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01_Transcript - 1 Introduction to the Language of...

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1 Introduction to the Language of Mathematicians 1.1 Welcome Welcome to the first module in our course on reading, writing and discovering proofs. These modules are built around Daniel Solow’s book How to Read and Do Proofs published by Wiley. Though the lectures may stand alone, they will be much more effective if you do the assigned reading first, then view the module, do the prescribed exercises and lastly, do the assignments. Before going on, please do the assigned readings. 1.2 The Language Mathematics is the language of mathematicians, and a proof is a method of communi- cating a mathematical truth to another person who speaks the “language”. (Solow, How to Read and Do Proofs ) Mathematics is an unusual language. It is extraordinarily precise. When a proof is fully and correctly presented, there is no ambiguity and no doubt about its correctness. However, understanding a proof requires understanding the language. This course will help you with the basic grammar of the language of mathematics and is applicable to all proofs. Just as in learning any new language, you will need lots of practice to become fluent. 1.3 Objectives The objectives of the course are simple. 1. Explain and categorize proof techniques that can be used in any proof. This course will teach not only how a technique works, but when it is most likely to be used and why it works. 2. Learn how to read a proof. This will require you to identify the techniques of the first objective. 3. Discover your own proofs. Knowledge of technique is essential but inadequate. Or, as we would say in the language of mathematics, technique is “necessary but not sufficient”. Discovering your own proof requires not only technique but also understanding, creativity, intuition and experience. This course will help with the technique and experience. Understanding, creativity,
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This note was uploaded on 10/13/2011 for the course MATH 135 taught by Professor Andrewchilds during the Spring '08 term at Waterloo.

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01_Transcript - 1 Introduction to the Language of...

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