS

MATHEMATICS COURSES (MATH)

Students must meet the University entrance requirement in mathematics, pass a departmental placement test, or pass MDEV 003 with a grade of C- or higher before enrolling in mathematics courses numbered above 100. Before enrolling in any mathematics course, students must have grades of C- or higher in all prerequisite courses.

MATH 105 FINITE MATHEMATICS 4

Introduction to mathematics, including algebraic concepts, sets, counting, probability, and descriptive statistics. Additional topics selected from geometry, logic, matrices, linear programming, game theory, mathematics of finance, and stochastic processes. Designed to meet the general studies requirement for the baccalaureate degree, but will not apply toward a major or minor in mathematics. Prerequisite: MDEV 003.or satisfactory departmental placement.

MATH 112, 113 MATHEMATICS FOR ELEMENTARY TEACHERS 3, 3

Study of topics in mathematics, including number theory, geometry, numeration, number systems, graphs, algebra, statistics, and measurements. Designed to meet the general studies requirement for the baccalaureate degree. Will not apply toward a major or minor in mathematics. Must be taken in sequence.

MATH 117 ACCELERATED PRECALCULUS 5

Introduction to college algebra and trigonometry including equations and inequalities; algebraic, exponential, logarithmic, and trigonometric functions; graphs; and complex numbers. Credit will not be allowed for both MATH 117 and MATH 121 or 122. Prerequisite: MDEV 003 or satisfactory departmental placement.

MATH 121 PRECALCULUS MATHEMATICS I 4

Study of college algebra including integers; rational, real, and complex numbers; equations and inequalities; polynomials; algebraic, exponential, and logarithmic functions; and graphs. Credit will not be allowed for both MATH 117 and MATH 121. Prerequisite: MDEV 003 or satisfactory departmental placement.

MATH 122 PRECALCULUS MATHEMATICS II 4

Study of college precalculus including trigonometric functions and graphs; trigonometric identities; matrices; determinants; sequences; mathematical induction; and the binomial theorem. Credit will not be allowed for both MATH 117 and MATH 122. Prerequisite: MATH 121 or satisfactory departmental placement.

MATH 123 SURVEY OF CALCULUS 4

Introduction to calculus, including topics such as functions, limits, derivatives, and integration in one or more variables; applications from business and social sciences. Will not apply toward a major or minor in mathematics. Credit will not be allowed for both MATH 123 and MATH 181. Prerequisite: MATH 117 or 121 or satisfactory departmental placement.

MATH 181 ANALYTIC GEOMETRY AND CALCULUS I 4

Study of functions, limits, continuity, derivatives, definite integrals, and the Fundamental Theorem of Calculus. Credit will not be allowed for both MATH 123 and MATH 181. Prerequisite: MATH 117 or 122 or satisfactory departmental placement. See technology requirements (http://math.wallawalla.edu/).

MATH 206 APPLIED STATISTICS 4

Study of applied statistics, including methods of describing data, distributions, sampling, confidence intervals, hypothesis testing including analysis of variance, correlation and regression. Designed to meet the general studies requirements for the baccalaureate degree, but will not apply toward a major or minor in mathematics. Prerequisite: MDEV 003 or satisfactory departmental placement.

MATH 250 DISCRETE MATHEMATICS 4

Introduction to discrete mathematical structures. Topics include combinatorics, sets, recursion, and graph theory. Prerequisite: MATH 123 or 181.

MATH 281 ANALYTIC GEOMETRY AND CALCULUS II 4

Study of indefinite integrals, calculus of inverse functions, and techniques and applications of integration. Prerequisite: MATH 181. See technology requirements (http://math.wallawalla.edu/).

MATH 282 ANALYTIC GEOMETRY AND CALCULUS III 4

Study of sequences, series, polar coordinates, parametric equations, and vectors. Prerequisite: MATH 281. See technology requirements (http://math.wallawalla.edu/).

MATH 283 ANALYTIC GEOMETRY AND CALCULUS IV 4

Study of differential and integral calculus of multi-variable functions, line and surface integrals, Green's theorem, divergence theorem, and Stokes' theorem. Prerequisite: MATH 282.

MATH 289 LINEAR ALGEBRA AND ITS APPLICATIONS 3

Study of matrices and determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, with applications. Prerequisite: MATH 123 or 181.

MATH 312 ORDINARY DIFFERENTIAL EQUATIONS 4

Study of solutions of first order differential equations, solutions of linear differential equations of order n, applications, linear systems, and series solutions. Prerequisite: MATH 283.

MATH 315 PROBABILITY AND STATISTICS 4

Study of counting and probability, probability distributions and densities, mathematical expectation, functions of random variables, sampling distributions, interval estimation, hypothesis testing, and analysis of variance. Prerequisite: MATH 283.

MATH 316 REGRESSION AND TIME SERIES ANALYSIS 4

Study of simple and multiple linear regression including estimation, hypothesis testing, data analysis, and appropriateness of models. Also includes a study of linear time series models including estimation, data analysis, and forecasting. Prerequisite: MATH 315. Offered even years only.

