# Mathematics

## Brief Description of Concentration

Mathematics is the science of order, and mathematicians seek to identify instances of order and to find notions and tools to perceive order where it is a priori hidden from view. Perhaps the most important concept of mathematics is that of function, which provides us with the means to study dependence and change. The study of real functions of a real variable (and later complex functions), particularly in connection with the limit concept, is called analysis. The most effective tool for this study is the infinitesimal calculus that analyzes the relation between functions and their derivatives. Then there are the notions and tools for the study of number systems and their generalizations; these form the branch of mathematics called algebra. Here the primary concepts are group, ring, field, and module. A third over-arching set of notions and tools concerns geometry, which now goes far beyond the classical study of the space we live in to include spaces of high dimension and topology, the abstract theory of shape.

## Learning Objectives

The concentration in Mathematics is designed to acquaint the student with the most important general concepts underlying the three over-arching areas of mathematics; analysis, algebra and geometry. Concentration in mathematics will provide an adequate basis for further study in either pure or applied mathematics.

## Gateway Courses

First year potential concentrators should enroll in a math course at the appropriate level.  This will determine which course should be considered. For almost all, it will be one of:

• Math Qa and Qb: Quantitative Analysis for Economics and the Social Sciences
• Math Ma and Mb: Introduction to Functions and Calculus
• Math 1a: Introduction to Calculus (Offered both semesters.)
• Math 1b: Calculus, Series and Differential Equations (Offered both semesters.)
• Mathematics 21a: Multivariable Calculus (Offered both semesters.)
• Math 21b: Linear Algebra and Differential Equations (Offered both semesters.)
• Mathematics 22a and 22b: Vector calculus and Linear Algebra with Introduction to Proof.
• Mathematics 25a and 25b: Theoretical Linear Algebra and Real Analysis I and II (fall and spring)
• Math 55a and 55b: Studies in Algebra and Group Theory (55a), Studies in Real and Complex Analysis (55b)
• Math 101: Sets, Groups and Topology (Offered both fall and spring)

Students thinking to enroll in other Math courses should talk to a Math Department advisor to determine if more is needed by way of background (for example, the Math Department's Director or Assistant Director of Undergraduate Studies).

See the Math Department concentration information web page for more about concentrating in mathematics.

## Alumni

Information Unavailable