# Mathematics

## Brief Description of Concentration Mathematics is the science of order, and mathematicians seek to identify instances of order and to formulate and understand concepts that enable us to perceive order in complicated situations. 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. The study of number systems and their generalizations is called algebra. Here the primary concepts are group, ring, field, and module. The last great branch of mathematics is 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 branches of modern mathematics. 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 of the following a first year student enrolls in.

• 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 23a and 23b and 23c: Linear Algebra and Real Analysis. (Math 23b,c option in the spring, Math 23c for Computer Science, Statistics and Data Science.)
• 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)