Math 406 (0401), Joel M. Cohen (Spring 2017)

This WEB page is jcohen406.org or http://www2.math.umd.edu/~jcohen/406/ and was last updated: 1/30/17

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

Office: Math 2313, Telephone: (301)405-5109

Class Time: Tu-Th 9:30 – 10:45
Location: Math 0106
E-mail address:  jcohen@umd.edu  Make sure to put "406" in the Subject.
Book: Lawrence Washington and James Kraft, Introduction to Number Theory with Cryptography, Taylor & Francis. ISBN: 9781482214413

Grader:  TBA

Prerequisite: One course with a minimum grade of C- from MATH 240, MATH 241, MATH 246, MATH 340, MATH 341 or MATH 461, or permission of Mathematics department.

Office Hours: Tu-Th 11:00 – 12:00.  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.

TOPICS

Before the course begins, please read Chapter 0.  If there is anything you would like to see explained or expanded upon, let me know the first day of class.

The course will cover most of the following chapters:
Chapter 1: Divisibility
Chapter 2: Unique Factorization
Chapter 3: Applications of Unique Factorization
Chapter 4: Congruences
Chapter 5: Cryptographic Applications
Chapter 7: Order and Primitive Roots
Chapter 9: Quadratic Reciprocity
Chapter 11: Geometry of Numbers
Chapter 14: The Gaussian Integers
Material from other chapters if there is enough time.

        Homework will be due each Tuesday.   You are required to turn in the homework.  The homework will be corrected but not graded.   This is an invitation to do the homework in groups.    I will be happy to explain homework problems that you have difficulty with.  Most of the problems in the exams will be based on the homework problems.

        Makeup exams will be given only for valid reasons: medical, University business, or court appearances.  Unexcused absences on exams will be counted as 0.  Except for a sudden medical emergence, a student with a valid reason to be excused should contact me prior to the exam either in person, 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 first week.

        Grading: A total of 450 points is available in the course: each midterm exam is 100 points, with the lowest exam counting half, and the final exam is worth 200 points.  The total number of points will be divided by 4.2, to get the usual letter grades. So, for example, 378 would translate to 90, or an A–, etc.  + and – grades will be used except for B+ and C+ which normally will not be given.   A final exam which is totally inconsistent with the midterm grades, may be treated differently: a very bad final cannot lower the semester grade by more than one letter grade, and an outstanding final may be counted for more than 200/450. 

        Quality: The quality of presentation of solutions will be taken seriously in this course.

The schedule of exams follows: 

Thursday, March 2
 		Test I
Tuesday, April 11 Test II
Tuesday, May 2
 		Test III
Monday, May 15, 8:00 – 10:00 (Oh No. Monday at 8 AM!)
Final

Sample exams are available at http://www-math.umd.edu/testbank.html

Homework Problems

Sections
 		Problem numbers to hand in.  Suggestion: do these and check the odd ones in the back of the book. Due Date
§§ 1.1 – 1.7
 		4, 5, 7, 8, 11, 14, 20 // 23, 28, 32, 34
 		1/31
§§ 1.9, 1.10, 4.1, 4.4
 		p.51 – 40, 42, 44, 46
 p. 152 – 14, 18, 30, 36
§§ 2.2, 3.1, 3.2, 3.3, 4.1
 		p.67 – 4, 8, 10; p.97 – 2, 4, 8, 10; p. 152 – 11
§§ 3.4, 3.5, 3.6, 4.3, 4.5
 		p. 96 –  14, 16, 20, 24, 26, 28, 30, 34; p. 154 – 26, 28, 38, 40, 42
§4
 p.184 – 2, 8, 12, 14, 18, 20, 22
§§6, 7.1, 7.2
 		p. 203 – 2, 3, 4, 5, 6; p. 234 – 2, 4, 6, 10, 14, 18, 22, 24, 26, 30
§§7.2, 7.5, 9.1
 		p. 237 – 38; p. 238 – 3; p. 286 – 2, 4, 6, 10, 16
§§12.1, 12.2
 p. 378 – 2, 4, 8, 10, 14, 18
§§12.3, 13.1
 p. 380 – 22, 24; p. 421 – 2, 6, 10, 18
§§13.4, 13.5
 p. 422 – 12, 14, 16



§§ 4.7–4.9 48, 50, 52, 54, 56, 68, 62, 68, 74
§§ 7.1, 7.2, 7.6
 		2, 4, 6, 10, 12, 20, 21, 22, 26, 30, 32, 34
§§ 9.1–9.5
 		2, 4, 6, 10, 14, 16, 22, 26, 28, 30, 32, 34, 36, 38, 41, 42
§§ 3.1–3.6
 		2, 4, 6, 8, 10, 12, 16, 18, 22, 26, 28, 30, 32, 34
§§ 12.1–12.3
 		2, 4, 6, 10, 12, 14, 15, 18, 24
§§ 8.1–8.3
 		2, 4
§§ 13.1–13.5
 		4, 6, 12, 16, 18
§§ 14.1–14.5 2, 4, 8, 12
§§ 15.1–15.5
 		2, 4, 6

 

     

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