Instructor: Filip Zivanovic, office hours: My SB card
NB. Most course information and materials will be posted on this page.
The exceptions are:
Gradescope will be used to submit homework assignments and to see your graded homework.
Brightspace will be used to make announcements, and solutions to problem sets will also be posted there.
Course Description: Finite-dimensional vector spaces, linear maps, dual spaces, bilinear functions, inner products. Additional topics could include: canonical forms, multilinear algebra, numerical linear algebra (if time permits).
Prerequisites: C or higher in MAT 211 or 305 or 308 or AMS 210; C or higher in MAT 200 or MAT 250 or permission of instructor.
Attendance: Strongly encouraged, but not mandatory.
MAT 310 STARTS TOGETHER WITH MAT 315, AND WE SPLIT AFTER MIDTERM 1.
Major Topics Covered: Matrices and Operations on Matrices; Determinants of Matrices; Vector Spaces and Subspaces; Linear Transformations and Linear Operators; Kernels and Images; Basis for Vector Space and the Dimension of a Vector Space; Eigenvalues, Eigenvectors and the Diagonalization of Linear Operators; the Cayley-Hamilton Theorem; Inner Product Spaces; Self-adjoint Operators, Normal Operators, Orthogonal Operators; the Spectral Theorem.
Grading:
Homework and quizzes account for 20% of the total grade; each Midterm is worth 20%; the Final is worth 40%.
Letter grades are calculated as: A 100-95% A- 94-90% B+ 89-86% B 85-83% B- 82-79% C+ 78-75% C 74-71% C- 70-67% D+ 66-62% D 61-58% F<57%
Syllabus:
Week. Lecture Dates. Topics covered from the Textbook.
Aug 24-26 Vector spaces. Subspaces (1A, 1B, 1C).
Aug 31-Sep 2 Span and linear independence. Bases and dimension (2A,2B,2C).
Sep 7-9 Monday: Labor Day. Linear maps (3A).
Sep 14-16 Null space and range. Matrices (3B, 3C).
Sep 21-23 Invertibility and isomorphisms. Products and quotients (3D, 3E).
Here are the lecture notes for the first five weeks.
Sep 28-Sep 30 Monday: Midterm 1 (in class). Wednesday: Duality (3F).
Oct 5-7 Polynomials. Invariant subspaces (4, 5A).
Oct 12-14 Monday: Fall break. Wednesday: Minimal polynomial (5B).
Oct 19-21 Upper-triangular matrices. Diagonalization. (5C, 5D).
Oct 26-28 Commuting operators. Inner products and norms. (5E, 6A).
Nov 2-4 Orthonormal bases. Orthogonal complements. (6B, 6C).
Nov 9-11 Monday: Orthogonal projections (6C). Wednesday: Midterm 2 (in class).
Nov 16-18 Self-adjoint and normal operators. Spectral theorem. (7A, 7B).
Nov 23-25 Monday: Positive operators (7C). Wednesday: Thanksgiving - no class.
Nov 30-Dec 2 Isometries. Generalized eigenvalues (7D, 8A).
Dec 7 Monday: Generalized eigenspaces (8B).
Dec 16 Wednesday: Final 8:00 - 10:45 am location TBA
Homework:
Homework is a fundamental part of this course. Late homework will not be accepted.
Your lowest three scores from the homeworks will be dropped; i.e., your best 8/11 homeworks will be accounted for.
The exercises will be taken from the course textbook. Homework is due to be submitted on Gradescope by the given date at 11:59 PM, as indicated below:
Number Due Exercises from the textbook.
1. Aug 31 1A: 4,9 1B: 3,7 1C: 1,12
2. Sep 7 2A: 3,6 2B: 3,9 2C: 1,12
3. Sep 21 3A: 1,4,7 3B: 1,6,13
4. Oct 5 3C: 1,3,1 3D: 2,9,11
5. Oct 12 3E: 1, 7 3F: 1 4: 4,6,9
6. Oct 19 5A: 6,8,9 5B: 4,6,7
7. Oct 26 5C: 1,2,9 5D: 2,3,13
8. Nov 2 5E: 3,4,5 6A: 2,6,14
9. Nov 23 6B: 2,8 6C: 2,3 7A: 1,2
10. Nov 30 7B: 2,5,8 7C: 1,6,10
11. Dec 7 7D: 2,3,4 8A: 1,2,6
Accessibility Support Center (SASC) Statement: If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center (SASC), 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.
Students who might require special evacuation procedures in the event of an emergency are urged to discuss their needs with both the instructor and DSS. For important related information, click here.
Academic Integrity Statement: 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. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html.
Critical Incident Management Statement: 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 behaviour 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.
AI policies:
Unless the instructor states otherwise, the use of AI tools is not allowed to obtain solutions to homework problems, other assignments, or tests. All work you submit should be your own, without any AI assistance. Any exceptions from this policy will be clearly specified by the course instructor.
If the course policy allows AI tools to be used for a particular project, such use must be disclosed in detail. (For example, you should write “Graphics for this presentation were created using ChatGPT”.) The final content of your work is your responsibility. Any mistakes or errors are reflected in your grade, even if they were introduced by AI tools. In particular, if AI tools suggest some references or citations, it is your responsibility to verify the accuracy of these references or citations.