Название: Understanding Proof: Explanation, Examples and Solutions of Mathematical ProofАвтор: Tom Bennison, Edward Hall
Издательство: Tarquin Group
Год: 2020
Страниц: 249
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB
Proof is central to any mathematics curriculum and indeed, all mathematical thinking. Now we are delighted to provide an International Edition of our guide to proof for students …and for their teachers too.
Throughout our early schooling we are taught that mathematics is about using and manipulating numbers, perhaps with some application in mind and sometimes with seemingly none. Of course, this is a part of what mathematics is about, but it is not the whole story. A professional mathematician is not somebody who sits around thinking about large numbers, for example. A mathematician is somebody who formulates conjectures about observations and then tries to show if these conjectures are true or false. In this way, a mathematician is similar to any other scientist, but rather than performing experiments to prove their claims, mathematicians rely on logic and reason in their proofs. This is perhaps the distinction between mathematics and other sciences, once a statement has been proved mathematically, the logic is undeniable and the statement will remain true forever more; the conjecture has become a theorem.
Contents: 1. Introduction to proof 2. Exploring Methods of Proof 3. Mathematical Language 4. Direct Proof 5. Indirect Proof 6. Proof by Induction 7. Proof and Applications of Pythagoras’ Theorem 8. Proof in Calculus 9. Proving Trigonometric Identities 10. Proof in Statistics and Probability 11. Worked Solutions
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