In this course, it is absolutely essential that you do the reading assignments. Your experience with previous math courses may make it seem unlikely, since it may have been possible to avoid reading the text, yet do adequately well by copying down examples the instructor did in class and then doing the homework exercises by just changing the numbers in those "pattern examples" and the pattern examples given in the text. Also, older-style texts subtly encouraged students to skip the reading assignments by putting procedures for doing exercises in boxes, thereby essentially telling the students that "everything you really need to know to do the exercises can be found inside the boxes; you might as well skip reading everything else."

Unfortunately, this approach resulted in students being able to do the mechanical computations quite well, but having no real understanding of the material and no real ability to apply it in situations that are even a little bit different from that covered by the pattern examples. In essence, students were only being programmed like computers to do computations that computers can do faster and more accurately anyway. It is this deficiency in the old-style math courses that led to the national movement toward reformed courses, like this one, which stress understanding. This modern approach to learning requires new methods in the classroom emphasizing learning rather than lecturing, as well as new texts such as the one for this course.

The difference between the text for this course and an old-style math text is apparent from even a cursory scanning of the first chapter. If you open the text and just begin turning pages, you will probably be struck by the following:

1. The amount of text to be read outside of examples is much greater than in old-style books. Older books would typically have brief explanations, sometimes single paragraphs, followed by one or more pattern examples. This book has longer explanations that attempt to convey understanding of the concepts involved rather than just the mechanics of how to do computations.
2. The examples tend to be much longer than those in an old-style text, and they often arise from actual real-world problems.
3. The exercises, which also tend to be much longer than those in an old-style text, are often quite different from each other and from the examples in the text, and use real-world numbers that are not as "nice" as the made-up numbers in the shorter exercises typical of old-style texts.

1. Plan to do the reading more than once, and do not make it an essential goal to understand everything in the reading the first time through it. The first reading should be devoted only to getting a general overview of the material in the section.
2. After the first reading, stop for a few minutes and attempt to summarize to yourself, in your own words, what the section is all about. Then immediately re-read the section.
3. During the second reading, make a serious effort to understand all of the material in the section. This does not mean to memorize it, but rather to understand all of the points before going on.

Do not get discouraged if some points require some time to understand. It is not uncommon to have to think about a point in a math text for a half hour (or more, for more complicated concepts) before it becomes clear what is really going on.