MATH3080  Number Theory  2018/19
Announcement
 Midterm 1 Review. Check back online for the latest version (last updated: Oct 15) [Download file]
 Midterm 1 Sample questions (questions only) (Last updated: Oct 5) [Download file]
 Midterm 1 Sample questions (questions with answers) (Last updated: Oct 15) [Download file]
 Midterm 1 Solution (reference only) [Download file]
 New CW10, due: Nov 22, during tutorial [Download file]
 New Final info and review notes (last updated: Nov 25) edit: Final score check location: LSB222 [Download file]
 New Sample final, Questions only (last updated: Nov 17) [Download file]
 New Sample final, Questions and solutions (last updated: Nov 17) [Download file]
General Information
Lecturer

Charles Li
 Office: LSB218
 Email:
Teaching Assistant

Wong Ka Fai
 Office: AB1 407A
 Email:
Time and Venue
 Lecture: Tu 10:30AM  12:15PM Y.C. Liang Hall 103; Th 5:30PM  6:15PM Lady Shaw Bldg C2
 Tutorial: Th 4:30PM  5:15PM Lady Shaw Bldg C2
Course Description
 Divisibility of integers, the division algorithm, gcd, the Euclidean algorithm
 The fundamental theorem of arithmetic, primes, factorization.
 modular arithmetic, Fermat's little theorem, Euler's theorem, Eulerphi function, Wilson's theorem, Fermat's theorem of sum of squares.
 Fast modular exponentiation algorithm, primality test, pseudoprimes.
 Basic cryptography, cryptocurrency
 Primitive roots and indexes
 The quadratic reciprocity law
 Quadratic forms
 (if time allowed) Numbertheoretic functions.
 (if time allowed) continued fraction, elliptic curve
Textbooks
 Burton, Elementary Number Theory, 7th edition, McgrawHill international edition
References
 Niven, Zuckermen, Montgomery, An Introduction to the Theory of Numbers 5th Edition
Lecture Notes
 Lecture 0: class information
 Lecture 1: introduction,
 Lecture 2: Divisibility
 Lecture 3: LCM and linear diophantine equations
 Lecture 4: The Fundamental theorem of Arithmetic
 Lecture 5: Infinitude of primes (Last updated: Sep 10)
 Lecture 6: Lecture 6: Modular Arithmetic (Last updated: Sep 16)
 Lecture 7: Modular Arithmetic II (Last updated Sep 16)
 Lecture 8: Fast modular exponentiation and primality Test (Last updated Oct 10), fix typo on the top of p.3
 Lecture 9: Cryptography (Last updated Sep 16)
 Lecture 10: Polynomials (Last updated Sep 16)
 Lecture 11: Primitive roots (Last updated: Oct 10)
 New Lecture 12: Primitive roots II (Last updated: Nov 15, remove reference to Lect 14)
 Lecture 13: The quadratic reciprocity Law (Last updated: Oct 10)
 Lecture 14: Binary quadratic forms (Last updated: Nov 26) Edit: fix typos of Example 11
Assignments
 CW1 with solution (last updated: Sep 23)
 CW2 with solution (last updated: Sep 23)
 CW3 with solution (last updated: Sep 30)
 CW4 with solution (last updated: Oct 10)
 CW5 with solution (last updated: Oct 15)
 CW6 with solution (last updated Oct 18)
 CW7 with solution (last updated Oct 31)
 CW8 with solution (last updated Nov 25) Typo at Q12(d) fixed
 CW9 with solution (last updated Nov 15)
 CW10 with solution (last updated: Nov 25) (type at Q15, r3=3 is changed to r3=7)
 CW11 with solution (last updated: Nov 25)
 CW12 with solution (last updated: Dec 4)
 CW13 with solution (last updated: Dec 7)
Assessment Scheme
Tutorial Classwork, max 10pts. Classworks will be given during tutorial. Each classwork counts 1pt. There are about 1213 tutorals and you need to attend at least 10 of the tutorials.  10%  
Midterm Oct 23 (Tue) During Lecture  30%  
Final  60% 
Assessment Policy Last updated: December 07, 2018 17:07:59