Mathematics 350 (3 credit hours)
Number Theory (Spring 2015)

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Related pages: [ The Prime Pages | Number Theory Web | RSA FAQ | MathSciNet | Integer Sequences | Listen to Primes ]

Dr. Caldwell, office 429 Holt Humanities, phone 7336. Department office 7360. Email:
Mathematics 314 (aka 241) 
Catalog Description:
The integers: well-ordering, different bases, divisibility, primes, and factoring.  The fundamental theorem of arithmetic and the division algorithm.  Diophantine equations and applications of congruences.  Pseudo-random numbers, pseudoprimes, and cryptography. 
Grading will be done according to the following weights in a "fair and subjective" manner 
  • 41 %   tests (approximately four one-hour tests) 
  • 29 %   homework (assigned daily) 
  • 19 %   final (comprehensive) 
  • 11 %   class project
When homework is assigned, I will tell you when it is due.  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 to fully complete--but you can show me what effort you made.
Number theory is the study of the integers which includes such things as cryptology, divisibility rules, finding massive primes, error correcting codes and magic tricks.  It is a great course for secondary education students as well as those looking for undergraduate research projects because of its many elementary and elegant problems that often lead to deep consequences.  Yes, number theory has proofs, though it is nowhere as proof intensive as Abstract Algebra or Real Analysis.
Honesty & Internet:

Students are encouraged to work together, but you must write up the solutions yourself, independently from others, while you are alone.  I urge you to use the internet honestly.  You may look up definitions but do not search for solution to the problems in assignments or ask about them on-line.

The library also has a great deal of useful books, many under the subject heading "elementary number theory." If you use ideas which are not your own, please indicate your source appropriately. If what you find makes the solution trivial, then check with me before submitting to make sure the abbreviated work will get full credit.  The point of excises is to develop your understanding, not to borrow from others.

I assume you understand the university policies found in the student handbook.

The student will: 
  • Identify and apply various properties of and relating to the integers including the Well-Ordering Principle, primes, unique factorization, the division algorithm, and greatest common divisors.
  • Identify certain number theoretic functions and their properties.
  • Understand the concept of a congruence and use various results related to congruences including the Chinese Remainder Theorem.
  • Solve certain types of Diophantine equations.
  • Identify how number theory is related to and used in cryptography. 

A Friendly Introduction to Number Theory, Joseph H. Silverman Fourth Edition, ISBN: 978-0-321-81619-1 © 2012 Pearson Education, Inc. ix + 409 + (56 on-line) pages.

We will cover the first 19 chapters and then continue based on student (and teacher) interests.