Introduction to Number Theory

MATH 506

Spring 2014 - Chris Pinner- 12387

MWF 9:30-10:20 CW120

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


Advanced Help Session Schedule


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 277-1, 1080+1 and 3031-1 (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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Printable 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 32+
42=52) and other Diophantine equations, Perfect Numbers (eg 6=1+2+3 is the sum of its proper divisors), rational versus irrational, arithmetic functions, rational approximation & continued fractions (eg pi is close to 22/7, 355/113 is better; how do we obtain approximations like these?), quadratic congruences & quadratic reciprocity. We may occasionally include material outside of the text.

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!

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:


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Some Number Theory Things