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, 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
- Quadratic forms
- (if time allowed) Number-theoretic functions.
- (if time allowed) 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 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 12-13 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