Mathematics courses provide an opportunity to study mathematics for its own sake and as a tool for the physical, social, and life sciences (applied mathematics). Most courses mix the two points of view to some extent, though some deal almost exclusively with one or the other. The department offers two separate major programs corresponding to these two areas.
All or part of the calculus sequence is required or recommended by several majors at Whitman and calculus is the most common mathematics course taken by students. However, the department offers other courses (Mathematics 108, 128, 167) that are intended for students who wish to take mathematics but are not interested in or not prepared for calculus. Courses in programing, or with an emphasis on computing, are 167, 235, 236, 270, 350, 467.
P-D-F policy: The department places no restrictions on the use of the P-D-F option for mathematics courses for majors or nonmajors, except that students choosing the mathematics major must take Mathematics 260 for a grade. The department strongly recommends that students majoring in mathematics or completing a joint major with mathematics not use the P-D-F option in mathematics courses.
The senior assessment in mathematics consists of a comprehensive examination in two parts: a four-hour written examination and a one-hour oral examination. The written examination covers three semesters of calculus and one of linear algebra — roughly the first two years of the program. The oral examination covers advanced topics.
Courses in mathematics apply to the quantitative analysis distribution area.
The Mathematics major: 225, 235, 236, 260, 300; any two of 385, 386, 455, 456; 495 and 496; 12 additional credits in mathematics courses numbered above 200, for a total of 36 credits. A grade of C (2.0) or better in Mathematics 260 is required and grades of B (3.0) or better in Mathematics 225 and 260 are strongly recommended for any student considering mathematics as a major. The following are strongly recommended: computer programming experience and the use of a variety of technical software packages; applied mathematics courses, such as Mathematics 338, 339, 350 and 467; and a minor in a subject which makes substantial use of mathematics; for example, a physical science or economics. Students planning graduate study should take Mathematics 386 and 456 and should acquire a reading knowledge of either French, German, or Russian.
The Applied Mathematics major: 167, 225, 235, 236, 244, 300, 338, 467, 495 and 496; nine additional credits in mathematics courses numbered above 200 (270, 339, 350, 367, 368 are good options) for a total of 34 credits; a minor (or major) in a related discipline, approved by the department. Students planning graduate study should acquire a reading knowledge of either French, German, or Russian.
A student who enters Whitman College without a good working knowledge of the material in Mathematics 125 and 126 will have to complete 42 mathematics credits to fulfill the requirements for the mathematics major, 40 credits for the applied mathematics major; both totals include six credits for Mathematics 125, 126.
Twenty-seven mathematics credits are required for the mathematics-physics major, 31 mathematics credits for the economics-mathematics major, and 27 mathematics credits for the 3-2 mathematics-computer science major. Students may not declare both a mathematics and applied mathematics major.
The Mathematics minor: Fifteen credits or more in mathematics courses numbered 200 or above.
The Economics-Mathematics combined major: Mathematics 167, 225, 235, 236, 244, 300, 338, either 339 or 350, and three additional credits chosen from mathematics courses numbered above 200. Economics 101 or 177, 102, 307, 308, 327, 428 plus one additional course in economics. For economics-mathematics majors, Economics 101 or 177, 102 and Mathematics 338 are the prerequisites for Economics 327, and Economics 227 does not apply toward the minimum major requirements. Courses completed in this major apply to the social science, science and quantitative analysis distribution areas.
The Mathematics-Physics combined major: Mathematics 225, 235, 236, 244, 300, and nine additional credits in mathematics courses numbered above 200; Physics 155 or 165, 156 or 166, 245, 246, 255, 256, 335, either 325 or 347, and five credits from physics courses numbered from 300-480, or from BBMB 324 and BBMB 334. Courses completed in this major apply to the science and quantitative analysis distribution areas.
Majoring in Computer Science. Please see the Combined Plans section of this catalog.
Students who wish to take calculus should note the following: Students with a strong background in high school mathematics not including calculus start with Mathematics 125. Students who have taken a high school course in calculus, but who have not taken the BC calculus Advanced Placement Test (see the statement below regarding college credit for the Advanced Placement Test) should take the Advisory Calculus Placement exam offered by the department of mathematics.
Students should note that several programs require the calculus labs, Mathematics 235 and 236, in addition to Mathematics 225. Because the lab courses teach skills that are useful in other mathematics and science courses, it is strongly recommended that students take Mathematics 235 and 236 as early as possible in their programs. Programs that require the calculus labs are the mathematics major, the economics-mathematics major, the mathematics-physics major, the physics major, the 3-2 engineering program, and the 3-2 mathematics-computer science major.
The policy for advanced standing and credit for the College Board Advanced Placement program is as follows:
A student has the option of repeating a course for which AP credit has been granted, but with a commensurate reduction in advanced placement credit.
