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 accounts for 20% of the total grade; each Midterm is worth 20% of the total grade; the Final is worth 40% of the total grade.
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).
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.
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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.