Information Sheet for Math 311 - Number Theory



INFORMATION SHEET FOR MATH 311 - NUMBER THEORY

INSTRUCTOR: Dr. Mark Mazur

OFFICE: 407 College Hall

PHONE: 412-396-1648 (Office)

412-396-6467 (Math Department)

E-MAIL: mazur@mathcs.duq.edu mazur1@

OFFICE HOURS: Wednesday: 11 A.M. to 1 P.M.

Tuesday & Thursday: 9:30 to 10:30 A.M.

Or by appointment

CLASS MEETINGS: Tuesday & Thursday – 12:15 to 1:30 P.M.

CLASSROOM: 446 College Hall

TEXT: Elementary Number Theory, Sixth Edition, by David M. Burton

COURSE: Most of the topics in the first twelve chapters in the text are discussed. Students should be familiar with the material in Chapter 1. Chapter 8 is omitted. Topics include divisibility properties of the integers, prime numbers, congruences, solutions to polynomial congruences, quadratic reciprocity, and cryptography. The course is primarily concerned with the mathematical development of the theory of numbers. But since this area of mathematics is one of the oldest, its history is rich. The historical development, including the key figures in this development, is discussed. Applications to other areas of mathematics as well as pedagogical and scientific applications are discussed.

GRADING: Your final grade will be based on homework, two quizzes, plus a midterm exam, and a comprehensive final exam. Homework will count

18 %, the two quizzes will each count 16 %, the midterm exam will count 20 %, and the final exam will count 30 % of your final grade. The final exam is scheduled for Tuesday, May 1 from 1:15 to 3:15 P.M. Graphing calculators may NOT be used during exams or quizzes. THERE WILL BE NO MAKE-UP EXAMS. You will receive a zero for each missed exam. In the event of serious illness, the student must notify the professor immediately and must provide an original, written, verifiable excuse. Final grades will be assigned according to the grading scale:

A: 90- 100

B: 80 - 90

C: 70 - 80

D: 60 - 70

F: Below 60

HOMEWORK: The only way to learn number theory is to do lots of problems. I will assign problems from the text at each class meeting and ask that you submit your solutions weekly. These assignments will be collected and graded. You will be able to resubmit for full credit any proof which was not completely correct on your first attempt. NO LATE HOMEWORKS WILL BE ACCEPTED.

QUIZZES: Each student will devise his or her own quizzes in the following way. I will give you lists of problems of four different types. For each of the two quizzes you will submit to me a list of 24 problems, 6 problems of each of the four types. I will randomly select one problem of each type from your list and these four problems will constitute your quiz. The only requirement is that you include on some exam at least one problem from each list that I give to you. These exams will not be taken in class, but rather outside of class at a mutually convenient time.

DEADLINES FOR QUIZZES:

Problems submitted by Quiz taken by

Quiz 1 February 15 February 22

Quiz 2 April 12 April 19

ATTENDANCE: You are expected to attend class, and attendance will affect your

grade only in borderline cases.

ACADEMIC HONESTY: Each student’s grade should reflect only that student’s

achievement. Thus cheating, plagiarism, or assisting or

allowing some other to violate academic honesty are each

grounds for receiving a grade of “F” FOR THE COURSE.

DISABILITIES: Students with documented disabilities are entitled to

reasonable accommodations if needed. If you need

accommodations, please contact the Office of Freshman

Development and Special Student Services in 309

Duquesne Union (412-396-6657) as soon as possible.

Please also contact the instructor. Accommodations will

not be granted retrospectively.

TOPICS:

Chapter 1: Some Preliminary Considerations

Sections 1.1 -1.2 (Students should be familiar with this material.)

Chapter 2: Divisibility Theory in the Integers

Sections 2.1 - 2.5

Chapter 3: Primes and Their Distributions

Sections 3.1 - 3.3 (Section 16.4, if time)

Chapter 4: The Theory of Congruences

Sections 4.1 - 4.4

Chapter 5: Fermat’s Theorem

Sections 5.1 - 5.4

Chapter 6: Number-Theoretic Functions

Section 6.1

Chapter 7: Euler’s Generalization of Fermat’s Theorem

Sections 7.1 - 7.3

Chapter 9: The Quadratic Reciprocity Law

Sections 9.1 - 9.4

Chapter 11: Numbers of Special Form

Sections 11.1 – 11.3

Chapter 12: Certain Nonlinear Diophantine Equations

Sections 12.1, 12.2

Chapter 10: Introduction to Cryptography

Section 10.1

ASSIGNMENT SHEET - MATH 311 - NUMBER THEORY

Chapter 1: (Optional)

Sec. 1.1: p. 6: 1, 3, 4, 9 Sec. 1.2: p. 10: 1, 3 a, b

Chapter 2:

Sec. 2.1: p. 15: Read 1, 2, 5

Sec. 2.2: p. 19: 2, 3 a, c, 5, 6

Sec. 2.3: p. 24: 1, 2, 3, 5, 6 a, 9, 12, 13 a, 20 a, Read 11

Sec. 2.4: p. 31: 1, 2, 3, 4 a, 8, 9, 10 b, 12

Sec. 2.5: p. 37: 1, 2 a, 3 b, 5 a, 6, 7, Read 8

Chapter 3:

Sec. 3.1: p. 43: 1, 2, 3 a, c, 4, 5, 7, 12, 17, Read 10

Sec. 3.2: p. 49: 1, 2, 4a, 5, 7, Read 6, 8

Sec. 3.3: p. 57: 1, 2 a, b, 3, 9 a, Read 7, 11, 17

Chapter 4:

Sec. 4.2: p. 67: 1 a, b, c, 2, 4 a, 5, 8a, 10, 11

Sec. 4.3: p. 73: 2 a, b, c, 4, 7 b, c, 18

Sec. 4.4: p. 82: 1 (all), 4 (all), 8, Read 9, 10

Chapter 5

Sec. 5.2: p. 92: 1, 3, 4 a, b, 7, 10 a, 14, Read 8

Sec. 5.3: p. 96: 1 a, 3, 4, Read 5

Sec. 5.4: p. 102: 1

Chapter 6

Sec. 6.1: p. 110: Read 1, 7, Do 2, 3, 5 b

Chapter 7

Sec. 7.2: p. 135: 1, 2, 4 a, b

Sec. 7.3: p. 140: 1 a, 7, 9

Chapter 9

Sec. 9.1: p. 173: 1, 4, Read 3, 6

Sec. 9.2: p. 184: 1, 2 (use any method)

Sec. 9.3: p. 190: 1 a, b, c, d, 3

Sec. 9.4: p. 195: 1, 2, 4

Chapter 11

Sec. 11.2: p. 224: 1 Sec. 11.3: p. 235: Read 1, 4

Chapter 12

Sec. 12.1: p. 251: 1, 6, Read 9

Chapter 10

Sec. 10.1: p. 206: 3 b, c

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