108 Introduction to Mathematical Thinking
x, 3 Guichard
This course will introduce students to mathematical thinking by studying a variety of mathematical topics. Topics may include problem solving strategies, recreational mathematics and puzzles, mathematics of finance, voting power, and game theory. This course is not designed to prepare students for calculus and is intended primarily for the nonmath major. Prerequisite: two years of high school mathematics.
119 Programming with Robots
x, 3 A. Schueller
An introduction to programming techniques applicable to most languages using personal robotics kits (Lego Mindstorm NXT’s provided). The programming language used is most similar to the C programming language. Frequent programming projects are required in both independent and group settings. Traditional computer science topics like logic and algorithms, simple networking, event loops, and threading will also be explored.
125 Calculus I
3, 3 Fall: Gordon, Guichard; Spring: Keef
A brief review of some precalculus topics followed by limits, continuity, a discussion of derivatives, and applications of the derivative. Prerequisites: two years of high school algebra; one year of plane geometry; and knowledge of trigonometry and conic sections or consent of the instructor.
126 Calculus II
3, 3 Fall: Cotts, L. Schueller
Spring: Balof, Cotts, Guichard
A continuation of Mathematics 125, covering integration, techniques for computing antiderivatives, applications of the definite integral, and infinite series.
128 Elementary Statistics
x, 3 Cotts
Probability and statistics including methods for exploring data and relationships in data, methods for producing data, an introduction to probability and distributions, confidence intervals, and hypothesis testing. Prerequisite: two years of high school mathematics.
167 Programming in C++
x, 3 Guichard
An introduction to programming techniques applicable to most languages. Emphasis is placed on the C++ language; frequent programming projects are required.
203, 204 Special Topics in Introductory Level Mathematics
1-3
On occasion, the mathematics department will offer courses on introductory topics in mathematics that are not generally covered in other introductory courses. Possible topics include Introduction to Number Theory, Chaos and Applied Discrete Probability.
203A ST: Number Theory
3, x Guichard
Number theory is really the study of the integers. In this course, we will study many standard topics in number theory including Diophantine equations, congruences, and Fermat’s Last Theorem. Prerequisite: Math 126 or consent of instructor.
204A ST: History of Mathematics
x, 3 Balof
The course will explore the roots of selected mathematical ideas and topics through examination of primary and secondary sources. The main emphasis will be on problem solving using the tools and ideas available to mathematicians of a given time period. Prerequisite: Mathematics 126.
225 Calculus III
4, 4 Fall: Balof; Spring: Hundley
Topics include partial derivatives, gradients, extreme value theory for functions of more than one variable, multiple integration, line integrals and various topics in vector analysis.
235, 236 Calculus Laboratory
1, 1 Fall: Hundley; Spring: L. Schueller
A laboratory to investigate ways in which the computer can help in understanding the calculus and in dealing with problems whose solutions involve calculus. No programming required; a variety of existing programs will be used. Prerequisite or corequisite for Mathematics 235: Mathematics 225; Prerequisite for Mathematics 236: Mathematics 235.
244 Differential Equations
3, 3 Fall: Hundley; Spring: Gordon
This course includes first and second order linear differential equations and applications. Other topics may include systems of differential equations and series solutions of differential equations. Prerequisite: Mathematics 225.
260 An Introduction to Higher Mathematics
x, 3 Gordon
An introduction to some of the concepts and methodology of advanced mathematics. Emphasis is on the notions of rigor and proof. This course is intended for students interested in majoring in mathematics; students should plan to complete it not later than the spring semester of the sophomore year. Prerequisite: Mathematics 225.
270 Data Structures with C++
3; not offered 2009-10
We study fundamental methods used to store, access, and manipulate data in computers. Storage structures to be covered include files, lists, tables, graphs, and trees. We will discuss and analyze methods of searching for and sorting data in these structures. Prerequisite: Mathematics 167 or consent of instructor.
281, 282 Independent Study
1-3, 1-3 Staff
A reading project in an area of mathematics not covered in regular courses or that is a proper subset of an existing course. The topic, selected by the student in consultation with the staff, is deemed to be introductory in nature with a level of difficulty comparable to other mathematics courses at the 200-level. May be repeated for a maximum of six credits. Prerequisite: consent of supervising instructor.
299 Problem Solving in Mathematics
1, x Balof
Students will meet weekly to discuss problem solving techniques. Each week a different type of problem will be discussed. Topics covered will include polynomials, combinatorics, geometry, probability, proofs involving induction, parity arguments and divisibility arguments. The main focus of the course will be to prepare students for the William Lowell Putnam Mathematics Competition, a national examination held the first Saturday in December. Students who place in the top 500 on this exam nationwide have their names listed for consideration to mathematics graduate programs. May be repeated for a maximum of four credits. Prerequisite: consent of instructor.
