Willamette University

900 State Street

Salem, Oregon 97301

503-370-6300 voice

The course will offer students the opportunity to solve challenging mathematical problems unlike standard homework problems in any course. Class time will be spent studying problems, discovering solutions, writing up solutions formally, and discussing the important ideas of each solution. Most problems will be of the kind appearing on the Putnam Exam, an annual international mathematics competition. This course may be repeated for credit.

**Offering:**Fall**Instructor:**Staff

A survey of contemporary topics in mathematics such as: voting systems and power, apportionment, fair division of divisible and indivisible assets, efficient distribution, scheduling and routing, growth and decay in nature and economics, symmetry and fractal geometry, probability and statistics. MATH 130 may not be taken for credit after any Mathematics course numbered above 140 has been completed.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning (*)

**Offering:**Every semester**Instructor:**Staff

This course is an introduction to descriptive and inferential statistical analysis. The following topics will be examined: scales of measurement; frequency distributions; graphing data; measures of central tendency, dispersion and skewness; sampling distributions; probability distributions; the binomial, Poisson and normal distributions; hypothesis testing; confidence intervals and interval estimation; t-tests; analysis of variance; correlational analysis; regression analysis; and analysis of nominal-level data.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning (*)

**Offering:**Every semester**Instructor:**Staff

A first course in calculus-differential and integral calculus of algebraic and exponential functions, with applications. (MATH 141 counts for only .5 credit if the student has completed MATH 139 Brief Calculus.)

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning (*)

**Prerequisite:** Placement exam required (high school math beyond Algebra II recommended)

**Offering:**Every semester**Instructor:**Staff

A second course in calculus: review of differential and integral calculus via trigonometric and logarithmic functions, techniques and applications of integration, polar coordinates and parametric equations, infinite series.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning (*)

**Prerequisite:** MATH 141 or placement exam (previous Calculus experience required)

**Offering:**Every semester**Instructor:**Staff

Introduction to basic techniques and modes of reasoning in combinatorial problem-solving. Topics will be chosen from combinatorial mathematics, logic and Boolean algebra, difference equations, graph theory and applied algebra.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning*

**Offering:**Spring**Instructor:**Staff

The objective of the course is to present mathematics in a format that prepares teachers to teach elementary school mathematics. Teachers need a firm foundation in the theory of mathematics as it pertains to the elementary school curriculum. They also need ideas and methods for teaching that will generate interest and enthusiasm among the students. Topics to be covered will include problem solving, mathematics as a method of communication, mathematics as a method of reasoning, and specifics of elementary school mathematics such as whole number operations, geometry and spatial sense, measurement and estimation, fractions and decimals, and patterns and relationships.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning

**Prerequisite:** Previous or concurrent enrollment in EDUC 305 or consent of instructor

**Offering:**On demand**Instructor:**Prothero

Three-dimensional analytic geometry; partial differentiation; maxima-minima problems; multiple integrals; vector fields, curl and divergence; line and surface integrals; applications.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning (*)

**Prerequisite:** MATH 142

**Offering:**Every semester**Instructor:**Staff

This course is intended as the first course after calculus for those students intending to major or minor in mathematics. It provides an introduction to logic and the methods of proof commonly used in mathematics. Applications covered in the course are the foundations of set theory, the real number system, elementary number theory and other basic areas of mathematics.

**General Studies Requirement Fulfillment:** Writing centered

**Prerequisite:** One year of college calculus credit

**Offering:**Every semester**Instructor:**Staff

Systems of linear equations, matrices, vector spaces and linear transformations.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning

**Prerequisite:** MATH 251

**Offering:**Every semester**Instructor:**Staff

Elementary differential equations; linear differential equations of second order; Laplace transformations; infinite series solutions; systems of linear differential equations.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning

**Prerequisite:** MATH 249. MATH 253 recommended.

**Offering:**Fall**Instructor:**Staff

Introduction to basic techniques and modes of reasoning in combinatorial problem-solving. Topics will be chosen from combinatorial mathematics, logic and Boolean algebra, difference equations, graph theory and applied algebra.