MATH 319 OPTIMIZATION (or ENGR 419) 4

Modeling and design within a formal optimization environment. Mathematical formulation of optimization problems including decision space paramterization, objective function selection, and constraint definition. Survey of algorithms for unconstrained and constrained optimization; techniques for solving multi-disciplinary and multi-objective problems. Applications to problems in mathematics, physics, and engineering. Prerequisites: MATH 283, MATH 289, CPTR 141, PHYS 253. Offered odd years only.

MATH 321 GEOMETRY 4

Study of geometries, concentrating on Euclidean, non-Euclidean, and projective geometries; examination of axiomatic foundations and qualitative study of the geometries; considers briefly Mohr-Mascheroni constructions and impossible constructions. Prerequisite: MATH 282 or permission of instructor. Offered even years only.

MATH 341 NUMERICAL ANALYSIS 4

Study of numerical methods with computer applications; topics include numerical solutions of nonlinear equations, systems of equations, ordinary differential equations, interpolation, and numerical integration. Prerequisites: MATH 289; MATH 312.

MATH 351 OPERATIONS RESEARCH 4

Introduction to deterministic models in operations research; includes linear programming, network analysis, dynamic programming, and game theory. Prerequisites: MATH 283; MATH 289 or permission of instructor. Offered odd years only.

MATH 360 INTRODUCTION TO THE HISTORY OF MATHEMATICS 4

Introduction to the history of mathematics from the beginning of hieroglyphic writing in Egypt and cuneiform in Mesopotamia to the influence of computers in the 20th century. Topics will include ancient mathematics, geometry and algebra from Greece, mathematics from China, India, and Islam, medieval algebra and geometry, mathematics from the Renaissance and the scientific revolution including analytic geometry and calculus, analysis and algebra through the 19th century, and topics from the 20th century. Prerequisite: MATH 283 or permission of instructor. Offered even years only.

MATH 413 PARTIAL DIFFERENTIAL EQUATIONS 4

Study of partial differential equations, boundary-value problems and Fourier series. Prerequisites: MATH 289, MATH 312. Offered even years only.

MATH 423 COMPLEX ANALYSIS 4

Study of functions of a complex variable, the geometry of elementary functions, integration, power series, calculus of residues, and conformal mapping. Prerequisite: MATH 283. Offered odd years only.

MATH 431, 432 MATHEMATICAL PHYSICS (or PHYS 431, 432) 3, 3

In-depth study of the mathematical foundations of physics and their applications to physical problems. Particular attention is paid to the theory of linear vector spaces in developing tensor analysis group theory and Hilbert Space theory. This course is recommended for students planning to attend graduate school in physics, or having a strong interest in the applications of mathematics to the physical world. Offered odd years only.

MATH 451, 452, 453 ADVANCED CALCULUS 4, 3, 3

Study of functions of one and several variables including continuity, differentiation, integration, infinite series, uniform convergence, and selected topics. Prerequisite: MATH 283. Offered odd years only.

MATH 461, 462, 463 ABSTRACT ALGEBRA 4, 4, 4

Study of groups, rings, fields, vector spaces, linear transformations, selected topics, and applications. Prerequisite: MATH 289. Offered even years only.

MATH 476 PUTNAM PROBLEM SOLVING 1; 2

Topics include problem solving with emphasis on both oral and written communication. This course prepares students for the William Lowell Putnam Mathematical Competition. Students will be required to participate in this competition which is held annually in early December. Prerequisite: Permission of the Department of Mathematics. Graded S or NC.

MATH 494 COOPERATIVE EDUCATION 0

Individual contract involving students, faculty, and cooperating employers which provides the student with practical experiences in an off-campus setting. Graded S or NC. Prerequisites: MATH 283, CDEV 210 or equivalent, minimum cumulative GPA 2.75 in college mathematics courses, minimum cumulative GPA of 2.75 in all college courses, and departmental approval. Open only to mathematics majors.

MATH 496, 497 SEMINAR 1, 1

Includes giving an oral report and writing a scholarly paper on an approved mathematical topic. Prerequisite MATH 451 or 461. Open to Junior/Senior mathematics majors only.

DEVELOPMENTAL MATHEMATICS COURSES (MDEV)

MDEV 001 ELEMENTARY ALGEBRA 4

Designed for students who enter university without having met the mathematics entrance requirement of a one-year course in high school algebra. Topics include fractions, radicals, factoring, linear and quadratic equations, and graphing. Credit does not apply toward graduation. (Course fees apply.)

MDEV 002 ELEMENTARY GEOMETRY 4

Designed for students who enter university without having met the mathematics entrance requirements of a one-year course in high school geometry. Topics include angles, polygons, circles, and triangles. Concepts and techniques of proof are integrated into this course. Credit does not apply toward graduation.

MDEV 003 INTERMEDIATE ALGEBRA 4

Designed for students who enter university without having met the mathematics entrance requirements of a one-year course in high school Algebra II. Topics include sets, numbers, exponents, polynomials, factoring rational algebraic expressions, graphs, first and second degree equations, and inequalities. Credit does not apply toward graduation. (Course fees apply.)

MATHEMATICS EDUCATION COURSES (MEDU)

MEDU 395 METHODS OF TEACHING MATHEMATICS 3

Methods, materials, and techniques of teaching mathematics on the secondary school level; requires observation, demonstration, and class presentation. Will not apply toward General Studies or toward a major or minor in mathematics. Offered odd years only.