Math 406, Joel M. Cohen (Summer, 2004)

This WEB page is http://www.math.umd.edu/~jmc/406sum.html, and was last updated:7-6-04

Title: Introduction to Number Theory
Instructor: Professor Joel M. Cohen

Office: MTH 2313, Telephone: (301)405-5109
Home phone: (202)546-1823.

Class Time: M-F 11:00-12:20
Location: Math 0101
E-mail address:  jcohen@umd.edu
Book:  Elementary Number Theory and Its Applications, 4/e ,Kenneth H. Rosen, 2000, Addison-Wesley, ISBN 0-201-87073-8
Supplement: There is some interesting supplementary material at  http://www.aw.com/rosen/resources.html .
Errors: Unfortunately, there are many errors in Rosen's book.  Here are some errata sheets:
http://math.berkeley.edu/~jvoight/115/2004-115-typos.pdf
http://www.math.berkeley.edu/~poonen/55/rosenerrors.pdf

Prequisite: MATH 141

Office Hours: MTWTh 12:30-1:30.  Occasionally, it may be necessary to change this time, so let me know if you are planning to see me.  You can also send me email. I will answer queries as quickly as possible during office hours, and as time permits otherwise.

Tutoring: The math department provides tutoring for Math 406 every day 12:30 - 2:30 p.m. in room 0409 with Greggo Johnson.

Web Posting:  If you have given written permission to post your grades under an alias, you may check the grades by clicking here.
 

Sample tests:  Sample tests are available by clicking here.
 

 TOPICS
                    The integers
                        Divisibility
                        Prime numbers
                        Greatest common divisor
                        Euclidean algorithm
                        Unique factorization
                    Congruences
                        Basic properties
                        Modular arithmetic
                        Euler's phi function
                        Fermat's, Euler's and Wilson's theorems
                        Chinese remainder theorem
                        Polynomial Congruences
                    Multiplicative Functions
                        Euler Phi, Sum & Number of Divisors Functions
                        Möbius Inversion
                    Quadratic Reciprocity
                        Quadratic residues
                        Legendre and Jacobi symbols
                        Law of quadratic reciprocity
                    Additional Topics
                        Primitive roots
                        Mersenne primes
                        Simple Continued Fractions and Lagrange's Theorem
                        Cryptology
 
 
 
 
 

        Makeup exams will not be given.  If you have an excused absence for an exam, the grade will be replaced by 1/2 of the final.  If you have taken both exams, the lowest grade will count for half.  Excused absences will be given only for valid medical reasons, University business, or appearances in court, and, except in emergency conditions, must be requested in advance, either by email or by phone.   There will be no excused homework assignments or quizzes, but approximately the lowest 15% will be dropped.

        If you need to be excused for a religious observance, you should let me know as soon as possible, but in any case no later than the end of the schedule adjustment period.
 
 

Homework:  Homework will be due each day.  Each day's homework will be based on what is covered in class that day.  If the assignment is not clear, make sure to ask before leaving the classroom!  Homework problems are listed below.  Requested problems will be discussed in class.   There may be occasional quizzes on homework problems or their equivalent.
 

Grading: A total of 400 points is available in the course:
 


Two hour exams (100 points,  lower counts half) 150

Homework/Quizzes 100

Final 150

Total 400

Quality: The quality of presentation of solutions will be taken seriously in this course in the grading of tests and homework.
 

The schedule of exams follows:
 

Monday, July 26 Test I
Monday, August 9 Test II
Friday, August 20 Final

A tentative list of homework problems follows.

§ Changes in the program are possible.  The Math 406 WEB PAGE (http://www.math.umd.edu/~jmc/406sum.html) will be kept up-to-date as changes are made.
You are responsible for checking these updates.

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