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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. 2 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