MAT 315: Advanced Linear Algebra

Stony Brook University - Spring 2021

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. The first five lectures will be joint with MAT 310. After the first midterm, the students will have to either stay with MAT 310 or move to MAT 315.


Textbook and additional materials

Linear Algebra Done Right ( 3nd edition) by Sheldon Axler, Springer, (c) 2015
Lecture notes and handouts by Oleg Viro.

Lectures time and location

Tuesdays and Thursdays 3:00pm - 4:20pm in Zoom,
Meeting ID 932 9061 8111
Required meeting password 237386

Handouts of lectures


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
Web page:

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

Teaching Assistant

Saman Habibi Esfahani, PhD Student
Arrived at Stony Brook in 2017
Email: Saman.HabibiEsfahani AT
Recitations: MAT 315.R01 - W 11:45am - 12:40am
Office Hours: F 8:00am-9:00am
Math Learning Center Hours:


Homeworks are assigned once a week. Problems should be submitted through Gradescope every Wednesday.

Office hours

Mondays 2:00pm - 3:30pm and Wednesdays 2:30pm - 4:00pm in Zoom,
Meeting ID 445-647-2936
Required meeting password 237386
or by appointment.

Grading policy

The final grade will be based on


There will be two midterms.
The first midterm: February 16, 3:00pm-4:20pm.
The date of the second midterms will be announced later.

Final Exam: Tuesday, May 11, 2:15pm-5:00pm.

Student Accessibility Support Center (SASC) statement:

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Student Accessibility Support Center, ECC (Educational Communications Center) Building, Room 128, (631)632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.
Student Accessibility Support Center (SASC)
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 is 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 University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Schedule, and the Faculty-Employee Handbook.

Student Absences Statement

Students are expected to attend every class, report for examinations and submit major graded coursework as scheduled. If a student is unable to attend lecture(s), report for any exams or complete major graded coursework as scheduled due to extenuating circumstances, the student must contact the instructor as soon as possible.  Students may be requested to provide documentation to support their absence and/or may be referred to the Student Support Team for assistance. Students will be provided reasonable accommodations for missed exams, assignments or projects due to significant illness, tragedy or other personal emergencies. In the instance of missed lectures or recitations, the student is responsible for review posted slides, review recorded lectures, seek notes from a classmate or identified class note taker. Please note, all students must follow Stony Brook, local, state and Centers for Disease Control and Prevention (CDC) guidelines to reduce the risk of transmission of COVID. For questions or more information click here