Applied Linear Algebra
MATH5112/6012, Fall semester, 2020
Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall.
Teaching mode
- All the lectures will be online, mixed with asynchronous and synchronous ones. See Canvas for meeting time of synchronous lectures.
- All lectures (videos) will be available via Canvas.
- I shall prepare slides for all the lectures and they will be made available as semester goes.
- Individual online meetings, in place of traditional OH, by email appointment (preferably Thurs b/w 4:30 and 6pm).
Textbook
- Applied Linear Algebra (2nd Edition), Olver and Shakiban, Springer, 2018.
This book is available from SpringerLink, which means that from UC VPN, at this website, you may
- download a free PDF, or
- (recommended) buy a softcover edition at USD 24.99 (MyCopy, see top-right of the website).
Course Description
We shall cover the following topics from core basic linear algebra (chapter numbers from the textbook),
- Matrices, vectors, Gaussian Elimination, matrix factorizations, Forward and Back Substitution, inverses, determinants: 1.1–1.6, 1.8–1.9.
- Vector spaces, subspaces, linear independence, bases, dimension: 2.1–2.5.
- Inner products and their associated norms: 3.1–3.3.
- Orthogonal vectors, bases, matrices, and projections: 4.1–4.4.
- Positive definite matrices and minimization of quadratic functions: 3.4–3.5, 5.2
and the following applications,
- Minimization, least squares, data fitting and interpolation: 4.5, 5.3–5.5.
- Signal processing: 3.6, 5.6.
Homework/Exams/Grades
There will be weekly homework sets, two midterm exams and a final exam. There will be optional projects on applications, for extra bonus, that would require programming skills (at your choice of programming languages: Python, R, MATLAB). The total points a student could obtain is 110 = 100 + 10 (bonus) as explained below. The letter grades will be A (90+), A- (85+), B+ (80+), B (75+), etc.
- MATH5112 students: homework (50%) + 2 $\times$ max(midterm 1, midterm 2) (30%) + final exam (20%) + extra bonus (10%)
- MATH6012 students: homework (50%) + midterm 1 (15%) + midterm 2 (15%) + final exam (20%) + extra bonus (10%)
Tentative Schedule
All homework (HW) due the Monday of the next week. Optional projects (P) will be due a few weeks later as indicated. Links to be provided as semester goes.
- Week 1 (Aug 24): Part 1, Linear algebraic systems, Chapter 1.1-1.4. HW1
- Week 2 (Aug 31): Chapter 1.5-1.6, 1.8-1.9. HW2
- Week 3 (Sep 7): Labor Day Holiday, Sep 7, Mon. Vector spaces and bases, Chapter 2.1-2.2. HW3
- Week 4 (Sep 14): Chapter 2.3-2.5. HW4
- Week 5 (Sep 21): Part 3, Inner products and norms, Chapter 3.1-3.3. HW5
- Week 6 (Sep 28): Part 4, Orthogonality, Chapter 4.1-4.3. HW6
- Week 7 (Oct 5): Chapter 4.4, P1. Midterm 1 (materials from weeks 1-6), Friday.
- Week 8 (Oct 12): Chatper 4.5. HW7.
- Week 9 (Oct 19): Part 5, Positive definite matrix and minimization of quadratic functions, Chapter 3.4-3.5. HW8.
- Week 10 (Oct 26): Application 1, Minimization, least squares, data fitting and interpolation, Chapter 5.2-5.3. P2.
- Week 11 (Nov 2): 5.4-5.5. HW9.
- Week 12 (Nov 9): Veterans Day Holiday, Nov 11, Wed. Application 2, signal processing, Chapter 3.6, 5.6. HW10, P3
- Week 13 (Nov 16): Midterm 2 (materials from weeks 7-12), Friday.
- Week 14 (Nov 23): Discussions on projects and/or expository lectures on other applications, TBD. (Chapter 9.3 Markov processes, 9.7 Wavelets.)
Thanksgiving Weekend Holiday, Nov 26-29.
- Week 15 (Nov 30): TBD
Class ends Dec 2, Wed.
- Examination: Dec 3-Dec 8: Final Exam, TBA.