Mathematical Algorithms I, Spring 2021

This is the course website for Mathematical algorithms I (수학적 알고리즘 1), M1407.000400, Spring 2021.


Homework

Weekly homework assignments should be submitted through eTL.

  1. Homework 1, due Friday Match 19, 5:00pm.

Lecture Plans and Reading

  • [Week 1] Algorithms, Euclid's algorithm, addition and multiplication. Very simple data structures: Karatsuba multiplication
  • [Week 2] Analysis of Karatsuba's method, and more on data structures. Lists, stacks, etc
  • [Week 3] Graphs and graph algorithms
  • [Week 4] Symbolic differentation via expression trees
  • [Week 6] Forward-mode automatic differentation
  • [Week 7] Reverse-automatic differentation
  • [Week 8] Floating point arithmetic, basic linear algebra subroutine
  • [Week 9] Fast Fourier transforms
  • [Week 10] Arithmetic modulo primes
  • [Week 11] Generating random numbers and some of their numerical background
  • [Week 12] Intersecting varieties, some motivation for Groebner bases
  • [Week 13] Buchberger's algorithm
  • [Week 14] Multivariate versions and Groebner bases

Course Information

Instructor

Ernest K. Ryu, 27-205, .

Lectures

Wednesday 1:00–5:00 pm over Zoom. Live (online) attendance is required. Meeting link and the password are available on eTL.

Exams

The class will have midterm and final exams.

  • Midterm exam: April 21, 1:00–5:00pm, location TBD.
  • Final exam: June 16, 1:00–5:00pm, location TBD.

Grading

Attendance 10%, homework 20%, midterm exam 30%, final exam 40%.

Prerequisites

Good knowledge of advanced calculus, linear algebra, basic abstract algebra, and basic probability is required. Prior background in programming is not required.

Textbooks

This class will not use a designated textbook.