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

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

Class Time: T-Th 11:00-12:15
Location: Math TBA
E-mail address:  jcohen@umd.edu
Book:  Elementary Number Theory and Its Applications, 5/e ,Kenneth H. Rosen, 2005, Addison-Wesley, ISBN 0-321-23707-2
Supplement: There is some interesting supplementary material at  http://www.aw.com/rosen/resources.html .

Prerequisite: MATH 141

Office Hours: T-Th 1:00 - 2:00.  Occasionally, it may be necessary to change this time, so  let me know if you are planning to see me. Feel free to make an appointment for a different time with me, if you cannot see me during those hours. You can also send me email. I will answer queries as quickly as possible.

Grader: TBA
E-mail address:  tba@umd.edu .

Web Posting:  If you have emailed me your permission to post your grades under an alias, you may check the grades 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
                    Multiplicative Functions
                        Möbius inversion formula
                        Number and Sum of Divisors
                    Primitive roots
                        Existence of primitives roots
                        Index arithmetic                
                    Quadratic Residues
                        Legendre and Jacobi symbols
                        Law of quadratic reciprocity
                    Possible Additional Topics
                        Non-linear Diophantine Equations
                        Perfect numbers, Mersenne primes
                        Continued Fractions
                        Cryptology
 

        Makeup exams will not be given.  If you have an excused absence for an exam, the grade will be replaced by 2/3 of the final exam grade.  The lowest grade will count for half.  Excused absences will be given only for valid medical reasons, University business, or appearances in court.  Excused homework will not be used in computing the final grade.   Any unexcused absences on exams or unexcused late homework will be counted as 0, including the final exam.  Any student with a valid reason to be excused from an exam must contact me prior to the exam, either by email or by phone, and present documentation at the next class session attended.   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.
 
Questions: If there is anything that you don't understand, please bring it up at least by the next class. If some concept is not understood, it can make everything after that mysterious.  Do not be embarrassed to ask any question.

Homework:  Homework will be due each Thursday.  It will be based on what is covered in class the previous week.  If the assignment is not clear, make sure to ask before leaving the classroom Thursday!  Homework problems are listed below.  Requested problems will be discussed in class after they are handed in.  
 

Grading: A total of 500 points is available in the course:
 

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

The tentative schedule of exams follows:

Sample exams are available at http://db.math.umd.edu/testbank/

A list of homework problems follows.

Sect 1.1: 4,8,11,34,39,40
Sect 1.2: 3,8,15,17
Sect 1.3: 5, 7,11,20,27
Sect 1.4: 4,14,32,34
Sect 1.5: 8,17,34,36,39

Sect 3.1: 3,6,13,16
Sect 3.2: 3,10,12,16
Sect 3.3: 5,16,21,23,32
Sect 3.4: 1,3,21
Sect 3.5: 9,10, 12,14,15,44,45
Sect 3.7: 2,4,13


Sect 4.1: 6,14,20,27
Sect 4.2: 8,13,15
Sect 4.3: 4,8,12
Sect 4.4: 2,3,4

Sect 6.1: 9,16,24,33,34
Sect 6.3: 4,6,10,15

Sect 7.1: 6,8,19,37,39
Sect 7.2: 8,9,22,30
Sect 7.3: 2,4,7
Sect 7.4: 3,4,5,12,14,17


Sect 9.1: 4,6,9,16
Sect 9.2: 2,6,8,12
Sect 9.3: 4,5,9,14
Sect 9.4: 2,3,5,9

Sect 11.1: 1,2,5,9,10,11,20
Sect 11.2: 1,3,4,15
Sect 11.3: 1,2,9,13


Sect. 13.1: 2,6,13,17, 18
Sect. 13.2: 1,3, 4,13
Sect. 13.3: 1,3,4, 16

Sect 12.2: 1 (b,c,d,h), 4 (a,e,f),6 (a,e,f),8, 12
Sect 12.3: 1 (a,d), 3, 5,7

Sect 5.1: 1,3,4,17,22

Sect. 8.1: 2,12,15
Sect. 8.2: 1,17
Sect. 8.3: 2
Sect. 8.4: 2,4
 

§ Changes in the program are possible.  The Math 406 WEB PAGE (http://jcohen.me/406) will be kept up-to-date as changes are made.

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