Theory

Information for Mathematics Students

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. 

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 several ways to begin study of calculus. Students who have had no significant prior exposure to the subject may consider the sequence Introductory Calculus (Math 117-118) or the sequence Elements of Calculus (Math 119-120). Math 117-118 is intended for students who are not likely to take mathematics courses beyond the 100-level. It covers the same material as the Calculus I sequence (Math 121-122), described below. Math 119-120 is a linked sequence with an emphasis on applications of calculus. After completing 119-120, students may choose to continue with Calculus I, Part II (Math 122).

Students who have had a significant exposure to calculus, or have completed a rigorous pre-calculus course may choose to begin in Calculus I, Part I (Math 121). Together with Calculus I, Part II (Math 122) covers a full year of derivatives, integrals, sequences and series, including theoretical aspects. Students who are planning to major in one of the physical sciences should choose either Math 119-120-122 or Math 121-122.

After completing the Math Placement Guide, a recommendation of the appropriate calculus course appears in a student's electronic portfolio.

In addition, members of the department are happy to answer any questions about placement, particularly at the Academic Forum. Students may also contact the chair or members of DADCOM.  We provide below our recommendations based on the AP Calculus exam.  Advanced students should consult the department for placement.

AP score & Recommendation

4 or 5 on AB Calculus exam & Math 122
3 on AB Calculus exam & Math 121 or Math 122
1 or 2 on AB Calculus exam & Math 121
4 or 5 on BC Calculus exam & Math 221 or Math 222
3  on BC Calculus exam &  Math 122
1 or 2 on BC Calculus exam & Math 121

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) and the topics course Introduction to Mathematical Thought (Math 111).

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.