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Is Euclid just about geometry? I have not read it, but others have written it is a good introduction to mathematical proofs. A few comments on HN over the years

Is Euclid just about geometry? I have not read it, but others have written it is a good introduction to mathematical proofs. A few comments on HN over the years said Hammack's "Book Of Proof" or Velleman's "How To Prove It" are more thorough, but are intended for 3rd/4th year math undergrad, and Euclid is easier to get through. My last math course was stats and business calc about 30 years ago.

wheelinsupial 4y ago
Are you looking for a book to learn proofs from? Are you looking to learn any math topics in particular? I think you can go through any of the books you listed and get an understanding of proofs. The proofs books usually use basic number theory or set theory for examples because the point is to learn the logic and structure of proofs. (If the book isn't enough for you, you can use Khan Academy as a refresher.) Learning more math is left to other books. I looked through the table of contents for the ones you've linked, but neither looks like an upper year math book. Typically, if there is an explicit course on proofs, it's covered in the lower division. The proofs course I took used "Mathematical Proofs: A Transition to Advanced Mathematics" by Chartrand, Polimeni, and Zhang. It's ridiculously expensive on Amazon right now, so I'm not sure I can recommend it for the cost. But it does cover more areas of math using proofs. It covers proofs in set theory, number theory, combinatorics, calculus, and group theory at a very basic level. The books you linked seem to cover less of those topics, so I think Chartrand et al. is a more gentle intro to different branches of upper division math.
- EFreethought 4y ago
  WRT math topics: probably Calculus and linear algebra. I will look into the proofs book you recommended. Thanks.
  - wheelinsupial 4y ago
    You can take four terms of calculus using the Stewart book and not need to do any proofs. You do need to review algebra and have a good grounding in that, though. You can also cover linear algebra without proofs. There are, of course, books that do cover proofs for calculus and linear algebra, but it depends on what you’re trying to get out of the material.
    - EFreethought 4y ago
      I have heard that proofs are a big part of advanced math, so that is one reason I am interested in proofs. I should have listed proofs as a third topic.
      - wheelinsupial 4y ago
        You're right it is a big part of advanced math, but you can cover calculus, linear algebra, and proofs in parallel! If you have enough time.
bandrami 4y ago
Books 1, 2 and 6 are plane geometry, books 3 and 4 are what we now call trig, book 5 is on what we now call real numbers, books 7-9 are on integer number theory, book 10 is on irrationals, and books 11-13 are on solid geometry.

wheelinsupial 4y ago

Are you looking for a book to learn proofs from? Are you looking to learn any math topics in particular? I think you can go through any of the books you listed and get an understanding of proofs. The proofs books usually use basic number theory or set theory for examples because the point is to learn the logic and structure of proofs. (If the book isn't enough for you, you can use Khan Academy as a refresher.) Learning more math is left to other books. I looked through the table of contents for the ones you've linked, but neither looks like an upper year math book. Typically, if there is an explicit course on proofs, it's covered in the lower division. The proofs course I took used "Mathematical Proofs: A Transition to Advanced Mathematics" by Chartrand, Polimeni, and Zhang. It's ridiculously expensive on Amazon right now, so I'm not sure I can recommend it for the cost. But it does cover more areas of math using proofs. It covers proofs in set theory, number theory, combinatorics, calculus, and group theory at a very basic level. The books you linked seem to cover less of those topics, so I think Chartrand et al. is a more gentle intro to different branches of upper division math.

EFreethought 4y ago
WRT math topics: probably Calculus and linear algebra. I will look into the proofs book you recommended. Thanks.
- wheelinsupial 4y ago
  You can take four terms of calculus using the Stewart book and not need to do any proofs. You do need to review algebra and have a good grounding in that, though. You can also cover linear algebra without proofs. There are, of course, books that do cover proofs for calculus and linear algebra, but it depends on what you’re trying to get out of the material.
  - EFreethought 4y ago
    I have heard that proofs are a big part of advanced math, so that is one reason I am interested in proofs. I should have listed proofs as a third topic.
    - wheelinsupial 4y ago
      You're right it is a big part of advanced math, but you can cover calculus, linear algebra, and proofs in parallel! If you have enough time.

bandrami 4y ago

Books 1, 2 and 6 are plane geometry, books 3 and 4 are what we now call trig, book 5 is on what we now call real numbers, books 7-9 are on integer number theory, book 10 is on irrationals, and books 11-13 are on solid geometry.