**Mode of Inquiry:** Quantitative and Analytical Reasoning

**Prerequisite:** MATH 251

**Offering:**Spring**Instructor:**Staff

The objective of this course is to present mathematics in a format that prepares teachers to teach mathematics in the public schools. Teachers need a firm foundation in the theory of mathematics as it pertains to their particular curricula. They also need ideas and methods for teaching that will generate interest and enthusiasm among the students. The course will emphasize mathematics as a method of communication and reasoning. Topics selected to be relevant to elementary, middle, and/or high school curricula will depend on the interests of the students, but will have a strong problem-solving emphasis. The course will require an extensive early field experience in the public school classroom.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning

**Prerequisite:** Previous or concurrent enrollment in EDUC 305 or consent of instructor

**Offering:**On demand**Instructor:**Prothero

Complex numbers, limits, differentiation, analytic functions, integration, conformal mapping, Riemann surfaces and applications.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning

**Prerequisite:** MATH 249

**Offering:**Alternate years in fall**Instructor:**Staff

Application of numerical methods to the solution of mathematical problems. Numerical differentiation, integration and the solution of differential equations.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning

**Prerequisite:** MATH 251 plus MATH 253 or MATH 256 and experience in computer programming

**Offering:**On demand**Instructor:**Staff

An introduction to the theory of numbers to include such topics as divisibility, congruence, diophantine equations, quadratic reciprocity, the theory of prime numbers and analytic number theory.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning

**Prerequisite:** MATH 251

**Offering:**Alternate years in spring**Instructor:**Staff

Formulation of problems in mathematical terms, solutions of the problems, interpretation and evaluation of the solutions. Topics will be chosen from inventory problems, growth and survival models, linear programming, scheduling, Markov chains, game theory and queuing problems.

**General Studies Requirement Fulfillment:** Quantitative and Analytical Reasoning

**Prerequisite:** MATH 253 or consent of instructor

**Offering:**On demand**Instructor:**Staff

A study of the concepts of calculus from an advanced standpoint. Includes the real numbers, real valued functions, differentiation and integration, vector valued functions, line and surface integrals. Other topics may be chosen from point set topology, measure and integration, differential geometry and calculus of variations.

**Prerequisite:** MATH 253 or consent of instructor

**Offering:**Twice every five semesters**Instructor:**Staff

Number systems, elementary number theory, groups, rings, fields, polynomials and applications. Additional topics may be chosen from linear algebra, multilinear algebra, Sylow theory and Galois theory.

**Prerequisite:** MATH 253 or consent of instructor

**Offering:**Twice every five semesters**Instructor:**Staff

Mathematical foundations of probability and statistical theory; application of derived formulae to the interpretation of data.

**Prerequisite:** MATH 253 or consent of instructor

**Offering:**Twice every five semesters**Instructor:**Staff

A modern approach to geometry. Topics will be chosen from Euclidean, non-Euclidean, affine, projective and differential geometry.

**Prerequisite:** MATH 253 or consent of instructor

**Offering:**Twice every five semesters**Instructor:**Staff

This course offers timely exposure to topics in mathematics which are not part of the regular curriculum. Examples of topics which might be offered: Cryptology, Differential Geometry, Vector Analysis, Topology.

**Offering:**On demand**Instructor:**Staff

Directed research to investigate topics of special interest under the guidance of a faculty member. Topics chosen on the basis of the background and interests of the individual student.

**Prerequisite:** Consent of instructor

**Offering:**On demand**Instructor:**Staff

A course of directed research designed to enable the exceptional student to continue the investigation of topics of special interest under the guidance of a faculty member.

**Prerequisite:** Consent of instructor

**Offering:**On demand**Instructor:**Staff

Study selected in consultation with the mathematics faculty and presented to the class. The seminar serves as the Senior Year Experience and involves oral and written presentation of research and reading topics. Required for Mathematics majors.

**Prerequisite:** Senior standing and consent of instructor

**Offering:**Spring**Instructor:**Staff