Mathematics 115, Spring, 1998

Professor Ken Ribet

Office hours: Tuesday, 11AM-12:30 PM; Friday, 3:30-5 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 11:10AM-noon.

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.

Some other books on number theory

Examinations

First Midterm: February 25, in class ( questions and answers)
Second Midterm, April 8, in class ( questions and answers)
Final Exam, May 18, 12:30-3:30 ( questions, but no answers)

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 |G-h_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
- TeachMath at Berkeley
- Teach for America (February 13, 1998)
- Large prime discovered by 19-year-old sophomore (February 3, 1998)
- Fermat's Last Theorem T-shirt (we will put in a group order if there's interest)
- Number Theory Web
- Life by the Numbers
Kenneth A. Ribet , Math Department 3840, Berkeley CA 94720-3840

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