Reading a Mathematics Text
Here are some suggestions we have compiled for reading a math textbook:
**LEARN BY DOING: Mathematics is not a spectator sport. We learn mathematics by participating, so "participate" while you read. When you read your textbook, you should do so with a paper and pencil.
* Take notes on definitions, theorems or key concepts in your notebook. You should try to state the material that you read in your own words. If you encounter an unfamiliar term, look it up and make a note of it.
For definitions, find examples of the defined objects and examples of objects that do not fit the definition.
Figure out why each piece of a theorem is necessary or sufficient.
* When you come to an example or theorem, work through it carefully step by step. Try to understand and follow how the author is progressing through it. After reading it, cover it up and try to work through the details on your own. Authors often omit steps. Fill in the gaps to deepen your understanding of the material.
* When you can work through an example, try to think of other examples that would fit the idea being discussed. Think of other relevant problems and try to solve them.
* Make a note of those things you do not understand and discuss them with your study group, in class, via email or during office hours.
* Discuss the text with other students. Even a short discussion of a concept or example may help deepen your understanding.
* Ask questions as you read: Why are the topics presented in this order? What may be a better order? What’s coming up next? Does this make sense? Is this a sound argument? If something does not make sense to you, explore it further. You may find mistakes. Keep track of mistakes/typos you find.
**SLOW DOWN!! Math is dense. The flow of a math book is not like the flow of a novel. Reading a mathematics textbook requires slow and careful reading of each word. A typical novel might be read at the rate of a page a minute. Expect to spend 30-60 minutes working through the few selected pages for each reading assignment thoroughly for the first time.
* Every word counts. Writers of math texts believe that extra words and repetition get in the way of clarity, so there is little chance of picking up missed information from reading on.
* Understand each sentence before you go on. Expect to re-read, and then to re-read again. It may take several passes through a section before you start to absorb the material.
* Study diagrams and other kinds of illustrative material.
* Read when you are relatively alert.
**DON'T GET DISCOURAGED. Even after you follow all the suggestions, you probably will not completely understand everything in the section, but the class meetings will be much more meaningful if you spend time to understand while you read.
When you encounter a new topic that is frustrating you, try to remember that previous topics were also difficult at first, but that there is great satisfaction in learning and mastering a concept. With hard work, you'll be able to gain that same sense of satisfaction with the material in this course.
**GIVE IT A RE-RUN! After we have discussed a section in class, go back and re-read the section -- Many points will be much clearer. Read the chapter over, soon after class. This second reading will help you store the information you've learned in your long-term memory.
**Print these suggestions and use them as a bookmark. Reread them as needed.
If all of this seems like too much work consider that it will take nearly as much work to fail. If it takes only a little more work to succeed, then take the time to succeed!
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