Math 406

Math 406, Joel M. Cohen (Summer, 2011)

This WEB page is jcohen.me/406, and was last updated:7-18-11

Title: Introduction to Number Theory

Instructor: Professor Joel M. Cohen Office: Math 2313, Telephone: (301)405-5109
Home phone: (202)546-1823. Class Time: M-F, 11:00-12:20
Location: Math 0303
E-mail address: jcohen@umd.edu
Book: Elementary Number Theory and Its Applications, 6/e ,Kenneth H. Rosen, 2005, Addison-Wesley, ISBN 978-0-321-50031-1.
Supplement: There is some interesting supplementary material at the book's website. This includes software for solving the computer problems which will not be assigned, but are very useful for understanding the material.

Prerequisite: MATH 141

Office Hours: T-Th 10-10:50. 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 questions. I will answer queries as quickly as possible during office hours, and as time permits otherwise.

Grader: Tim Mercure
E-mail address: mercure@math.umd.edu .

Tutoring: The math department provides tutoring for Math 406 every day 12:30 - 2:30 p.m. in room 0305 with Ariel Hafftka.

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 Depending on Time
                        Non-linear Diophantine Equations
                        Perfect numbers, Mersenne primes
                    Continued Fractions
                        Cryptology

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

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 the day before. 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.

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

	Three hour exams (100 points, lowest counts half)	250
	Homework/Quizzes	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:

Friday, July 22	Test I
Friday, August 5	Test II
Friday, August 19	Final

A tentative list of homework problems follows.

A list of homework problems follows. Problems in parentheses are the numbers of the same problems in the 5th edition.

Sect 1.1: 4,8,11,28,34,39,40

Sect 1.2: 3, 10, 19, 21 (3,8,15,17)
Sect 1.3: 7,11,20

Sect 1.4: 4,14,32,34 (same)

Sect 1.5: 16, 25, 42, 44, 47 (8,17,34,36,39 )

Sect 3.1: 3,6,13,16 (same)

Sect 3.2: 3, 12, 14, 18 (3,10,12,16)
Sect 3.3: 5, 18,23,25, 40 (5,16,21,23,32)

Sect 3.4: 1,3,21 (same)

Sect 3.5: 9 - 13, 42, 43 (9 - 15, 44, 45)
Sect 3.7: 2,4,13 (same)

Sect 4.1: 6,14,20,27 (6, 10, 12, 19)
Sect 4.2: 8,13,15 (same)
Sect 4.3: 4,8,12 (same)
Sect 4.4: 2,3,4 (same)

Sect 6.1: 9,16,24,33,34 (same)
Sect 6.3: 4,6,10,15 (4, 6, 10, 12)

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

Sect 9.1: 6, 8, 11, 18 (4, 6, 9, 16)
Sect 9.2: 2,6,8,12 (same)
Sect 9.3: 4,5,9,14 (same)
Sect 9.4: 2,3,5,9 (same)

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

Sect. 13.1: 2,6,13,17 (same)
Sect. 13.2: 1,4,13 (same)
Sect. 13.3: 1,3,4 (same)

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

Sect 5.1: 1,3,4,17,22 (same)

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

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

You are responsible for checking these updates.

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