Introduction to Number Theory

MATH 506

Spring 2008 - Chris Pinner- 17070

MWF 9:30-10:20 CW144

Chris Pinner
CW113
pinner@math.ksu.edu
532-0587
Office Hours TBA
Home-Page: http://www.math.ksu.edu/~pinner/math506


Updates

Exam 3 is scheduled for Wednesday April 16 & covers up to & including Chinese Remainder Theorem.

Exam 2 is rescheduled to Wednesday March 26.

We have a Homework box (near main doors in Cardwell). Homework
is due in the box by 5pm on Fridays.

Advanced Help Session Schedule


Homeworks

Hw1: Ch0: 2,4,5,6,7,10,12.
Hw2: 1.1: 8,10,16,20,24.  1.2: 2,4,10,16,20,32,33.
Hw3: 1.2: 29,30,31,35,36.  1.3: 4,6,8,18,28.
Hw4: 1.4: 6,18,24,34,36,39.  1.5: 10,16,32,36,45.
Hw5: 3.4: 16,17,18,19.  2.4: 22,24,28,38,40,42.
Hw6: 1.6: 22,25,32,39,46,49.
Hw7: 2.1: 27,30,39. 2.3: 22,30,42. 7.1: 20,22,28,30.
Hw8: 2.4: 16,52. 2.5: 4,12. 2.6: 10,12,14,32,43,46.
Hw9: 2.5: 17,19,20. 2.6: 24,28,30,44. 3.1: 8.  A) Prove that 361/3  and (8/9)1/4  are irrational.
Hw10: 2.6: 17,18,20. 3.1: 14,22,30,36. 3.2:10,20,25.
Hw11: 3.2: 22,24. 3.3: 27,28,30. 3.6:2,10,12,17,18,20.
Hw12: 3.5: 22,34,36,52. 4.1: 26,32,34. 4.2:2,10,12.
Hw13: 4.2: 16,20,24,32,34,37,51. 4.3:28,30,43.
Hw14: 4.3: 4,8,20,36,47. 4.4: 4,8,14,25. 4.5: 20.
Hw15: 4.5: 30. 6.4: 6,14,34,36,42. 6.2: 22,26. 6.3: 4,8,16.


Exam Solutions:

Blank Exam 1   Solutions

Blank Exam 2   Solutions

Blank Exam 3   Solutions

Blank Final Exam   Solutions


Syllabus

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.

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


Grade Scheme:
Homework (200 points)
Exam 1 Wed Feb 13 (100 points)
Exam 2 Wed Mar 12 (100 points)
Exam 3 Wed Apr  16 (100 points)
Final Exam Fri May 16 11:50-1:40 (200 points).

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 21 - MLK Holiday
Feb 6 - Last day for 100% refund
Feb 13 - Last day for 50% refund
Feb 21 - Last day to drop without a W
Mar 17-21 - Spring Break
Mar 24 - Last day to drop with a W
May 9 - Last Day of Class May 9.

Old Exams:

Spring2006:

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Blank Exam 2   Solutions
Blank Exam 3   Solutions
Blank Final Exam    Solutions
Spring2004:

Exam 1   Solutions: pg1:   pg2:   pg3:
Exam 2   Solutions: pg1:   pg2:   pg3:
Exam 3   Solutions: pg1:   pg2:   pg3:
Final Exam Solutions: pg1:   pg2:   pg3:  pg4:
Spring2003:

Exam 1 Solutions: pg1: pg2: pg3  
Exam 2 Solutions: pg1: pg2: pg3  
Exam 3 Solutions: pg1: pg2: pg3
 Final Exam Solutions: pg1:   pg2:   pg3:  pg4:



Some Number Theory Things