Explore Math World: Best Books for Recent HS Grad Heading to College

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Discussion Overview

The discussion centers around recommendations for mathematics books suitable for a recent high school graduate preparing for college. Participants share various titles that provide an overview of mathematical concepts, methods, and philosophical insights, rather than focusing on specific mathematical techniques or advanced topics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for math books that provide a broad overview, suitable for someone transitioning to college-level mathematics.
  • Another participant suggests "Foundations and Fundamental Concepts of Mathematics" by Howard Eves as a good starting point.
  • Additional recommendations include "Concepts of Modern Mathematics" by Ian Stewart and "What is Mathematics?" by Courant, Robbins, and Stewart, with one participant expressing a preference for the first recommendation.
  • Another title mentioned is "Mathematics: Its Content, Methods and Meaning" by Aleksandrov, Kolmogorov, and Lavrent'ev.
  • Timothy Gowers' "Mathematics: a very short introduction" is highlighted as particularly suitable for young adults heading to university, along with a suggestion to explore "The Number Sense: How the Mind Creates Mathematics" by Stanislas Dehaene for a psychological perspective on math.
  • Other titles mentioned include "A Pure Course in Mathematics" by Hardy and "How to Prove It" by Velleman, noted for their usefulness despite not being overviews.
  • One participant points out that Gowers' "further reading" section is valuable, recommending books across various interests, including history and philosophy of mathematics, while also humorously noting the complexity of "Principia Mathematica" by Russell and Whitehead.

Areas of Agreement / Disagreement

Participants generally agree on the value of the recommended books, but there is no consensus on a single best choice, as preferences vary based on individual interests and perspectives on mathematics.

Contextual Notes

Some recommendations may depend on the reader's specific interests in mathematics, such as historical context, applicability, or philosophical considerations, which could influence their suitability for different readers.

phrygian
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I just graduated high school having taken AP calculus and am heading off to college this fall. I really enjoy math and have a great interest in it and am wondering if anyone can recommend me any good books on math to read this summer. I will be taking math classes at college so obviously I am not trying to learn everything in math but more looking for an overview of the world of mathematics if that makes sense.
Thanks
 
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I recommend Foundations and Fundamental Concepts of Mathematics by Howard Eves.
 
There is also Concepts of Modern Mathematics by Ian Stewart and What is Mathematics? by Courant - Robbins - Stewart. My personal favorite is the first recommendation, though.
 
Mathematics: Its Content, Methods and Meaning - AD Aleksandrov, AN Kolmogorov, MA Lavrent'ev
 
"Mathematics: a very short introduction" by fields medallist Timothy Gowers FRS, Rouse Ball Professor of Mathematics at Cambridge University (i.e. the biggest of big cheeses in UK Maths -- Roger Penrose held the identical chair at Oxford). The book is especially appropriate for an 18 year old about to go off to University. Website:

http://www.dpmms.cam.ac.uk/~wtg10/

It's the best short overview I've encountered, though Ian Stewart is good as well.

From a totally different angle (psychological) try The Number Sense: How the Mind Creates Mathematics by Stanislas Dehaene. It's full of fun examples, like how they got Dobbin to count, chimps doing arithmetic, and babies spotting disappearing puppets...
 
"A Pure Course in Mathematics" by Hardy.
"How to Prove It" Velleman (sp?)

Not really overviews, but I would think very useful indeed.
 
Gower's "further reading" section is superb. He recommends books to readers with different kinds of interest -- history, applicability, formality, philosophy -- and for areas he doesn't cover, e.g., probability, women in mathematics. I like his subtle "maybe not for further reading" recommendations:

"Russell and Whitehead's famous Principia Mathematica (Cambridge University Press, 2nd edn., 1973) is not exactly light reading, but if you found some of my proofs of elementary facts long-winded, then for comparison you should look up their proof that 1 + 1 = 2."
 

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