MAT 447 Number Theory, CRN 22111, Spring 2017



Class meets MW 1:00 PM – 2:15 PM in SBS D121.


Instructor: Serban Raianu

Office: NSM E-108; Office phone number: (310) 243- 3139

e-mail address:; URL:;

Office hours: Monday, Wednesday: 8:50 AM - 9:50 AM, Friday: in the Toro Learning Center: 11:30 AM – 12:30 PM, in my office: 1:00 PM – 2:00 PM, or by appointment.


Course Description: MAT 447, Number Theory, covers most of Chapters 1-5 and parts of Chapter 6 from the textbook: prime numbers, the ring of integers modulo n, public key cryptography, quadratic reciprocity, continued fractions, and elliptic curves.


Text: Elementary Number Theory: Primes, Congruences, and Secrets, by William Stein, available for download for free at


Objectives: After completing MAT 447 the student should be able to solve simple problems, do simple proofs and state basic definitions and theorems involving the notions studied.


Prerequisites: MAT 271 or equivalent with a grade of "C" or better.


Grades: Grades will be based on three in‑class full‑period examinations (60% total), a comprehensive final examination (25%), and quizzes and attendance (15%) for the remainder. The exact grading system for your section is the following: each of the three full-period exams will be graded on a 100 scale, then the sum of the scores is divided by 5 and denoted by E. Homework will not be collected, but all problems on quizzes and exams will be similar to the problems in the homework

5 to 10 minutes quizzes will be given in principle every Monday class meeting, with the exception of the review and exam days, and will be graded on a scale from 1 to 10. The average of the quizzes scores is denoted by Q. There are also 5 points awarded for attendance and class participation, this portion of the grade is denoted by A. The final exam will be graded out of a maximum possible 200, then the score is divided by 8 and denoted by F. 

To determine your final grade  compute E+Q+A+F. The maximum is 100, and the grade will be given by the rule:

        A: 93‑100;      A‑: 90‑92;      B+: 87‑89;      B: 83‑86;   B‑: 80‑82

        C+: 77‑79;      C: 73‑76;        C‑: 70‑72;      D: 60‑69;   F: Less than 60.


Makeups: No makeup examinations or quizzes will be given. If you must miss an examination for a legitimate reason, discuss this, in advance, with me, and I may then substitute the relevant score from your final examination for the missing grade.


Accomodations for Students with Disabilities: Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH B250. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.


Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)


Tentative schedule and homework assignments


M 1/23: 1.1 Prime factorization: 1.1,1.8-1.13

W 1/25: 1.2 The Sequence of Prime Numbers: 1.2-1.5,1.14

M 1/30: 2.1 Congruences modulo n:  2.1,2.2,2.4,2.7,2.8

W 2/1: 2.2 The Chinese Remainder Theorem: 2.13,2.14,2.15,2.17,2.19

M 2/6: 2.3 Quickly Computing Inverses and Huge powers: 2.10-2.15,2.30,2.31     

W 2/8: 2.4 Primality Testing: 2.17-2.20

M 2/13: 2.5 The structure of (Z/pZ)*: 2.23-2.26

W 2/15: Review        

M 2/20: Presidents’ Day Holiday    

W 2/22: Exam I

M 2/27: 3.1 Playing with Fire : 3.4

W 3/1: 3.2 The Diffie-Hellman Key Exchange: 3.5

M 3/6: 3.3 The RSA Cryptosystem: see Blackboard 

W 3/8: 3.4 Attacking RSA: 3.7(b)

M 3/13: 4.1 Statement of the Quadratic Reciprocity Law: 4.1,4.3     

W 3/15: 4.2 Euler’s Criterion: 4.7

M 3/20: 4.3 First Proof of Quadratic Reciprocity: 4.8           

W 3/22: Review

M 3/27: Spring Recess         

W 3/29: Spring Recess

M 4/3: Exam II

W 4/5: 5.2 Finite Continued Fractions: 5.1,5.2

M 4/10: 5.3 Infinite Continued Fractions: 5.3

W 4/12: 5.4 The Continued Fraction of e: 5.4

M 4/17: 5.5 Quadratic Irrationals: 5.5

W 4/19: 5.6 Recognizing Rational Numbers: 5.7,5.8

M 4/24: 5.7 Sums of Two Squares: 5.9,5.11

W 4/25: Review

M 5/1: Exam III

W 5/3: 6.3 Integer Factorizations Using Elliptic Curves: 6.1,6.2

M 5/8: 6.4 Elliptic Curve Cryptography: 6.3

W 5/10: Review        


Final examination: Monday, May 15, 1:00 PM - 3:00 PM.






Important Dates:


January 21



Classes Begin

January 21-February 9



Late Registration Add/Drop  (fees due 48 hours after registration)

February 1



Summer 2017 Graduation Application Deadline

February 3



Instructor Drop Deadline

February 9



Credit/No Credit and Audit Grading Deadline

February 9



Last Day to Drop from FT to PT Status with Refund

February 17



Drop without Record of Enrollment Deadline

February 17



Student Census

February 18-April 20



Serious and Compelling Reason Required to Drop/Withdraw

February 20



Presidents’ Day Holiday- Campus Open, No Classes

March 13-May 21

Monday- Sunday


Spring 2017 Intersession Registration

March 20-July 7



Summer 2017 Registration

March 24



Last Day for Pro-rata Refund of Non-Resident Tuition and Tuition Fees





March 27-April 2



Spring Recess (includes Cesar Chavez Holiday)

March 31



Cesar Chavez Holiday Observed-Campus Closed, No Classes

April 17



Summer 2017 Graduation Application-Late Deadline (with late fee)

April 21-May 11  

Friday- Thursday


Serious Accident/Illness Required to Drop/Withdraw

April 24-August 18



Fall 2017 Registration

May 12



Last Day of Scheduled Classes

May 13



Study Day

May 13-May 19



Final Examinations

May 16



Grade Submission Begins

May 19



Evaluation Day

May 19




May 20




May 24, 3 pm



Final Grades Due- *Extended Education grades always due 72 hours after course end date