I need to teach an intro course on number theory in 1 month. I was just notified. Since I have never studied it, what are good books to learn it quickly?
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What about "The Little Book of Bigger Primes" by Ribenboim (see 1 for the Amazon link)? I personally think this is a great introduction to the field of number theory and I have enjoyed it very much a few years ago. It is clear and nicely written. (Just to be clear: We are not talking about a course that also involves notable parts of algebraic number theory, are we?) |
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For an introductory undergrad course I'd say the book to use by a long-shot is Kenneth Rosen's Elementary Number Theory and its Applications The theory is all there, but it's placed nicely in a context appropriate for a mixed bag of undergrad students by a large number of interesting-but-doable exercises and informative historical notes. Modern applications to computer science, cryptography, etc are all there and can be emphasized (or not) as you see fit. This is what I'd read if I were you. Last time I checked, the book was annoyingly expensive - but this is the only criticism of it I have. Most students give this book very favorable reviews, too. |
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Stein's book may be useful (and it is free): http://wstein.org/ent/ |
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I don't think the OP has provided enough information to get a useful answer to his/her precise question (what text to learn quickly from). What level is the course being taught at? High school? Undergraduate for non-majors? Undergraduate for majors but without specific knowledge of any other undergraduate math courses beyond calculus? Undergraduate assuming some basic analysis and/or algebra? Graduate level? Something else?? As others have said, a perfectly reasonable thing to do when you are teaching any course for the first time and don't have strong opinions / too much expertise about it is to look at the textbook(s) that others have used who have taught the course recently. Thumb through them a little bit, then ask them how they liked the book and how well it worked for the course. If you found anything confusing or problematic in the book, ask them about that. I think someone with a PhD in mathematics (for the sake of argument, I'll assume the OP has one) should be able to pick up and read a textbook for any undergraduate class within a month and then be able to teach the class with a reasonable amount of competence. Of course, real insight takes more time than that, and it is not reasonable to expect that someone conscripted into service with one month's worth of notice (why is this, exactly?) will be able to provide that. |
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I think Jones + Jones http://www.amazon.com/Elementary-Number-Theory-Gareth-Jones/dp/3540761977 would be a good all-around introduction. It has solutions to every problem in the back, which can be helpful for self-study. |
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If it is a course elementary number theory, look at "Elementary Number Theory" by Dudley. http://www.amazon.com/Elementary-Number-Theory-Underwood-Dudley/dp/048646931X |
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