Is euclid a good book for self-study?

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Discussion Overview

The discussion revolves around the suitability of Euclid's Elements for self-study in mathematics, particularly in geometry and trigonometry. Participants explore various book recommendations and resources for learning these subjects independently.

Discussion Character

  • Debate/contested
  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • Some participants suggest that Euclid's Elements contains good proofs but may be difficult for self-learners, especially younger students.
  • Alternatives to Euclid are proposed, including "Introduction to Geometry" by Rusczyk, "Geometry" by Jacobs, and "Kiselev's Geometry: Books I & II" by Givental, with Rusczyk's book being highlighted as particularly suitable for self-study.
  • One participant expresses a strong preference for Euclid, recommending a specific edition and additional resources for guidance.
  • Concerns are raised about the clarity of Richard Rusczyk's ideas and whether his teaching methods are preferable to traditional schooling.
  • Participants discuss the sufficiency of the Art of Problem Solving books for self-study, with some asserting that they are adequate without accompanying courses.
  • It is noted that Euclid in its original form may be very challenging for self-learners, but there are online resources that can aid understanding.
  • One participant advises pacing oneself with Euclid, suggesting that even partial completion of the text can provide a solid grasp of geometry.

Areas of Agreement / Disagreement

There is no consensus on the recommendation of Euclid's Elements; some participants advocate for it while others caution against its difficulty. Multiple competing views on the best resources for self-study remain unresolved.

Contextual Notes

Participants express varying opinions on the accessibility of Euclid's work and the effectiveness of different teaching resources, highlighting the subjective nature of learning preferences and experiences.

Who May Find This Useful

This discussion may be useful for students interested in self-studying geometry and trigonometry, educators seeking resource recommendations, and anyone considering the merits of classical texts in mathematics education.

phynoldus
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Hi, I am a thirteen year old boy with a great interest in math and physics.
I just want to ask which books is good for self-studying trigonometry all the way to physics?
 
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Do you mean geometry? Euclid's Elements has good proofs but it may be difficult to learn from. Here is a book that should be better, and it seems to have a lot of knowledge packed into it.

As for more modern books, they are either grade-specific or advanced or very expensive. I could not find a cheap book to recommend.
 
If you are interested in geometry, then I can recommend the following 3 books:

Introduction to Geometry by Rusczyk
Geometry by Jacobs (1st Edition)
Kiselev's Geometry: Books I & II - Givental

I think in your situation, the book by Rusczyk would be best; it is designed for self-study. He is the founder of The Art of Problem Solving and I would highly recommend that you check out any and all of their other books. As for trigonometry, you can look at:

Trigonometry by Gelfand
Precalculus by Rusczyk

These are tough books, but they are great for self study.
 
I would not personally recommend Euclid to most people.
 
dustbin said:
If you are interested in geometry, then I can recommend the following 3 books:

Introduction to Geometry by Rusczyk
Geometry by Jacobs (1st Edition)
Kiselev's Geometry: Books I & II - Givental

I think in your situation, the book by Rusczyk would be best; it is designed for self-study. He is the founder of The Art of Problem Solving and I would highly recommend that you check out any and all of their other books. As for trigonometry, you can look at:

Trigonometry by Gelfand
Precalculus by Rusczyk

These are tough books, but they are great for self study.

Thanks. I have already ordered it from Amazon:)
 
If you bought the Art of Problem Solving books, they (AoPS) also offer online courses (even over the summer) for reasonable prices ($200-300). Just a thought if you are interested! Enjoy.
 
A warning: according to this page by Richard Rusczyk, the "Calculus Trap" is not about calculus and is not a trap. So his ideas don't seem too clear to me. Do I trust him to teach me better than a school can? Not sure about that. Hopefully his books are better than his articles.
 
I recommend Euclid above all other books. I suggest the beautiful paperback edition by Green Lion press. As a guide you may consult my free epsilon camp notes on my website at uga math dept, or buy the fantastic book by Robin Hartshorne, Geometry: Euclid and beyond.
 
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dustbin said:
If you bought the Art of Problem Solving books, they (AoPS) also offer online courses (even over the summer) for reasonable prices ($200-300). Just a thought if you are interested! Enjoy.

If i buy the books could i learn just from those or do i need the course aswell?
 
  • #10
The books are completely sufficient on their own! I just suggested the courses in case you were interested, as I think they are a fine deal for someone who prefers a class setting.

Mathwonk's suggestion is great, also, but I would have struggled with that approach when first learning geometry (especially on my own).
 
  • #11
dustbin said:
The books are completely sufficient on their own! I just suggested the courses in case you were interested, as I think they are a fine deal for someone who prefers a class setting.

Mathwonk's suggestion is great, also, but I would have struggled with that approach when first learning geometry (especially on my own).

Okey, thanks for the suggestion i will check it out!
 
  • #12
Euclid in its orginal form (translated, of course) would be very, very difficult for a self-learner of any age, let alone someone your age. But there is a website that accompanies Euclid with Java applets and explanatory comments that is one of the true gems of the internet.

http://aleph0.clarku.edu/~djoyce/java/elements/elements.html
 
  • #13
Difficult, but you'd be way ahead if you get through any of it. I would advise you pace yourself. Don't think you're going to get through all 13 books. If you get through just he first, you'll have an excellent grasp of geometry. Even half of the first. If you REALLY want to get something out of it, you should seriously sit there with a protractor and a ruler and follow the arguments in a physical way. The site posted by brocks and any help or commentaries you can find are good.


-Dave K
 

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