An Introduction to Number Theory

by Edward B. Burger

An Introduction to Number Theory (2 volume set)

Genres: Mathematics, Audiobook, Science

400 pages, Paperback

First published January 1, 2010

Reviews

[Bruce · Rating 4 out of 5]

This is a book that accompanies a series of lectures sold by The Great Courses. It’s not a transcript, but is detailed enough to read and follow, depending on your knowledge of math. Burger focuses a lot on prime numbers and modular math to develop some very deep concepts, and weaves quite a bit of math history into the lectures. I think you can read it at different levels, though it’s not really a “popularization” like some math books. I was able to get the course from my local library, though it would be worth buying if you got it on sale. Note that typically you couldn’t get the book without the DVDs. You can learn a lot more about it by visiting the Great Courses website.

[György · Rating 5 out of 5]

Here is a problem to solve:
1+4=5
2+5=12
3+6=21
8+11= ?
I'll claim the result is 40! The problem here is pretty axiomatic. The math is strict, disciplined, there are rules, they are clear, yet, if let your imagination a freedom to explore, you might come up with some other numbers... Enjoy!
Back to the review...
All my respect goes to professor Burger! I'll avoid to present all the fields lurking behind this lecture, but by mentioning some I'll make an attempt to point on values of this Course! Sure, the beginning is about the numbers, about their attributes. Then the things start to unfold in some logical order that gave me an impression as I'm in some kind of Mathematical CERN where instead of particles, numbers are not accelerated, but all numbers, axioms, operations, equations are slowed down so I could follow comfortably what and how things happen, and suddenly all become clearer. I saw very clearly geometric progressions, the exponential growth, the recurrence sequences, the Binet and the Euler's formula, met the division algorithm and the modular arithmetic, I was surprised when had to engage cryptography with Fermat's little theorem, his method of Ascent, and his Last theorem...and so on. When start something exciting I'm always nurturing some secret hope to encounter at least one "anticipated serendipity", that is something new, something big, a sort of a mesmerism! Well, it doesn't happens so often, but this time I was lucky! Despite of the burning desire to share it with you, I'll tell you only that it is related to Fibonacci and the Golden ratio....
The Course is brilliant, it's a real pabulum that will make you feel pretty elysian. Enjoy!