# Department of Mathematics

## A Guide for the Perplexed On the College Calculus Sequences

This guide is meant to dispel a widely held misconception about calculus at the U. of C. The misconception is that the mathematical theory of calculus is taught only in the 16000's. In a related matter, some people think that the 13000's sequence is for those who have "never been any good at mathematics." Neither of these views is correct (as hinted by the use of 'misconception'). Here are the facts (or some facts--a kind of distinction you should get used to at the U. of C.).

The sequence Mathematics 16100-16200-16300 is called Honors Calculus; it might be better referred to as Introduction to Mathematical Analysis. The course starts with the mathematical definition of the real numbers, and concentrates on theory all year. The mechanics of differentiation and integration and all the standard applications are covered, but the emphasis throughout the year is on rigorous proof. Students in the 16000's are expected to prove things in their homework assignments and on tests. You don't have to be a mathematics major to take the 16000's, and you don't have to take the 16000's to be a mathematics major.

Mathematics 15100-15200-15300 and Mathematics 13100-13200-13300 focus less on theory, in the sense that students don't prove as many things for themselves. However, it is not the case that these courses only provide students with recipes and formulas (plug and chug). Students are expected to understand the definitions of key concepts (limit, derivative, integral) and to be able to apply definitions and theorems to solve problems. In particular, ALL calculus courses require students to do epsilon-delta limit proofs.

The major difference between the 13000's and 15000's is the amount of mathematics students have seen and mastered before coming to the U. of C. The 13000's sequence is designed for those who are less familiar with pre-calculus mathematics, specifically trigonometry, logarithms, and exponential functions, and to a lesser extent, high school algebra. Therefore, these subjects are covered more thoroughly in the 130's than in the 15000's. The 13000's and 15000's sequences end up covering almost the same material, but 15000's classes usually see more advanced applications.

Placement in these courses depends on tests you took during Orientation Week. Many students entering the U. of C. took calculus in high school; this fact alone will not determine your placement.

Despite our best efforts, some students will find themselves placed in the wrong level of calculus. It's easy to switch from the 16000's to the 15000's. Switching from the 15000's to the 13000's requires a little more persuasion. Going the other way is unusual but can be done. If you are convinced that you are in the wrong class, talk to your instructor and to Diane Herrmann.

The College only requires two quarters of calculus. Many departments (including the physical sciences, HiPSS, and economics) require concentrators to take three quarters of calculus. So, even if you don't like calculus, it may be worth taking all three quarters your first year so that you don't have to worry about taking the third quarter later on when you find out that your concentration requires it.