# The Undergraduate Mathematics Major

#### The Mathematics Major

In the mathematics major, each student's course of study is designed to provide an introduction to the basic areas of mathematics, an acquaintance with computer programming and computer science, and to provide the technical tools that will be useful later in a career. This course of study is planned in consultation with the student's faculty advisor, and the department's advisory committee (DADCOM). Through small upper-level classes and activities run by the Math Club, majors have close contact with the faculty. There is also a Math-Econ major, designed especially for students who plan to go to graduate school in economics.

Advanced undergraduates may enroll in graduate courses. Interested students should inquire about the combined B.A./M.A. and B.A./Ph.D. programs. The department offers Master's degree programs in both Mathematics and Computer Science and the Ph. D. degree program in Mathematics. In addition, the department offers three routes to honors in mathematics: examination, thesis, or coursework. The last two routes require a presentation to the faculty.

#### Calculus Sequences

There are two distinct first year calculus sequences. **Introductory
Calculus** (Math 117-118) is intended for students who are prepared to
begin studying calculus immediately, but who have had no significant
prior exposure to the subject. It is expected that students in
this course are not likely to take mathematics courses beyond the
100-level. **Calculus I** (Math 121-122) is intended for students who
have
had a significant exposure to calculus, or are planning to major in
one of the sciences. Students place themselves in one of Math 121 or
122 with guidance from department members, particularly at the Academic
Forum. Students who have achieved a 4 or a 5 on an Advanced Placement
Calculus exam (or equivalent experience) generally place out of the
first year calculus sequence, and may register for **Vectors and
Matrices** (Math 221) or **Multivariable Calculus** (Math 222).
More advanced students should consult the department for placement.

#### Computer Science Courses

Math majors typically take one or more computer science
courses. **Introduction to Programming** (Comp 112) provides an
introduction to a high-level programming language. The emphasis is on writing
programs that implement a variety of basic algorithms. **Computer
Science I** (Comp 211) provides an in-depth introduction to the fundamental ideas in
the field of computer science: languages, algorithms, and computational
models.

#### Other Courses Offered

The department also offers other courses at the 100-level, including
**Elementary Statistics** (Math 132), **Review of
Algebra-Graphing-Precalculus** (Math 107), and the topics course
**Introduction to Mathematical Thought ** (Math 111 and Math 112).

#### Learning Goals

The department has the following learning goals for mathematics majors.

- Develop a basic understanding of, and computational facility with, major objects of mathematical and applied interest, such as functions, vector spaces, and groups.
- Understand abstract mathematical reasoning, e.g., understand an abstract system of rules, find examples of objects that satisfy those rules, conjecture theorems from those examples, and prove those theorems.
- Understand some mathematical applications and ways to use mathematics in practice, and also to be able to make connections to topics outside of the strict course content.
- Students should be able to write about and speak about mathematics.

The department has the following learning goals for our general education students:

- Students should learn that mathematics involves understanding ideas, not simply getting the correct answer; and that mathematics is a branch of science that involves exploration with ideas rather than physical objects.