MAD 6403 Computational Mathematics (Fall 2018)

MAD 6403 Computational Mathematics (Fall 2018)

Instructor:  Dr. Shi Bai
Office:  Science Building (SE43), Room 230.
Email:  sbai@fau.edu
Lecture time and location:  Tuesday & Thursday 12:30PM -- 01:50PM in IS 113.
Office hours:  Tuesday & Thursday 2 - 3 pm; and by appointment.
Course Syllabus


Schedule

 
Week Dates Topics Announcement
1 Aug 21
Aug 23
Chap 2. Basic representation (2.1, 2.2); algorithmic complexity.
Sagemath basics.
Lec-1
Lec-2
2 Aug 28
Aug 30
Chap 2. Fundamental algorithms (2.3, 2.4) Lec-3
Lec-4
Homework 1
3 Sep 4
Sep 6
Chap 3 & 4. Euclidean algorithm (3.1-3.3, 4.1, 4.2)
Chap 5. Evaluation and interpolation (5.1-5.3)

Lec-6
4 Sep 11
Sep 13
Chap 5. Evaluation and interpolation (5.4)
Chap 8. Karatsuba (8.1)
Lec-7
Lec-8
Homework 2
5 Sep 18
Sep 20
Chap 8. FFT (8.2) Lab session Sep 17 (9-11am SE 271)
6 Sep 25
Sep 27
First mid-exam. (Tue class moved to lab session)
Mid-exam 1 (Thur)
7 Oct 2
Oct 4
Chap 8. FFT (8.2)
Chap 8. Schönhage and Strassen (8.3).
Lec-13
8 Oct 9
Oct 11
Chap 9. Fast division (9.1).
Chap 20. Public key cryptography (20.1, 20.2).
Lab session
9 Oct 16
Oct 18
Chap 14. Distinct-degree decomposition (14.2)
Chap 14. Cantor-Zassenhaus; square-free factorization; root-finding (14.3-14.6)
Lec-17
Homework 3 (review mid-exam)
10 Oct 23
Oct 25
Chap 19. Trial division, Pollard's rho method (19.2, 19.4)
Chap 19. Dixon's method (19.5)
Lec-19
Lec-20
Homework 4
11 Oct 30
Nov 1
Chap 16. Lattices; Gram-Schmidt. Lec-21
Lab session and group meeting
12 Nov 6
Nov 8
Chap 16. SVP; enumeration algorithm. Group meeting
Mid-exam 2 (Thur)
13 Nov 13
Nov 15
Chap 16. LLL algorithm. Lec-25
Lab session and group meeting
Homework 5
14 Nov 20
Nov 22

Thanksgiving break
Lab session and group meeting
Monday, Tuesday
15 Nov 27
Nov 29
Group presentation
16 (no class)



Documentation:
  A Tour of Sage
  Sage tutorial
  Visualize Python Execution
  Mathematical Computation with SageMath

Some websites for Python tutorials/exercises.
  Interactive tutorial (snakify.org)
  Python Tutorial
  Project Euler (more mathematical/computational problems)