Chris Pinner

CW205

pinner@math.ksu.edu

532-0587

Office Hours (tentative): MWF 10:30 & other times by
appt.

Home-Page: http://www.math.ksu.edu/~pinner/math506

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Session
Schedule

Homeworks

**Hw1: Ch0**: 6,12. **1.1:
**8,10,16,17. **1.2: **6,8,12,18,20,33,34. (Due Fri Jan 31). (HW1 Questions)

**Hw2: 1.2:**
14,16,30. **1.3: **4,6,21,28. (Due Fri Feb 7).

**Hw3: 1.****4:** 2,6,24,26.
**1.5:** 2,4,16,22,32,36,45,47. (Due Fri Feb 14).

**Hw4: 2.4:** 22,28,32,38,40,42,51. **2.3:** 42. **1.6: **18,19,39,44.
(Due Fri Feb 21).

**Hw5:** Homework 5
Questions (Due Fri Feb 28).

**Hw6: 2.2:** 2,4,18,23. **2.3:** 22,28,30. **7.1: **20,22,26,28,30.
(Due Fri Mar 7).

**Hw7: 2.3:** 4,20,34,40. **2.4:** 16,52. **2.6: **10,32.
**3.4: **16,17,18,19.

A) Give a non-trivial factor for 2^{77}-1, 10^{80}+1
and 30^{31}-1 (Due Fri Mar 14).

**Hw8: 2.5:** 4,11,17,19. **2.6: **18,20,24,26,28,30,34,43,46.
(Due Fri Mar 28).

**HW9: 3.1: **8,14,18,30,36,40,44.** 3.2:**
8,10,13,20,25,26. (Due Fri Apr 4).

**HW10: 3.6:** 2,10,12,17,18,20. **3.5: **22,36,42,44.**
3.2:** 22,24. **3.3:** 30. (Due Apr 11).

**HW11: 4.1: **26,28,34,42,43. **4.3: **28,30,44. **4.2:
**2,8,10,16,32. (Due Apr 18).

**HW12: 4.2: **37,51. **4.3:** 4,6,8,20,36,45,47. **4.4:**
4,8,13,25. (Due Apr 25).

Exam
Solutions:

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Solutions

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Syllabus

Text: Elementary Number Theory, Charles vanden Eynden, 2nd edition, Waveland Press, ISBN 1-57766-445-0 (McGraw-Hill ISBN 0-07232-571-2 is the same edition).

Course Outline

Number theory is essentially the study of the natural numbers 1,2,3,...and their properties. It is one of the oldest branches of mathematics but continues to be an active area of research. For example a major modern day application is cryptography (the National Security Agency is the largest employer of Number Theorists in the country). Its problems, often simple to state, have in many cases remained unsolved for centuries.

We should cover much of Vanden Eynden. In particular proof by induction, divisibility, primes, uniqueness of factorization, congruences, Chinese Remainder Theorem, Cryptography, Pythagorean triples (eg 3

Prequisites

MATH 220 & 221 recommended but all that is required is a sound knowledge of College Algebra and some mathematical maturity.

Grade Scheme:

Homework (130 points)

Exam 1 Wed Feb 19 (100 points)

Exam 2 Wed Mar 26 (100 points)

Exam 3 Wed Apr 18 (100 points)

Final Exam Wed May 14 11:50-1:40 (150 points).

Exam dates are tentative!

Assignments

Homework will be assigned in class (due in the HW box by 5pm on the Friday of the following week). You will generally have about a week to complete the assignment. Don't leave your homework to the last minute (many of the questions will involve proofs or may require extended thought). Show all your work. Include your name and Math 506 on the front. The lowest homework score will be dropped.

General Information

If you have any condition such as a physical or learning disability, which will make

it difficult to carry out the work as I have outlined it or which will require academic accommodations, please notify me in the first two weeks of class. There will be no late homework or make-up exams. If you have to miss a test for a valid reason then your course grade will be determined from your remaining work (notify me as soon as possible).

Some Useful Dates

Jan 20 - MLK Holiday

Feb 10 - Last day for 100% refund

Feb 17 - Last day for 50% refund

Feb 25 - Last day to drop without a W

Mar 17-21 - Spring Break

Mar 31 - Last day to drop with a W

May 9- Last Day of Class.

Mandatory Syllabi Statements

See mandatory syllabi statements concerning

1. Academic honesty. 2. Accommodations for students with disabilities. 3. Expectations for classroom conduct.

Old Exams:

Spring2012:

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Solutions

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Solutions

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Final Exam Solutions

Spring2008:

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2 Solutions

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Solutions

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Spring2004:

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Some Number Theory Things

- The Prime Page.
- Archimedes Cattle of The Sun Problem.
- Certicom (Elliptic Curve Cryptography Area).
- The Number Theory Web.