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< URL: http://www.math.uiuc.edu/~pppollac/595/ > |
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Course summary |
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This is a course on elementary methods in number theory. This means that we will concentrate on problems which can be attacked without significant mathematical prerequisites.
We will use the textbook Not Always Buried Deep, which will be published by the AMS later this year (2009). A preliminary copy of this text will be made available to you electronically.
Possible topics that may be covered include:
The infinitude of primes
Cyclotomy as Gauss knew it and Jacobi's rational cubic reciprocity law
Chebyshev's and Mertens's elementary results in prime number theory
An elementary proof of Dirichlet's theorem on primes in arithmetic progressions
An elementary proof of the Legendre—Gauss theorem on sums of three squares
An elementary proof of the Waring—Hilbert theorem on representing integers as sums of kth powers
Introduction to sieve methods and applications
The Erdös—Selberg proof of the prime number theorem
What we know and don't know about perfect numbers
What gets covered depends on what you want to see, so don't be shy!
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Paul Pollack |
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Office: 301 Altgeld |
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Office hours: 2-3 PM MWF |
Please feel free to drop by and ask questions!
There are no exams in this class. (Whew!) Your grade is based entirely on homework, which will be assigned/collected every 1-2 weeks. You should expect to put substantial effort into the homework problems. I intend for those of you who (correctly!) answer more than 50% of the homework problems to receive an A in the class – and there's no reason why this can't include everyone.
I strongly recommend that you collaborate with others on the homework problems. Many of the problems are based on expository articles or research papers. If you are stuck on a problem, feel free to look at the article which inspired it. (Usually a citation is given with the problem.) I ask only that you understand whatever solution you turn in to me.