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
This course serves as an alternative to MAT 310. It is an intensive course, primarily intended for math majors in Advanced Track program.
- C or higher in MAT 211 or 308 or AMS 210;
- C or higher in MAT 200
- or a permission of instructor.
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.
Tuesdays and Thursdays 2:30pm - 3:50pm in Zoom,
Meeting ID 445-647-2936
Required meeting password 237386
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.
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.
Tuesdays and Thursdays 5:30pm - 7:00pm in Zoom,
Meeting ID 445-647-2936
Required meeting password 237386 or by appointment.
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
The final grade will be based on
- Homeworks 20%,
- Midterm 1 15%,
- Midterm 2 20%,
- Final exam 45%.
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.
If you have a physical, psychological, medical, or learning disability that
may impact your course work, please contact Disability Support
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.
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
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.