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.
CONTENT:
- All sections
- Section 1
- All Sections
- Sections 1, 2, 3, and 4
- Sections 1 and 3
- Sections 1 and 2
- Sections 1 and 2
- 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
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
Andrews, George E., Number Theory,
Dover Publications Inc.,
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.,
Rosen, Kenneth, Elementary Number Theory, Addison
Wesley Publishing Co.,
Relevant Web Sites:
The MacTutor History of Mathematics archive
Things of interest to Number Theorists
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,
Biographies of Women Mathematicians
Please send your comments: Hassen@rowan.edu
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This page was last updated on 8/31/07