Syllabus for Theory of Numbers

Dr. Abdul Hasten

Office:  Robinson Hall,  Mathematics Department Room 229E

Phone  (856) 256-4500 ext 3888. e-mail:  hassen@rowan.edu

Office Hours: M 11:00am - 12pm, TR 11:00am - 12pm,   and by appointment

PREREQUISITE: Calculus II

CATALOG DESCRIPTION: (For mathematics majors; open to others with permission; background in abstract or linear algebra is recommended.) This course includes divisibility properties of the integers, theory of congruence, Diophantine Analysis, quadratic and nonquadratic residues, history, and famous problems in number theory.

OBJECTIVES: It is the objective of this course to present the students an introduction to an area of pure mathematics which has intrigued nonprofessionals as well as the greatest minds of human kind since the dawn of history. A brief history of the development of numbers and some of the influential number theorist will be presented. Some application will also be considered.

TEXT:  Kenneth H. Rosen, Elementary Number Theory and Its Applications, 5th ed., Addison-Wesley Pub. Co.


CONTENT:

Chapter 1. The Integers

  • All sections

Chapter 2.   Integer Representations and Operations

  • Section 1

Chapter 3. Primes and Greatest Common Divisors

  • All Sections

Chapter 4.   Congruences

  • Sections 1, 2, 3, and 4

Chapter 6. Some Special Congruences

  • Sections 1 and 3

Chapter 7. Multiplicative Functions

  • Sections 1 and 2

Chapter 11. Quadratic Residues

  • Sections 1 and 2

Chapter 13. Some Nonlinear Diophantine Equations

  • Pythagorean Triples
  • Fermat Last Theorem
  • Sums of Squares
  • Pell's Equations

GRADING POLICY: Students will be graded based on three tests (80% of grade), a short biography of two Mathematicians,  presentations on number theory articles, class participation, and homework  (20 % of grade).

For Homework Exercises click here

The materials in each test will be as follows:

Test 1 (30%) Covers all sections of chapters 1 and 2 and sections 1 to 4 of chapter 3.
Test 2(30%) Covers the remaining sections of chapter 3, all sections of chapters 4 and 5.
Test 3(20%) Covers the remaining chapters.

Numerical grades will be converted to letter grades by the following scale.

 A (-)= 90 to 100   B(-,+) = 80 to  89    C(-,+) = 70 to 79     D(-,+)= 60 to 69     F=  0 to 59


Attendance Policy:

Attendance is mandatory. An attendance sheet will be passed around at the beginning of each class period. Please write your signature next to your printed name on the list. If you are absent/tardy from a class, you must submit a note requesting that the absence/tardiness be excused by the next class meeting. Each student is allowed a total of three unexcused absences/tardies (combined). If you miss a class, it is your responsibility to study the section(s) covered and do the homework.
          
If you are absent the day of a regularly scheduled test, a grade of zero is automatically recorded as your test score. You will be permitted to make up this zero only when you can confirm that you were absent for reasons beyond your control.  In such cases, you must telephone 256-4500 extension 3888 (or send me an e-mail) and leave a message including your name and telephone number, the reason for your absence and the date you anticipate returning. Students who fail to leave the above information will be assigned the grade of zero for that test.



Academic Honesty: Cheating on a test or assignment seriously undermines the integrity of the academic system and will not be tolerated.  If I determine that a student has cheated, I will assign the grade of F for this course and send a letter to this effect to his advisor.  Although a student is not cheating, he or she is expected to refrain from actions that could be suspicious.  Using common sense on your part should avoid unnecessary embarrassment.



Classroom rules:

ˇ Students will abide by Rowan's student code of conduct and policy on academic honesty (p. 19 and p. 28 of Rowan 1999-2000 undergraduate catalog, respectively).  Improper behavior will not be tolerated.
ˇ Students are not permitted to leave the classroom during class period except for emergencies or unless prior arrangements have been made with the instructor. Please use the restrooms before class begins.



Students with Disabilities and Special Needs: Please speak with me as early in the semester as possible so that we can make appropriate accommodations for you. If necessary, you can also contact the Office of Special Services.



Questions in Class: The best time to ask questions is during class. Many times students fear that their questions will seem foolish, while in fact, many others also have the same question.  I urge you to ask your questions during class. If you have questions that were not answered in class, you may stop by my office during the following office hours.



MATHEMATICA PROGRAMS

Mathematica Notes

GCD

Primes of the form n^2+1

Sum of  Three Squares


ARTICLES OF INTEREST

Playing with Partition on the Computer by  Abdul Hassen and Thomas Osler

For other readable and accessible papers visit the web page of Thomas Osler


REFERENCES

           Ore, Oystien, Number Theory and Its History, Dover Publications Inc., New York, 1988.

Andrews, George E., Number Theory, Dover Publications Inc., New York, 1994.

Niven, Evan, Zuckerman, Herbert S., and Montgomery Hugh L., Introduction to the Theory of Numbers, 5th Ed., John Wiley and Sons Inc., New York, 1991.

Hadry, G. H. and Wright E.M., Introduction to the Theory of Numbers, 4th Ed., Oxford University Press, London, 1965.

Rosen, Kenneth, Elementary Number Theory, Addison Wesley Publishing Co., Reading, MA, 1988.


Relevant Web Sites:

The MacTutor History of Mathematics archive

 Things of interest to Number Theorists

What is New in Mathematics

Topics of interest on the Web


Mathematics Organizations

The American Mathematical Society

The Mathematical Association of America


Some of the famous Number Theorists:

Pythagoras Euclid, Erdös, Euler, Fermat, Gauss, Goldbach, Hilbert, Lagrange, Ramanujan,

Female mathematicians

Biographies of Women Mathematicians


Please send  your comments: Hassen@rowan.edu

Back to Abdul Hassen's Home Page

This page was last updated on 8/31/07