Mathematics
115, Spring, 1998
Office hours: Tuesday, 11AM12:30 PM; Friday, 3:305 PM
885 Evans
Hall
Office telephone: 642 0648
Fax number: 642 8204
Secretary: 642 5026
email:
ribet@math.berkeley.edu
Our class meets in 3111
Etcheverry
Hall, MWF 11:10AMnoon.
Textbook
An Introduction to the Theory of Numbers
by Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery.
You want the fifth edition. Publisher is John Wiley & Sons, Inc.
This is a classic number theory textbook (``Niven & Zuckerman''), updated
by Hugh Montgomery. It is renowned for its excellent problems.
In this course, it is traditional
to discuss properties of the integers (factoring,
congruences, primitive roots, ...), quadratic reciprocity, and continued
fractions. I propose to follow the book in order, covering roughly
the first seven chapters.
Examinations
Please bring blue books to the examinations.
Homework
Homework will be assigned roughly every week. The grader expects to
grade papers very rapidly. He accepts no late homework!

Assignment due January 26, pp. 17,
1 (a, c), 2, 4a, 6, 11, 12.

Assignment due February 4:

p 20, #49

pp. 28ff, 2, 4, 8, 11, 12, 16, 17, 29, 30, 31

Assignment due February 13:
 pp. 40, #3, 4, 5
 pp. 56, #2, 5, 7, 8, 11, 13, 18, 28, 53, 54

Assignment due February 20:
 § 2.2: 1, 5 (a, c, e), 9, 11, 14, 15
 § 2.3: 2, 4, 7

Assignment due March 2:
 § 2.3: 28, 31, 36, 37
 § 2.6: 3, 4, 9

Assignment due March 9:
 § 2.7: 3, 8, 11
 § 2.8: 2, 8, 9, 10, 12, 18, 20, 21

Assignment due March 16:
 § 3.1: 4, 6, 7, 9, 13, 19, 23

Assignment due March 30:
 § 3.3: 7, 8, 9, 13, 14, 15

Assignment due April 10:
 § 4.2: 12, 13, 14
 § 4.3: 1, 2, 8
 § 7.1: 1, 3, 4, 5
 § 7.2: 1
 § 7.3: 1

Assignment due April 20:
 § 7.4: 3, 4, 7
 § 7.7: 1, 2, 3
 § 7.5: 2, 3, 4

Assignment due April 27:
 § 7.6: 2, 3, 4, 5
 Let G be the Golden Ratio. For which values of n do we have
Gh_n/k_n < 1/(k_n^2 sqrt(5))?
 § 2.4: 13, 14 (parts a, b, c), 15, 16

Assignment due May 4:
 § 5.1: 1, 3a, 4d, 5, 16
 § 5.3: 2, 3, 4, 5, 6, 7
Miscellaneous links related to number theory and/or this course
Kenneth A. Ribet
,
Math Department 3840, Berkeley CA 947203840
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