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C00002 00002	To:  Ph.D. students planning to take the comprehensive exam in January
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To:  Ph.D. students planning to take the comprehensive exam in January

I have proposed that the concrete math part of the comp syllabus be revised
to refer to the new CS260 text by Graham, Knuth, and Patashnik.

I have proposed the specific sections listed below, with some expansion of the
topics covered in the old syllabus.  I believe the better exposition in the
new text will hold the labor of preparation constant, having myself learned some
of this material from the new book.

Specifically, I proposed including recurrence relations, the mod function,
divisibility, primes and relative primes, modulo arithmetic, generating
functions, and discrete probability theory.  I do not propose to include
Abel's theorem, Eulerian numbers, Bernoulli numbers, the Euler
summation formula, or any advanced case studies.

As I understand it, CS260 covers all these proposals.  I believe that the 
GKP exposition is very clear, and that it provides a powerful and accessible
problem-solving tool.  I believe that elementary probability theory is an 
mail davis@scorepirical as for theoretical computer scientists.  The other new
topics are just plain easy.

I am least decided about Sections 1.3, 8.5, 9.4  This is my proposed list:

1.1, 1.2; Chapter 2; 3.1, 3.2, 3.4; 4.1-7; 5.1-4;
6.1, 6.3, 6.6; 7.1-5; 8.1-4; 9.1-3

I invite comments, on behalf of the theory subcommittee.