Which Introductory Number Theory Book for High School?

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Discussion Overview

The discussion revolves around recommendations for introductory number theory books suitable for high school students. Participants express preferences for self-study materials and discuss various resources, including textbooks and online courses.

Discussion Character

  • Exploratory
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for an introductory number theory book appropriate for high school.
  • Another participant mentions a free online course by Dr. Keith Devlin, suggesting it includes a textbook available for purchase.
  • A participant expresses a preference for self-study books over video lectures.
  • Questions arise regarding the mathematical background of the original poster and the specific topics they wish to cover in number theory.
  • The original poster lists topics of interest, including congruences, primes, and Euler's function.
  • One participant suggests that learning some basic abstract algebra or discrete math could be beneficial for understanding number theory.
  • A recommendation is made for the book "A Book on Abstract Algebra" by Pinter, noting its comprehensive coverage of relevant topics but also its lengthy progression to number theory.
  • Another participant shares concerns about time constraints for self-studying and the quality of school textbooks, emphasizing the need for a more comprehensible resource.
  • Links to free online pages and another book are provided as additional resources that may be more immediately accessible.
  • The original poster indicates a decision to purchase a book by Dudley based on the suggestions received.

Areas of Agreement / Disagreement

Participants express varying preferences for learning materials, with some favoring textbooks and others online courses. There is no consensus on a single recommended book, as different resources are suggested based on individual needs and learning styles.

Contextual Notes

Participants discuss the need for a book that covers specific topics in number theory while also considering the prerequisites and the time required for self-study. The discussion reflects a range of mathematical backgrounds and learning preferences.

Kevin Licer
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Hello, I'm looking for an introductory number theory book for high school. Any recommendations are welcome. Thanks.
 
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Dr. Keith Devlin at Stanford offers a free online course: https://www.coursera.org/course/maththink
After you sign up, it takes you to his video series. Click on Lecture 9A (Introduction to Number Theory).
The accompanying textbook is available on Amazon for about $10.
 
Thanks! I'll look into it, but I'd prefer studying from a book written in a somewhat self-study fashion. I'm not so big on watching videos.
 
What math do you know? What number theory do you want this to cover?
 
Well, I have an understanding of basic high school algebra and geometry, some rudimentary linear algebra (2x2, 3x3 and their properties, and solving system linear equations), basic trigonometry (we are going to start learning about the graph of trig functions soon) and etc. Well I want it to contain things like congruences, primes, multiplicative function, divisibility, euler's function and theorem and so on.
 
Would you be alright with learning some basic abstract algebra or discrete math?
 
Well, I suppose since I do want to learn the subject without any gaps, I mean if it is more beneficial, then why not?
 
The book by Pinter "A book on abstract algebra" can be found for very cheap, and it contains all the topics you listed. On the downside, you need to complete quite some bit of the book to reach those topics. But Pinter is really well-written and elementary (which can not be said from similar books on the same topic), and the topics found in Pinter are very useful if you want to go on in number theory.

If you want some help with self-studying Pinter, feel free to PM me!
 
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I saw the book on amazon (the second version) and it does seem to take time to get to number theory. I would like to self-study it, but I don't know if I'm going to have that much time for it because the reason I'm looking for a book on number theory is that our school books are terrible and incomprehensible and we're studying the subject matter right at the moment. So that's why I wanted to self-study the material, to actually understand some of it. Even though the book definitely looks like a must have.
 
  • #11
Looks like I'm going to get the book by Dudley. Thanks to everyone for the suggestions, it was really helpful.
 

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