# Mathematics at Pitzer

Pitzer's mathematics courses are designed to serve three purposes: general education; service to courses in social, behavioral, and natural sciences; and the basis for the Mathematics major.

• General Education Courses in Mathematics

What is mathematics? What are its major methods and conclusions? How is it related to other subjects? What do modern mathematicians do? Several Pitzer courses specifically address these questions. These courses are: Math 1, Mathematics, Philosophy, and the "Real World" ; Math 6, Pencil and Paper Games ; Math 7, The Mathematics of Games and Gambling ; Math 8, Mathematics, Art, and Aesthetics ; Math 10, The Mathematical mystery Tour . These courses cover mathematical material that is exciting and sophisticated, and yet accessible to students with a high school education in mathematics. As such they offer students an excellent opportunity to break fresh ground in kinds of mathematics they are not likely to have seen before. All of these courses meet Pitzer's Educational Objective in Formal Reasoning.

• The Precaclulus and Calculus Sequence

Math 20, Elementary Functions studies algebraic equations and functions, graphs, and their relationship to each other. It serves as the first semester of the Math 20-23 sequence, which is designed to prepare students for Math 30, Calculus I. Math 23, Transcendental Functions, the second semester of the precalculus sequence introduces the exponential, logarithmic, and trigonometric functions. These are the functions most widely used in the quantitative social sciences and natural sciences.

Math 30, 31, and 32, Calculus I, II and III, comprise the calculus sequence. The calculus, since it studies motion and change, is the key mathematical tool in understanding growth, decay, and motion in the physical, biological, and social sciences.

• Linear Algebra

Math 60, Linear Algebra, studies vector spaces and functions from one vector space to another, called linear transformations. These transformations can be represented by matrices. The theory of linear transformations and the associated matrices is extremely important to many areas of mathematics and has many practical applications. This course has Math 31 as prerequisite and is a prerequisite itself to most upper division mathematics courses.

For mathematics and science majors, Pitzer offers several courses beyond calculus and linear algebra. Math 108, History of Mathematics , Math 141, Hyperbolic Geometry, Math 145, Surface Topology and Combinatorial Group Theory, and Math 148, Knot Theory , are usually offered every other year. And, of course, Pitzer students may (and should!) take advanced mathematics courses at the other Claremont Colleges. Please see the list of Mathematics Courses in Claremont for a complete description of all mathematics courses offered by all of the Claremont Colleges.

## Requirements for the Major

A student must take a total of 12 courses for the Mathematics major, distributed as follows:
• I. Calculus (3 courses)

Three semesters of Calculus (Math 30, 31, 32) with a grade of C or better in each course. In some cases, a suitable score on the Pitzer Mathematics Placement exam, or the Calculus AP exam, may be substituted for one or more of these courses.

• II. Core (3 courses)

• Linear Algebra
• Differential Equations or a Mathematical Modeling course making extensive use of differential equations.
• Probability
• III. Depth and Breadth (4 courses)

Two 2-courses sequences of upper division mathematics courses chosen from the same area of mathematics in consultations with the advisor. Normally the first course will be prerequisite for the second and will itself have courses from I or II as prerequisites. Examples include, but are not limited to:

• Probability and Statistics
• Analysis I and II
• Algebra I and II
• Functions of a Complex Variable and Complex Analysis
• Combinatorics and Graph Theory
• Geometry and Topology

Students who count the sequence of Probability and Statistics under this requirement must then take one additional upper-division mathematics course of their choice.

• IV. Applications and Connections (2 courses)

Two courses outside of mathematics that emphasize the application of mathematics or its connections to other disciplines: for example, courses in Computer Science, Science, Engineering, and History or Philosophy of Mathematics. These courses will be chosen in consultation with the advisor, and normally will have mathematics courses from I, II, or III as prerequisites.