300 Linear Algebra
3, 3 Fall: Keef; Spring: Balof
This course first considers the solution set of a system of linear equations. The ideas generated from systems of equations are then generalized and studied in a more abstract setting, which considers topics such as matrices, determinants, vector spaces, inner products, linear transformations, and eigenvalues. Prerequisite: Mathematics 225.
337 Geometry
3; not offered 2009-10
Essential for prospective high school mathematics teachers, this course includes a study of Euclidean geometry, a discussion of the flaws in Euclidean geometry as seen from the point of view of modern axiomatics, a consideration of the parallel postulate and attempts to prove it, and a discussion of the discovery of non-Euclidean geometry and its philosophical implications. Prerequisite: Mathematics 126.
338 Probability and Statistics
4, x Cotts
Topics include discrete and continuous probability spaces, distribution functions, the central limit theorem, estimation, tests of hypothesis, regression, and correlation. Prerequisite: Mathematics 225.
339 Operations Research
3; not offered 2009-10
Operations research is a scientific approach to determining how best to operate a system, usually under conditions requiring the allocation of scarce resources. This course will consider deterministic models, including those in linear programming (optimization) and related subfields of operations research. Prerequisite: Mathematics 300.
350 Mathematical Modeling and Numerical Methods
3, x Hundley
This course explores the process of building, analyzing, and interpreting mathematical descriptions of physical processes. Topics may include feature extraction, partial differential equations, neural networks, statistical models. The course will involve some computer programming, so previous programming experience is helpful, but not required. Prerequisite: Mathematics 300.
358 Combinatorics and Graph Theory
3; not offered 2009-10
Topics in elementary combinatorics, including: permutations, combinations, generating functions, the inclusion-exclusion principle, and other counting techniques; graph theory; and recurrence relations. Prerequisites: Mathematics 260 or consent of instructor.
367 Engineering Mathematics
3, x A. Schueller
An introduction to mathematics commonly used in engineering and physics applications. Topics may include: vector analysis and applications; matrices, eigenvalues, and eigenfunctions; boundary value problems and spectral representations; Fourier series and Fourier integrals; solution of partial differential equations of mathematical physics; differentiation and integration of complex functions, residue calculus, conformal mapping. Prerequisite: Mathematics 244.
368 Complex Variables
x, 3 A. Schueller
Complex analysis is the study of functions defined on the set of complex numbers. This introductory course covers limits and continuity, analytic functions, the Cauchy-Riemann equations, Taylor and Laurent series, contour integration and integration theorems, and residue theory. Prerequisite: Mathematics 225.
385, 386 Abstract Algebra
4; not offered 2009-10
The first semester is an introduction to groups and rings, including subgroups and quotient groups, homomorphisms and isomorphisms, subrings and ideals. Topics for the second semester may include fields, simple groups, Sylow theorems, Galois theory, and modules. Prerequisite: Mathematics 260.
455, 456 Real Analysis
4, 4 Gordon
First semester: a rigorous study of the basic concepts of real analysis, with emphasis on real-valued functions defined on intervals of real numbers. Topics include sequences, continuity, differentiation, integration, infinite series, and series of functions. Second semester: content varies from instructor to instructor but includes topics from metric spaces, the calculus of vector-valued functions, and more advanced integration theory. Prerequisite: Mathematics 260.
467 Numerical Analysis
x, 3 Hundley
An introduction to numerical approximation of algebraic and analytic processes. Topics include numerical methods of solution of equations, systems of equations and differential equations, and error analysis of approximations. Prerequisite: Mathematics 167; Prerequisite or corequisite: Mathematics 300.
471, 472 Special Topics
1-3
On occasion, the mathematics department will offer courses on advanced topics in mathematics that are not found in other course offerings. Possible topics include topology, number theory, and problem solving.
481, 482 Independent Study
1-3, 1-3 Staff
A reading or research project in an area of mathematics not covered in regular courses. The topic is to be selected by the student in consultation with the staff. Maximum of six credits. Prerequisite: consent of supervising instructor.
495 Senior Project I
3, x Keef
Preparation of the senior project required of all graduating mathematics majors. Aid will be given in choosing a senior project during the first two weeks. Once a project is defined, each student will be matched with a faculty mentor from the math department. Short oral reports will be given weekly for the remainder of the semester on the progress of the senior project.
496 Senior Project II
x, 1 Keef
Finalization of the senior project for mathematics majors. A final written and oral report on the senior project is completed and submitted. During the semester drafts of the senior report are submitted regularly and evaluated for content and style. Proper mathematical writing will be emphasized.
498 Honors Thesis
3, 3 Staff
Preparation of an honors thesis. Required of and limited to senior honors candidates in mathematics. Prerequisite: admission to honors candidacy.
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