MAT 315: Advanced Linear Algebra

Stony Brook University - Spring 2020

About the course

This is an advanced mathematically rigorous course with complete proofs. Topics covered will include vector spaces, linear maps, dual spaces, linear transformations, eigenvalues, dual spaces and inner products, bilinear and quadratic functions and quotient vector spaces. the characteristic and minimal polynomial of a linear operator, various classes of linear operators and their normal forms, multilinear algebra, tensors.
This course serves as an alternative to MAT 310. It is an intensive course, primarily intended for math majors in Advanced Track program.

Prerequisites

C or higher in MAT 211 or 308 or AMS 210;
C or higher in MAT 200
or a permission of instructor.

Textbook and additional materials

Linear Algebra Done Right ( 3nd edition) by Sheldon Axler, Springer, (c) 2015
Notes on Polylinear Algebra by Oleg Viro, updated and expanded

Lecturer

Oleg Viro
Professor, Ph.D. 1974, Doctor Phys-Mat.Sci. 1983,
both from Leningrad State University.
Arrived at Stony Brook in 2007.

Phone: (631) 813 5908
Email: oleg.viro AT stonybrook.edu
Web page: www.math.stonybrook.edu/~oleg

Research fields: Topology and Geometry,
especially low-dimensional topology
and real algebraic geometry.

Lectures time and location

Tuesdays and Thursdays 2:30pm - 3:50pm in Zoom,
Meeting ID 445-647-2936
Required meeting password 237386

Handouts of lectures

Lecture 1 of MAT 310/315 Vector spaces, subspaces, sums and direct sums.
Lecture 1 of MAT 315 Linear maps, language of categories, Null space.
Lecture 2 The range of a linear map, lists of vectors vs. linear maps, isomorphism classification of vector spaces and linear maps.
Lecture 3 Classification of linear maps, revisited and continued, back to matrices.
Remarks on Lecture 4

Slides of lectures

Here are pdf files with slides for some of the lectures. These files are designed for viewing on a computer screen. Don't print them, because each contains more than one hundred pages, most of which differ from the next page by a single line.

Lecture 1 Linear maps, language of categories, Null space.
Lecture 2 The range of a linear map, lists of vectors vs. linear maps, isomorphism classification of vector spaces and linear maps.
Lecture 3 Classification of linear maps, revisited and continued, back to matrices.
Beginning of Lecture 4 Quotient spaces.

Online lectures

Lecture 1, 3/31
Lecture 2, 4/02
Lecture 3, 4/07
Lecture 4, 4/09
Lecture 5, 4/14
Lecture 6, 4/16
Lecture 7, 4/21
Lecture 8, 4/23
Lecture 9, 4/28

Homeworks

Homeworks are assigned once a week. Problems should be submitted through Blackboard, Assessments.

homework 1
homework 2
homework 3
homework 4
homework 5
homework 6

Office hours

Tuesdays and Thursdays 5:30pm - 7:00pm in Zoom,
Meeting ID 445-647-2936
Required meeting password 237386 or by appointment.

Teaching Assistant

Ying Hong Tham, PhD Student
Arrived at Stony Brook in 2016
Email: yinghong.tham AT stonybrook.edu
Recitations: MAT 315.R01 - W 12:00am - 12:53am
Office Hours: W 9:00am-10:00am
Math Learning Center Hours:

W 2:30pm-3:30pm
W 10:00am-11:00pm

Grading policy

The final grade will be based on

Homeworks 20%,
Midterm 1 15%,
Midterm 2 20%,
Final exam 45%.

Exams

There will be two in-class midterms.
The first midterm: February 13, 2:30pm-3:50pm.
The date of the second midterms will be announced later.

Final Exam: Tuesday, May 14, 5:30pm-8:00pm.

Disabilities

If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services or call (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the Evacuation Guide for People with Physical Disabilities.

Academic Integrity

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website.

Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.