MATH3080 - Number Theory - 2017/18
Announcement
- CW4. Hand it in on Oct 3 [Download file]
- Midterm Review (last updated: Oct 9) [Download file]
- More ex for midterm ( (last updated: Oct 9) [Download file]
- New Final information and review (Last updated: Dec 3) [Download file]
- New Sample final (questions only) (Last updated: Dec 3) [Download file]
- New Sample final (questions and solutions) (Last updated: Dec 3) [Download file]
- New Midterm solution. [Download file]
General Information
Lecturer
-
Li, Chun Che
- Office: LSB 218
- Email:
Teaching Assistant
-
Wong Siu Fung
- Office: AB1 407A
- Email:
-
Gu Dalin
- Office: AB1 407B
- Email:
Time and Venue
- Lecture: Mo 12:30PM - 1:15PM LSB LT4, Tu 4:30PM - 6:15PM LSB LT4
- Tutorial: Mo 1:30PM - 2:15PM LSB LT4
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, Euler-phi 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
- Number-theoretic functions.
- (if time allowed) Quadratic forms, continued fraction, elliptic curve
Textbooks
- Burton, Elementary Number Theory, 7th edition, Mcgraw-Hill international edition
References
- Niven, Zuckermen, Montgomery, An Introduction to the Theory of Numbers 5th Edition
Lecture Notes
- Lecture 0:Class info, last updated: Sep 2
- Lecture 1: Intro
- Lecture 2: Divisibility, gcd, Euclidean algorithm last, updated: Sep 2
- Lecture 3: LCM, linear diophantine equation, last updated: Sep 2
- Lecture 4: The fundamental theorem of arithmetics, last updated: Sep 2
- Lecture 5: Infinitude of primes
- Lecture 6: Modular Arithmetics I
- Lecture 7: Modular Arithmetics II
- Lecture 8: Fast modular exponentiation and primality Test
- Lecture 9: Cryptography
- Lecture 10: Polynomials
- Lecture 11: Primitive roots
- Lecture 12: Primitive roots II
- Lecture 13: Quadratic reciprocity
- Lecture 14: Quadratic forms (third draft)
Assignments
- CW1 with solution (reference only)
- CW2 with solution (reference only) (Last updated: Sep 24)
- CW3 with solution (reference only) (Last updated: Sep 30)
- CW4 with solution (reference only) (Last updated: Oct 9)
- CW5 with solution (reference only) (Last updated: Oct 9)
- CW6 with solution (reference only) (Last updated: Oct 21)
- CW7 with solution (reference only) (Last updated: Nov 3)
- CW8 with solution (reference only) (Last updated: Nov 3)
- CW9 with solution (reference only) (Last updated: Nov 22)
- CW10 with solution (reference only) (Last updated: Nov 22
- CW11 with solution (reference only) (Last updated: Nov 26)
- CW12 with solution (reference only) (Last updated: Dec 3)
- CW13 with solution (reference only) (Last updated: Dec 7)
Assessment Scheme
| Tutorial Classwork, max 10pts. Classworks will be given during tutorial. Each classwork counts 1pt. There are about 12-13 tutorals and you need to attend at least 10 of the tutorials. | 10% | |
| Midterm Oct 17 Tue During Lecture | 30% | |
| Final | 60% |
Assessment Policy Last updated: December 11, 2017 14:37:50