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Math Foundations by Norman Wildberger

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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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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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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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The World Science Festival is a production of the Science Festival Foundation. The Foundation's mission is to cultivate a general public informed by science, inspired by its wonder, convinced of its value, and prepared to engage with its implications for the future.

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