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FROM THE SHARED SHELF · 2006–2026 SAMPLE
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THE WORD OF MOUTH
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In order: 1. Book of Proof 1a. How to Prove It: A Structured Approach 2. Elements of Set Theory - Enderton 2a. Naive Set Theory - Halmos 3. Foundations of Analysis - Landau 4. Basic Mathematics - Lang 5. Principles of Mathematics - Allendoerfer & Oakley 6. A Transition to Advanced Mathematics 6a. Concept of Modern Mathematics - Stewart 7. Calculus - Apostol or Spivak Don't skip any
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Some of the books that you mention seem a bit too hard for a teen, so you have to be careful not to demotivate them by expecting too much of them; instead i suggest a simpler approach before tackling the big ones; * Functions and Graphs by Gelfand et al. - A small but great book to develop intuition. * Who is Fourier? A Mathematical Adventure - A great "manga type" book to build important concepts from first principles * Concepts of Modern Mathematics by Ian Stewart - A nice overview in simple language. * Mathematics: Its Content, Methods and Meaning by Kolmogorov et al. - A broad but concise presentation of a lot of mathematics. * Methods of Mathematics Applied to Calculus, Probability, and Statistics by Richard Hamming - A very good applied maths book. All of Hamming's books are recommended. There are of course plenty more but the above should be good for understanding.
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In addition to all the other good suggestions, the following are recommended (have not seen these mentioned so far); - Concepts of Modern Mathematics - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo... (https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Books/dp/0486284247/ref=sr_1_1?crid=214QSPLG829VY&keywords=concepts+of+modern+mathematics&qid=1571974129&s=books&sprefix=concepts+of+modern+ma%2Cstripbooks-intl-ship%2C1448&sr=1-1) - Methods of Mathematics Applied to Calculus, Probability, and Statistics - https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... (https://www.amazon.com/Methods-Mathematics-Calculus-Probability-Statistics/dp/0486439453/ref=cm_cr_arp_d_product_top?ie=UTF8) (all books by Richard Hamming are recommended) - Calculus: An Intuitive and Physical Approach - https://www.amazon.com/Calculus-Intuitive-Physical-Approach-... (https://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536/ref=cm_cr_arp_d_product_top?ie=UTF8) For a Textbook reference, the following are quite good;…
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That thread recommends many very few good books, but probably mostly books too hard at first for the participant who has posted this new thread. I'll recommend a couple of books from that thread: http://www.springer.com/physics/book/978-0-306-45036-5 http://www.amazon.com/Mathematics-Short-Introduction-Timothy... (http://www.amazon.com/Mathematics-Short-Introduction-Timothy-Gowers/dp/0192853619/) I agree with the recommendation of An Introduction to Mathematical Reasoning in this thread. Another participant has already recommended my favorite for background reading, Concepts of Modern Mathematics by Ian Stewart. http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar... (http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewart/dp/0486284247/) Get that right away. Sawyer's A Mathematician's Delight is surely also good (I've read other books by Sawyer). http://www.amazon.co.uk/gp/product/0486462404/ Read those for background as you get my favorite overviews of mathematics: Basic Mathematics by Serge Lang and Numbers and Geometry by Joseph Stillwell.…
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Concepts of Modern Mathematics http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar... (http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewart/dp/0486284247/ref=pd_sim_b_88)