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The power and attractiveness of the subject of mathematics is often hidden from students who are in introductory courses. In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory.

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In talking about the distinction between Mathematicians and Physicists, Feynman touches upon the distinction between Mathematical and Scientific Inquiry.

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This is not an easy book to read, but if you have a reasonable background in mathematics, your hard work will pay off.

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Volume 1 - Induction and Analogy in Mathematics

Volume 2 - Patterns of Plausible Inference

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This book explores the tendency to synchronize, found all over nature. It is a great introduction to the discipline of applied mathematics.

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The book/essay frames learning mathematics as an artistic and imaginative pursuit which is not reflected at all in the way the subject is currently taught.

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In How to Solve It, mathematician Polya suggests the following steps when solving a mathematical problem: First, you have to understand the problem;
After understanding, then make a plan;
Carry out the plan;
Look back on your work. How could it be better?

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mathematics mathematical inquiry book
Does modern pure mathematics make logical sense? No, unfortunately there are serious problems! Foundational issues have been finessed by modern mathematics, and this series aims to turn things around. And it will have interesting things to say also about mathematics education---especially at the primary and high school level.
The plan is to start right from the beginning, and to define all the really important concepts of basic mathematics without any waffling or appeals to authority.

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Through larger-than-life characters and an inspired story line, Ian Stewart's book Flatterland explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. The journey begins when our heroine, Victoria Line, comes upon her great-great-grandfather A. Square's diary, hidden in the attic. The writings help her to contact the Space Hopper, who tempts her away from her home and family in Flatland and becomes her guide and mentor through ten dimensions.

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mathematics mathematical inquiry book