Number Theory (3)

Dr. Caldwell's Math 350 Syllabus
(This Math 350 syllabus and other course resources are avaiable at www.utm.edu/~caldwell)

Teacher:

Dr. Caldwell, office 429 Humanities, office phone 7336.  Department office 7360.  E-mail: caldwell@utm.edu.  Web page: www.utm.edu/staff/caldwell.  I will use your e-mail as stored in Banner, usually an @ut.utm.edu account, to contact you (if the school closes, to send additional notes, ...) so please make sure that it is accurate.

Catalog Description:

Math 350:  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.

Image of textbook

Text:

Friendly Introduction to Number Theory, 4th Edition, Joseph H. Silverman.  ISBN-13: 9780321816191 (which is the 4th Classic Edition 9780134689463).

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

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.

Grading:

Grading will be done according to the following weights in a "fair and subjective" manner

Homework:

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.

Learning Outcomes for Major:

Upon completion of his/her degree from the University of Tennessee at Martin with a major in mathematics, the graduate will be able to:

  1.   apply mathematical concepts and principles to perform numerical and symbolic computations;
  2.   use technology appropriately to investigate and solve mathematical and statistical problems;
  3.   write clear and precise proofs;
  4.   communicate effectively in both written and oral form; and
  5.   demonstrate the ability to read and learn mathematics and/or statistics independently.

Teaching Objectives:

The student will:

  1.   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.
  2.   Identify certain number theoretic functions and their properties.
  3.   Understand the concept of a congruence and use various results related to congruences including the Chinese Remainder Theorem.  Solve certain types of Diophantine equations.
  4.   Identify how number theory is related to and used in cryptography.

Relates sites

Syllabus:

The Department of Mathematics and Statistics publishes a syllabus for each of it courses which may be viewed in my office or on the departmental web pages.

Canceled classes:

You (and the state) have paid well for the courses taught here so mathematics and statistics teachers very (very) rarely cancel classes. However, sometimes (especially in the spring) the university closes due to bad weather.  If this happens, I will contact you by the e-mail address stored in the Banner system to let you know how we will make up the work.  I will also adjust the homework schedule on-line as needed.

Disability Services:

The University of Tennessee provides reasonable accommodations (academic adjustments and auxiliary aids) to ensure equal access to educational content and university programs for students with disabilities.  Any student eligible for and requesting accommodations due to a disability must provide instructors with a letter of accommodation from Disability Services.  For additional information, please contact the Disability Services office at 209 Clement Hall, (731) 881-7605.

 

Questions:

If you have any questions: