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- #1

I am looking for applications which will motivate the student in this subject.

Are there good resources on elementary number theory?

- Thread starter matqkks
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- Thread starter
- #1

I am looking for applications which will motivate the student in this subject.

Are there good resources on elementary number theory?

- Jan 29, 2012

- 661

An Introduction to Number Theory

- Jan 30, 2012

- 2,526

Another interesting topic that touches number theory is squaring the circle. It took us a third of a semester during the fourth year in college to cover the theorem that $\pi$ is transcendental, so this fact should probably be given without a proof. However, it is interesting why every line segment built from a segment of length 1 using only compass and straightedge has an algebraic length. I don't think I have ever studied a rigorous proof. However, this may be more of a geometrical than number-theoretical theorem.

Finally, I would look at public-key cryptography, but I don't know if it is possible to omit enough details to make it into both an accessible and a rigorous course.

- Jan 30, 2012

- 2,526

From the title page:

An Introduction to Number Theory

"An Introduction to

Number Theory

With 16 Figures"

I wanted to exclaim, "Yeah, this is not geometry, baby! You should be happy with just a handful of pictures". Also, the beginning of "Alice in Wonderland" comes to mind.

Alice was beginning to get very tired of sitting by her sister on the bank, and of having nothing to do: once or twice she had peeped into the book her sister was reading, but it had no pictures or conversations in it, `and what is the use of a book,' thought Alice `without pictures or conversation?'

- Jan 26, 2012

- 644

I don't think so. It's fun and all as an example of applications of number theory but without computational complexity theory and an actual course in cryptography the students are going to be lost. Cryptography needs its own separate course IMHOFinally, I would look at public-key cryptography, but I don't know if it is possible to omit enough details to make it into both an accessible and a rigorous course.

Also, on topic: modular arithmetic. The single most important tool. No elementary number theory course is complete without it.