Topics in Number Theory

UNIVERSITY OF WAIKATO

Department of Mathematics

MATH509-08B – Topics in Number Theory - 2008

Paper Outline

Due date for the handing in of assignments is 5pm Friday 31st October.

Web Site:

The URL for this is http://www.math.waikato.ac.nz/~kab: click on the link pointing to this page.

Lecturer:

Associate Professor Kevin Broughan, Office G3.22,
Tel 838-4423, x4423, email kab@waikato.ac.nz
Office Hours: Thursdays 3-5pm in G3.22 for weeks 2-12.

Timetable:

Tuesday 10-11am in G3.22,
Friday noon-1pm in G3.22

Prescribed Text:

Introduction to Analytic Number Theory, by Tom Apostol (Springer). The library has a copy.

Syllabus:

This will be run as a reading course, leading to the analytic proof of the prime number theorem. To get there about a chapter a week will need to be digested. The sessions with the lecturer will be devoted to an examination of the steps in the argument which are unclear or cannot be followed without difficulty.

Week 1: Historical intro and Ch 1 all sections. Suggested exercises: p21 # 5-7, 11, 14-17, 20, 23, 28.
Week 2: Ch2 sections 2.1-2.10 and 2.12. Suggested exercises: p46 # 1,2,6,8,11,12,14,15,16,18,21,27,30.
Week 3: Ch3 all sections except 3.6. Suggested exercises: p70 # 1,2,6,9(a),13,18.
Week 4(5): Ch 4 all sections except 4.10,4.11, Suggested ex: p101 # 8, 11-16,18,19,21,26.
Week 5: Ch5 sections 5.1-5.9. Suggested ex: p126 # 1,2,6,7,9,11,16,18-21. (some of these look quite hard.)
Week 6: Ch 6 all sections. Suggested ex: p143 # 9,11,12,15.
Week 7: Ch 7 all sections. Suggested ex: p155 # 1-3, 5-7.
Week 9: Ch 11 all sections. Suggested ex: p246 # 1(a)(c), 3,4,5,15.
Week 10 and 11: Ch 12 sections 12.1-12.8, 12.14-12.16. ex: p273 # 1,5,6,7.
Week 12: Ch 13 sections 13.1-13.9. ex: p300 # 1,2,4,5.

Assessment:

There are exercises in the text and you should try some of these. The solutions to two exercises, should be written out and handed in each week in 10 or more lots. The assessment will be based on the best 10.

Associate Professor Kevin Broughan (Convenor)

14th October 2008