**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.