Daily Homework, Math 131, Fall 2010
 General Suggestions

The Daily Assignments Page of the syllabus gives you recommended problems correseponding to each lecture. (It's possible that there will be some adjustments in the assigned problems as the course moves along, so it's probably a good idea to revisit the page weekly.) However, these problems are not collected. Most of the suggested problems are odd-numbered and the answers are in the back of the text, and more complete solutions are available in the Student Solutions Manual.   Occasionally, when an even-numbered problem is assigned, the answer (or maybe even a fuller solution) will be posted in the syllabus online at the end of the week. You'll probably find the lectures more valuable if you read the assigned material and attempt some of the problems before coming to class. It's essential that you try to do as many problems as possible, because Math is not a "spectator sport."  You can't learn calculus just by watching your instructor or TA solve problems Doing problems is the best way to test whether you understand the material and to find areas where you need more work Sometimes, quiz and exam questions will be similar to assigned homework problems and textbook examples.  Not understanding these problems simply guarantees that you'll throw away quiz points and exam points. Some of the problems suggested each day are just routine "drill" exercises. There are certain basic techniques in calculus that should become completely mechanical procedures for you -- things you can "do with your spine rather than your brain."  Other problems require more thought. Sometimes you'll think that you can do a problem but get stuck if you actually try to write down the details. It's important to write out neat careful solutions for yourself, even for problems that are not collected. It's good to organize these in a separate notebook or file folder. You'll appreciate having them in one place when you want to review, especially if you can read them easily and don't have to waste time trying to understand what you wrote a few weeks earlier. After you finish and write up your solution, go back and talk to yourself (or others) about the problem.  For example, ask  "What are the main ideas involved?",  "What's involved with this problem that puts it in this section of the book?" (or, "Why couldn't I have done this problem last week?").  "Is there some other way to solve the same problem?"  You can learn much more by solving the same problem in a different way, if possible, than by solving several problems all in more or less the same way. If a problem seems hard, don't just give up and turn to the solutions manual.  You can often learn a lot more by spending hours (perhaps not all at once!) grappling with a hard problem than by working many simpler problems in the same amount of time. Personally, I actually recommend against constantly running to the Solutions Manual: students become too dependent on it and don't develop confidence in their own work. Usually, you and your friends should be able to confirm solutions by comparing your work.  Moreover, convincing a friend that your solution is correct and theirs is wrong (or vice-versa) helps teach the skill of communicating mathematical arguments.   The Principles for Problem Solving in the text (pp. 83 ff.) might be helpful.  They're not magic, but they can help you organize your thoughts.  At the end of each chapter, there's a section called Focus on Problem Solving that  illustrates how to apply these principles to some harder problems.