Math 416 - Fall 2019

Abstract Linear Algebra

Instructor

Zhao Yang
Email: zhaouiuc@illinois.edu
165 Altgeld Hall
Office hours: M 1-2p, T 9:30-10:30, W 1-2p, or by appointment

Course info

Time and Place: MWF 12:00-12:50 at 341 Altgeld Hall.

Textbook: Linear Algebra, Fourth Edition, by Steven Friedberg, Arnold Insel, and Lawrence Spence.

Notes: A course notes will collect key ingredients taught in class. However, it cannot be used as a substitute of your textbook.

Aim: Math 416 is a rigorous, abstract treatment of linear algebra. Topics to be covered include vector spaces, linear transformations, linear system, eigenvalues and eigenvectors, diagonalizability, and inner product spaces. The course concludes with a brief introduction to the theory of canonical forms for matrices and linear transformations. Credit is not given for both MATH 416 and either MATH 410 or MATH 415.

Prerequisite: MATH 241; MATH 347 is recommended.

Grading Policy: Weekly homework 20%; Midterms 45% (15% each); Final 35%.

Inclusive statement: This classroom is a place where you will be treated with respect. I welcome individuals of all ages, backgrounds, beliefs, ethnicities, genders, gender identities, national origins, religious affiliations, sexual orientations, abilities - and other visible or non-visible differences. All members of this class are expected to contribute to a respectful, welcoming and inclusive environment for every other member of the class. The effectiveness of this course is dependent upon the creation of an Sexual Misconduct Reporting Obligation encouraging and safe classroom environment. Exclusionary, offensive or harmful speech (such as racism, sexism, homophobia, transphobia, etc.) will not be tolerated and in some cases subject to University harassment procedures. We are all responsible for creating a positive and safe environment that allows all students equal respect and comfort. I expect each of you to help establish and maintain and environment where you and your peers can contribute without fear of ridicule or intolerant or offensive language.

Exams

There will be three midterms and a final exam on the material covered in the lectures. Our midterm exams will be held in class. Our final exam will be scheduled by the registrar's office and I will let you know once it is scheduled. If you make travel arrangements before the final exam is scheduled, you should assume that the final will be held on the last day of the final exam period.

Exam 1: Exam is on Sept. 27th and is based on materials taught before Sept. 21st.
Exam 2: Exam is on Oct. 25th and is based on materials taught before Oct. 19th.
Exam 3: Exam is on Nov. 22nd and is based on materials taught before Nov. 16th.
Final Exam: Dec. 17th 8am-11am at 341 Altgeld; Comprehensive.

Homework

Mathematics (and problem solving in general) is a collaborative discipline. You are strongly encouraged to work in groups and to discuss homework problems with your classmates. However, you must write-up the solution on your own and it must be in your own words. Anything else is plagiarism and will be treated as such.
Your solution needs to be complete and correct (of course!), but to recieve full credit your write-up should also meet the following criteria.

All of the important logical steps in the proof should be present and fully explained.
All assumptions should be clearly identified.
Your write-up should be clear and concise. (I.e., if a sentence or paragraph does not advance the reader's understanding of the solution, it does not belong in the write-up.)
Use full and complete English sentences. Symbols should be used only as a tool to distill a complex mathematical relationship into a readable format.

I highly suggest that you write up your solution sets using the typsetting program LaTeX which is designed for the production of technical and scientific documentation. Overleaf is an online LaTeX editor that allows real-time collaboration and online compiling of projects to PDF format. This online editor also provides a number of beautiful templates for completing math homework assignments.

I will upload homework here as the course progresses. Homework is due at the beginning of class on every Wednesday. Late homework will not be accepted under any circumstances, however your lowest homework scores will be dropped.

Homework #1 due Wednesday, September 6th: [Homework 1.pdf].

Homework #2 due Wednesday, September 11th: [Homework 2.pdf].

Homework #3 due Wednesday, September 18th: [Homework 3.pdf].

Homework #4 due Wednesday, September 25th: [Homework 4.pdf]. Solutions to extra credit problems can be found [here].

Homework #5 due Wednesday, October 2nd: [Homework 5.pdf].

Homework #6 due Wednesday, October 9th: [Homework 6.pdf].

Homework #7 due Wednesday, October 16th: [Homework 7.pdf].

Homework #8 due Wednesday, October 23rd: [Homework 8.pdf].

Homework #9 due Wednesday, October 30th: [Homework 9.pdf].

Homework #10 due Wednesday, November 6th: [Homework 10.pdf].

Homework #11 due Wednesday, November 13th: [Homework 11.pdf].

Homework #12 due Wednesday, November 20th: [Homework 12.pdf].

Homework #13 due Wednesday, December 4th: [Homework 13.pdf].

Homework #14 Not to be turned in: [Homework 14.pdf].