Math 406, Introduction to Number Theory

Fall 2012

MWF 9:00 – 9:50am, MTH 0103

Instructor: Dr. Niranjan Ramachandran, MTH 4115, 5-5080, atma @ em eh tee h dot u m d dot edu

Text: Elementary Number Theory by Kenneth Rosen, 6^th edition, 2010 (768 pages) 978-0321500311

Course page: www2.math.umd.edu/~atma/406.html

(This document is a slight modification of one due to Professor S. Antman available here.)

Syllabus. This is a first course in elementary number theory. Our main goal is to understand the fundamental theorems about prime numbers and divisibility of integers. Although the mathematical prerequisites for the course are few, there will be many proofs done in class, and you will also need to prove results on your own in the homework and provide (simpler) proofs on exams. The core topics covered are divisibility, prime numbers, congruences, the theorems of Fermat, Euler, and Wilson, primitive roots for primes and the law of quadratic reciprocity.

You are only responsible for the material covered in lecture and for the corresponding material in the text book.

Grades. Two midterms (100 points each) + Homework (150 points) and Final Exam (150 points). Total: 500 points.

Tests and homeworks. There will be two 50-minute midterm exams, tentatively on 9/28 and 11/16. There will be weekly homeworks due Wednesdays which will be graded. These homeworks are due at the beginning of class. The final will be cumulative with an emphasis on material covered since the second midterm exam.

The test papers must be clear and legible. Illegible material will not be given a positive grade. Explanations supporting the mathematical arguments must be given in coherent English sentences. The grader will not guess your thought processes.

Minor algebraic and numerical errors on a test or homework, such as missing a sign, that are not symptomatic of a conceptual misunderstanding will be penalized minimally. Egregious errors, such as + = or ln(a + b) = ln a + ln b, will be penalized severely.

Since the course emphasizes concepts, technique, and analytical skill, there is no need for calculators on any test. Accordingly they are prohibited.

Make-up exams will only be given for compelling and documented reasons.

Each student is allowed TWO late homeworks (further late homeworks will not be graded).

If you feel that you are entitled to more points on a test or a homework set, resubmit the paper with a covering note explaining precisely why you feel your grade should be changed. (Since each questioned problem will be very carefully reexamined, it is possible that you could actually end up losing points in the reevaluation.)

Office Hours: TBA or by appointment. Since I am occasionally called away for pressing and unexpected business, it is a good idea to check with me as to whether I will be in my office at the indicated hours, especially if it would inconvenience you to come at that time. Unless I am notified to the contrary, I presume that if no students arrive within the first 15 minutes of office hours, then I am free to leave my office. Students coming to office hours should have specific and well-defined questions: Office hours are not designed for extensive private tutoring.

E-mail: I can always be contacted by e-mail, but I cannot always be contacted instantaneously by e-mail, and even if I am, I cannot always respond within 24 hours.

Academic Integrity: The student-administered Honor Code and Honor Pledge prohibits students from cheating on exams, plagiarizing papers, submitting the same paper for credit in two courses without authorization, buying papers, submitting fraudulent documents and forging signatures. On every examination, paper or other academic exercise not specifically exempted by the instructor, students must write by hand and sign the following pledge:

I pledge on my honor that I have not given or received any unauthorized assistance on this examination (or assignment).

(Discussing homework problems with other students is ok, even encouraged, but please do write up your solutions by yourself. In exams and quizzes, of course, you are assumed to be working by yourself.)

Students With Disabilities. If you have a documented disability and need academic accommodations, please contact me as soon as possible.

Religious Observances. If you will be absent from class because of religious observances, please submit a list of the dates of your absences within a couple of days.

Miscellaneous. Matters such as class cancellations, room changes, etc. will be communicated to the students by email (and will be reflected on the class webpage). Please notice that class lectures and other materials are copyrighted and that they may not be reproduced for anything other than personal use without written permission of the instructor.

You may find useful the links “How to study” and “Guidelines on proofs” from here

Final Exam: Monday December 17^th, 8:00am – 10:00am, MTH 0103.