Lectures: Wilkinson Hall 221, MW 1:00-2:15pm
Instructor: Dr. Mihaela B. Vajiac
Office: VN 102
Office hours: Announced on Webpage.
Webpage:
http://www1.chapman.edu/~mbvajiac
Moodle Webpage:
http://mathv.chapman.edu/moodle
Credits: 3
Text: Two required texts:
We will cover most of the concepts in the book and unlock the mysteries and usefullness of Advances Linear Algebra.
Other helpful books:
Possible Topics and/or Projects:
1. Matrix Limits and Markov Chains
2. Invariant Subspaces and the Cayley-Hamilton Theorem
3. Inner Products and Norms
4. The Gram-Schmidt Orthogonalization Process and Orthogonal Complements
5. The Adjoint of a Linear Operator
6. Normal and Self-Adjoint Operators. Computations of eigenvalues of self-adjoint matrices.
7. Unitary and Orthogonal Operators and Their Matrices
8. Orthogonal Projections and the Spectral Theorem
9. The Singular Value Decomposition and the Pseudoinverse
10. Bilinear and Quadratic Forms
11. (Project: Einstein's Special Theory of Relativity)
12. (Project: Conditioning and the Rayleigh Quotient)
13. The Geometry of the Orthogonal Operator
14. The Jordan Canonical Form
15. The Minimal Polynomial
16. (Project: The Rational Canonical Form)
17. Pfaffian; Symplectic Matrices
18. Tensor Product
19. (Project: Lattices)
20. (Project: Fast Fourier Transform)
21. Spectral Radius
22. (Project: Lorentz Group)
23. (Project: Compactness of the Unit Ball)
Homework: Homework, mostly from the text, will be assigned in class, usually on Wednesdays and will be due in class one week later. (An exception is the first homework, assigned today and due on Monday, Feb 5th). Homework will also be posted on the Web.
Collaboration: You are encouraged to work together on homework and to learn from each other. However, the paper you eventually turn in should represent your own understanding -- you should be able to justify every sentence. There is a fine line between collaborative learning and turning in another's work.
Exams: There will be one midterm exam, announced in class one week before it is given. The midterm exam will include presentations of individual or group projects, the on-going and changing list to be announced every two weeks or so. The final exam is scheduled on Wednesday, May 16th, 8:00 - 10:30 AM .
Grading Policy: Midterm 30%, the homework counts 30%, and the final exam counts 30%, class participation 10%.
Proofs: Mathematics is about proving things as much as it is about calculating things. The first homework is given mainly to see how well you understand the art of proof. If you have trouble with proofs, we can work on it, but there is no avoiding the concept of proof in (honest) mathematics.
Help: Office hours are there for a reason. Please come. You are not only doing yourself a favor, but also giving me valuable feedback. The more questions you ask, the better my next lecture will be.
Fun: We'll have loads of fun, that's a promise!
Disabilities: Any student in this course who has a disability that may prevent him or her from fully demonstrating his or her abilities should contact me personally as soon as possible so we can discuss accommodations necessary to ensure full participation and facilitate your educational opportunity.Academic Integrity: Students are assumed to be familiar with the Academic Integrity Code. Any violations of this code will be strictly dealt with in accordance with this code.
Disclaimer: The information in this syllabus is subject to change in the event of extenuating circumstances.
Mihaela Vajiac