Teacher:

Dr. Caldwell, office 429 Holt Humanities, phone 7336. Department office 7360. Email: caldwell@utm.edu.  
Mathematics 314 (aka 241)  
The integers: wellordering, different bases, divisibility, primes, and factoring. The fundamental theorem of arithmetic and the division algorithm. Diophantine equations and applications of congruences. Pseudorandom numbers, pseudoprimes, and cryptography.  
Grading will be done according to the following weights in a "fair
and subjective" manner


Homework is due at the beginning of the following class meeting (it must be on the table before class begins). Homework may be turned in early (place it in my mail box, my hand, or gently slide it under my door). Late homework will be reduced in value by 50% for each day, or fraction thereof, it is late. Some of the homework will be easy, some difficult and some may be impossible (because that is the way problems are in real life)! Part of what you are to learn is what you can and cannot do.  
Number theory is the study of the integers which includes such things as cryptology, divisibility rules, finding massive primes... It is a great course for secondary education students because of its many simple and curious problems. Yes, number theory has proofs, though it is nowhere as proof intensive as Abstract Algebra or Real Analysis.  
Objectives:

The student will:


Elementary Number Theory (5th Edition, 2004) by Kenneth H. Rosen, Addison Wesley, 744 pages, ISBN10: 0321237072, ISBN13: 9780321237071. 

To be determined based on student/teacher interests, one possibility follows.  
topic  days  
The Integers  5  
Primes Greatest Common Divisors  6  
Congruences  5  
Some Special Congruences  5  
Multiplicative Functions  5  
Cryptology  6  
Other (e.g., primality proofs, "mathemagic")  5  
37  
One Hour Tests  3  
40 