TEXAS A&M UNIVERSITY-Corpus Christi
Division of Computing and Mathematical Sciences

MATH 1390.001
Topic: NUMBER THEORY, 2 credit hours
Fall 2004

I. COURSE INFORMATION

• Meeting Time & Place: Flour Bluff High School Advanced Mathematics Course; Consultations on Wednesdays, 6th period (2 to 2:50 PM)
• Professor: George Tintera
• Office Phone: 825-6028
• Office Address: Center For Instruction 303
• E-MAIL Address: tintera@falcon.tamucc.edu
• Web Page Address: http://www.tamucc.edu/~tintera
• Office Hours by appointment 

II. COURSE DESCRIPTION

The course is an introduction to the theory of numbers. Topics covered include the Euclidean algorithm, greatest common divisors, diophantine equations, the Chinese remainder theorem, unique factorization of integers and rings of integers, Fermat's little theorem and RSA codes. The development will include a balance of algorithms and computation versus rigorous development and a balance of exploration and conjecture versus axiomatic presentation.

III. PREREQUISITES for the COURSE

Permission of instructor.

IV. TEXT and OTHER SUPPLIES REQUIRED

 A Pathway into Number Theory, R. P. Burn, Cambridge University Press, 2nd Ed.

V. COURSE OBJECTIVES

This course is designed to enable students to:

1. develop a means for exploring and understanding basic topics such as the Euclidean algorithm, greatest common divisors, diophantine equations, and the Chinese remainder theorem, and
2. be able to compute g.c.d.'s solutions to diophantine equations and Chinese remainder problems, and
3. understand unique factorization , and
4. be able to understand exponentiation as a one-way function and make basic applications of RSA codes.

VI. INSTRUCTIONAL METHODS AND ACTIVITIES

Methods and activities for instruction include: independent investigations of number theory by the student using the text as a guide, cooperative work with other students in programming activities to complement the investigations, class discussions to summarize the investigations and programming.

VII. EVALUATION AND GRADE ASSIGNMENT

The theory of numbers is the result of observation of calculations with positive integers and a summary of that experience. The students in this class will be evaluated according to the results of their observations and summary.

The methods of evaluation and the criteria for grade assignments are: class participation (25%), work on exercises from the text (50%), demonstration of an understanding of number theory through and testing (midterm = 10% and final = 15%).

Grading Scale: A - at least 90% average on all work; B - between 80% and 90%; C - between 70% and 80%; D - between 60% and 70%; F - less than 60%.

Grade Reports will be prepared on the following dates: September 3, September 24, October 15, November 5, December 3.

The Midterm (subject to change) is scheduled for the week of October 25. The Final Exam is scheduled for the week of December 6.

VIII. TENTATIVE COURSE SCHEDULE

August 18 - September 24: Chapter 1
September 27 - November 5: Chapter 2
November 8 - December 3: Chapter 3

IX. COURSE POLICIES

There are notes and answers to problems at the end of each chapter. You should not read them until after working on the problem yourself, and if necessary, contact the instructor for hints. Also, you are officially discouraged from seeking help from other books and sources until after you have solved a given problem. You should contact your instructor for hints instead.