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MATH 3083/5523 Elementary Number/Intro Number Theory Fall 2007
Day and Time: W 6:00-8:50 PM, Room: MCL 403
Instructor:
Dr. Ellina Grigorieva, Department of Mathematics and Computer Science
Office: MCL 414
Phone: 940-898-2452
E-Mail: [email protected]
(Please leave a voice mail message or email if I’m not in –I’ll get back to you)
Office Hours:
2:30 p.m.-4:00 p.m.
5:00 p.m.-6:00 p.m.
Tuesday
W-TH
(Don't hesitate to call or email for an appointment, if you cannot see me during these
hours.)
Class Materials: * Text: 1. Elementary Number Theory by Strayer, James
Text 2. Complex Math Problems and How to Solve Them, Chapter 1, by E.
Grigorieva (This chapter 1 will be given to you during the first week of class as a
free handout-supplement for the course)

A calculator TI 83 Plus (TI 83) is allowed for this class
Course Objective and Description:
Graduate course: This is a graduate course designed to help students not only to understand in
depth the underlying concepts but also start solving some really complex problems in number
theory. Graduate students will be asked to go to the board to do proof and learn oral presentation
skills. Though 5523-3083 will meet at the same time, all graduate students must be prepare to
take more difficult tests in order to satisfy the requirements for graduate level course. For example,
all graduate students will be getting individual projects on solving some number theory problem,
where they will demonstrate cumulative knowledge they gained over years of study and
particularly during this course.
Undergraduate course: This course is designed to help students develop their proficiency in
number theory, and so strengthen their understanding of the underlying concepts. This course will
teach students to solve problems in integers and do proofs.
Tests: There will be 3 major tests and a comprehensive final exam, 100 points each. You
will know the exam dates well in advance so long as you regularly attend class. Every test must be
done neatly. You should explain every major step and use your most readable handwriting. Makeup tests may be given only if a valid excuse is given and only when I am contacted within one
week of the aforementioned test date. A final exam will be given on December 12, 2007. at 6PM
Grades: There are will be 400 point possible. The grading scale is:
1
360-400=A
320-359=B
280-319=C
240-279=D
0-239=F
Class procedure: First, I will answer questions over previous material for 20-30 minutes.
After that, I will introduce a new material. Assignments will be given one day and discussed the
next class day. Students should be prepared to present problems in class. Classroom
presentations will count 20% of the final grade.
Attendance: Students who regularly attend class generally have a better understanding
of course material, which is reflected by higher exam scores. In addition, your attendance record
could be the determining factor in your final course grade if your grade is on borderline. Whether
you are present or not you are fully responsible for all deadlines and material taught or assigned.
Note: Since communications between students and their instructors is crucial in any
learning process, you are always welcome to discuss our coursework with me. My main
duty here is to serve you. In order to best serve you, I welcome and encourage your
comments and suggestions. It is my belief that through our joint effort we can make this
course both beneficial and enjoyable.
The last day to drop class without, but not TWU and receive a refund is September 12.
The last day to drop class without academic penalty is October 5.
The last day of Fall 2007 classes is December 8, 2007
Texas Woman’s University seeks to provide reasonable accommodations for all
qualified individuals with disabilities.
This university will adhere to all applicable federal, state, and local laws,
regulations, and guidelines with respect to providing reasonable
accommodations as required to afford equal educational opportunity. It is the
student’s responsibility to register with Disability Support Services at (940)8983835 (3830) and to contact the course instructor during the first two weeks of
the course to arrange for appropriate accommodations/ Also please be aware
that free tutoring is available through the Department of Mathematics and
Computer Science.
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MATH 3083/5523 Fall 2007 W 6-8:50PM MCL 403
Dr. Ellina Grigorieva
THIS SYLLABUS IS SUBJECT TO CHANGE!!!
DAY
Date
SECTIONS
PROBLEMS
1
08.29
1. Integers
2. Prime factorization
p2 Ex 2, p3 Ex 3, p9 #1, 2, 3, 4, 6, 8, 10, 12, 14, 15
p 19 # 1, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15
2
09.05
p26 #1, 2, 3, 4, 5, 6, 7, 8, 10
3
09.12
4
09.19 no class Spain
5
09.26
6
7
8
10.03
10.10
10.17
9
10.24
10
10.31
11
11.07
3. Linear Dioph. Eq.
3.
4. Congruences
4.
5. Linear Congruences
5. and Review
5. Linear
Congruences+review
Test 1
2.4 Wilson Theorem
2.5 Fermat’s Theorem
7. Divisor Functions
7.
8. Perfect Numbers
8. Review
9. Euler’s Function
Test 2
11. Quadratic
Congruences
12
11.14
13
11. 21 Thanksgiven
Holiday
14
11.28
12.05
16
12.12
p40 #1,2,3,4,7,9,11,12,13,14,15,16
on sections 1-5
P59 #1,3,5,7,9,11,12,15,17
p55 #1,4,5,6,7,9,12,13,14
p61 #1,2,3,5,6,7,8,12,13,14
p 71 # 1,3,5,7,8,14,17,18,21,22
on sections 6, 7, 8, 9
p93 #1,3,5,7,9,12,15,16,17,2
12. Quadratic reciprocity
13. Numbers in Other
bases
16. Pythagorean Triangles
17. Infinite Descent and
Fermat’s Conjecture
18. Sums of Two Squares
20. x  Ny  1 Review
Test 3
Review for the Final Exam
2
15
p30 ex.6-9; p32 #1,3,4,7,8,11,12,13,14,15,19
2
FINAL EXAM
6PM-8:50PM
Over sections 11, 12, 13, 16, 17, 18, and 20
CHAPTERS 1-20
CHAPTERS 1-20
3