### Courses Overview

Students usually begin by taking Calculus I-II (110.106-107), which is offered in three versions to meet the needs of students with different goals and interests.

Students in mathematics, the physical sciences, and engineering are encouraged to begin with the 110.108-109 sequence or 110.113; students majoring in other subjects may wish to take the 110.106-107 sequence, which relates the methods of calculus to the biological and social sciences.

A one-term pre-calculus course 110.105 is offered for students who could benefit from additional preparation in the basic tools (algebra and trigonometry) used in calculus. Entering students may receive course credit for Calculus I or Calculus I-II on the basis of the College Board AP exams. Students without AP credit should take the math placement exam to determine which course would be appropriate for them.

Linear Algebra (110.201), Calculus III (110.202), and Differential Equations (110.302) may be taken in any order after completing Calculus II (110.107 or 110.109). These courses are especially designed to acquaint students with mathematical methods relevant to engineering and the physical, biological, and social sciences.

The department offers honors course Honors Multivariable Calculus (110.211) and Honors Linear Algebra (110.212). Additional courses oriented toward applications include Methods of Complex Analysis (110.311), Partial Differential Equations for Applications (110.417), and Fourier Analysis and Generalized Functions (110.443).

All students must take a basic introductory course in the foundations of abstract algebra with either 110.401 Introduction to Abstract Algebra or 110.411 Honors Algebra I, and analysis with either 110.405 Real Analysis I or 110.415 Honors Analysis I. Students interested in the theoretical foundations of mathematics may select the honors track with 110.411-2 Honors Algebra I & II and 110.415-6 Honors Analysis I & II, along with course like 110.413 Introduction to Topology and 110.439 Introduction to Differential Geometry.

Students planning to pursue further study in mathematics should work toward taking these theoretical courses as early as possible in their undergraduate years and are encouraged to take graduate-level courses as soon as they are qualified.