Computational Mathematics

MATH 490 (Section AH), Spring 2020

239 Altgeld Hall (now online), MWF 11:00 AM

University of Illinois at Urbana-Champaign, Department of Mathematics

Instructor: Anil Hirani (email), Altgeld Hall Room 375
TA: Vaibhav Karve (email).

Office Hours:
Anil Hirani: By appointment.
Vaibhav Karve: Tuesdays 4-4:50pm and by appointment.

All course grades and announcements will be posted on Moodle. All worksheets from class will also be available there. Class worksheets and Homework assignments will be released on CoCalc.

Prerequisites: Successful completion of CS 101 or 125 or prior programming experience in Python, C, C++ or Java; as well as successful completion of Math 347 (or CS 173).

Description: This is a project-based course that will guide students through a computational way of approaching problems. Topics covered will include network and graph algorithms, topological data analysis, computer algebra and cryptography algorithms. If time permits, we will also cover basics of building simple neural networks. Programming will be done in Python and its extension that the SageMath environment provides. The format will be short lectures and short programming exercises twice a week with longer project work once a week. In addition students will select a longer final project and do an in-class presentation in the last week or so of class.

Goals: The 4 main goals of this course are: (1) Improve programming skill and algorithmic thinking; (2) Prepare for industrial computational math work; (3) Prepare for future math courses by learning to use computation to play with examples; (4) Prepare for research in mathematics using a computer as a tool.

Textbook: There is no required textbook. However for SageMath, the free book Computational Mathematics with SageMath is recommended.

Grading: Homeworks 20%, Three exams 15% each, Final Project 30%, Class participation 5%. Your lowest homework score will be dropped.

Homeworks will be posted on Friday mornings and will be due the next Wednesday (on CoCalc). Late homeworks will not be accepted (however, your lowest homework score will be dropped). You are encouraged and welcome to collaborate with other students on homeworks. That means you can talk to others and discuss the homework problems. But you must write up the solutions on your own (and acknowledge the contributions of your colleagues by name, if applicable).

Exam 1: (Friday) February 21, 2020. 5:00 - 6:30 pm. 239 Altgeld Hall. Syllabus: Lectures 01 to 13.

Exam 2: (Friday) March 27, 2020. 5:00 - 6:30 pm. Online.

Exam 3: (Friday) May 1, 2020. 5:00 - 6:30 pm. Online.

Final Project: See shared Google doc for details and timeline. Final project will require you to apply some of the skills and techniques learnt in class to one problem from a list of possible project ideas. You will be required to work in groups for the final project and present your project to the class.

Course Diary:

Page maintained by Anil N. Hirani
Last modified: Wed Apr 22 17:14:26 CDT 2020