Introduction

If you are reading this introduction then this book is probably not for you. This book is directed at calculus students who have better things to do with their time than read wordy preambles that won't be on the exam. But just in case you haven't actually bought this book yet and are considering a purchase while flipping through the pages in a bookstore, we'll tell you what it's all about.

If you want to know the tricks of the trade that will make learning the material of first-semester calculus a piece of cake, then this is the book for you. If you want to learn lots of cool things while having a good time, then this is the book for you. If you want to carry around a book that makes people think you are surfing the wave of knowledge, then this is the book for you.

Do you remember being in a class and being hopelessly confused? Perhaps your attention wandered at some important moment, or the lecturer thoughtlessly slipped into ancient Greek when explaining the basic idea. After class, you asked your brainy friend over a cup of coffee, "What was going on in that class?" Your friend explained it all in five minutes flat and made it crystal clear. "Oh," you said, "is that all there is to it? Why didn't they just say that in the first place?" Later, you wished that friend was around to explain all the lectures to you.

This book aims to play the role of your friend. It gives informal explanations of the key topics of calculus, getting across the ideas without the technical details and fine print that would be found in a formal text. This book does not substitute for a calculus textbook, but it should make it much easier to figure out what the textbook is talking about.

If you approach it with the right point of view, learning calculus can be not only a mind-expanding experience but also fantastic fun, just about as good as something not involving whipped cream and maraschino cherries can get. This book is going to tell you how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams. This is the stuff we wish we'd known when we had to take calculus. So, enough stalling. Why don't you go up to that nice cashier, plunk down some money and buy this book, and we can talk more after?

Exactly Who and What Is Your Instructor?

2.1 Choosing an instructor

Here we give a brief introduction to mathematicians, their pecking order, and their identifying characteristics.

READ THIS BEFORE CHOOSING AN INSTRUCTOR.

Understanding mathematicians is a lot like bird watching. You need to know enough distinguishing features to say, "Ah, a yellow-bellied sapsucker" with conviction.

Choosing the best instructor is the single decision most likely to determine whether your calculus experience will be a series of intellectual delights or whether you schedule dental appointments during calculus lectures because they are less painful.

You can often figure out the specifics about your instructors by looking at their doors. Generally a small sign will be posted containing some clue to the instructor's official title. There are several possibilities:

A. Permanent faculty, tenured (sign on door says Professor or Associate Professor). Tenured means that they cannot be fired, even if they are grossly incompetent. Associate Professors are a rung below Professors. Sometimes this is because they are at an earlier stage in their career, sometimes because their career stalled after they were discovered hiding in the chimney of the dean's apartment.

B. Permanent faculty, untenured (sign on door says Assistant Professor). These people can be fired, but if they are, it will not be for reasons related to their ability to teach calculus. In Europe, Assistant Professors really are assistants, whose job is to mow the Professor's lawn, carry the Professor's briefcase, and teach the Professor's class. In the United States, the Assistant title just means that they are in the preliminary, untenured stage of their career.

C. Visitors (sign on door says Visiting Professor, or Visiting Assistant Professor). "Visiting" means that their welcome is due to expire at the end of one or two years. It does not necessarily mean that they have anywhere to go afterward.

D. Temporary faculty (sign on door says: Lecturer or Instructor or Adjunct Professor). Some colleges hire temporary faculty mainly to teach classes. This may mean that they really care about their teaching.

E. Graduate students (sign on door just gives their name, with no title, or has some pseudo-title like Adjunct Instructor).

F. No sign on door: A very bad omen. It may mean that the instructor is too disorganized to post a sign or that revengeful former students keep ripping it down. Perhaps the instructor is trying to avoid previous generations of students? Investigate further.

G. No door: Danger, danger. Could mean that the instructor is deemed unworthy of an office. This makes it hard to hold office hours. Also could mean that you're looking in the wrong building.

Almost everyone in categories A, B, C, and D has a Ph.D.

Permanent faculty members, with their ranks, should be listed in the course catalog, where you can look them up. At large universities, permanent faculty are usually either the people who do research in really high-level mathematics or the people who have been around forever and control the math department political machine. Sometimes the best teachers are found in this group. The worst teachers are often found here. These faculty will be teaching all the advanced mathematics courses, as well as...