Subject |
In brief, this course introduces the fundamentals of linear algebra in the context of computer science applications. It includes definitions of vectors and matrices, their various operations, linear functions and equations, and least squares. It also includes the basics of floating point computation and numerical linear algebra. The list of covered topics are mentioned in details below. In this course, the students will become comfortable working with the basic tools in linear algebra and also familiar with several computer science applications throughout the semester. . |
Prerequisites |
Mathematical maturity; Requires prerequisite courses of (CSCI 2270 or CSCI 2275) and APPM 1360 or MATH 2300 (all minimum grade C-). If you have not taken those classes but believe that your background is close to being sufficient, please make sure you have filled up any potential gaps by the end of the second week of classes. If you are not sure whether your background suffices, please see the instructor. |
Instructor |
Alexandra Kolla (alexandra.kolla [at] colorado [dot] edu) 122 ECES [AK] |
Canvas |
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Course Staff |
GSS: Nivetha Kesavan (Nivetha.Kesavan@colorado.edu), Rick Gentry (Rick.Gentry@colorado.edu). CA: Zackary Jorquera (Zackary.Jorquera@colorado.edu)
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Times |
TTh 02:20 PM - 03:35 PM |
Class location (Zoom Link) |
https://cuboulder.zoom.us/j/7640842775 |
Office Hours |
Alexandra Kolla: Tuesdays 1:20-2:20 pm at this zoom link. Nivetha Kesavan: M W F 3:30 pm -4:30 pm at this zoom link, and Passcode: 345353. Rick Gentry: Tuesdays 4-5 pm, Thursdays 11am-12 noon at this zoom link. Zackary Jorquera: M 1:00-4:00 pm, Th: 3:30-6:00 pm, F 1:00-4:00 pm at this zoom link. |
| # | Date | Topic | Lecture Slides | Lecture Videos | Textbook Chapters |
|---|---|---|---|---|---|
| 1 | T August 25 | Introduction to Vectors | Slides (accidentally deleted the annotated slides, please read book chapters instead) | Video Recording | 1.1-1.3 |
| 2 | Th August 27 | Linear Combinations of Vectors, Inner Product, Complexity | Slides | Video Recording | 1.4-1.5 |
| 3 | Tu September 1 | Linear Functions | Slides | Video Recording | 2.1 |
| 4 | Th September 3 | Norm and Distance | Slides | Video Recording | 3.1, 3.2 |
| 5 | Tu September 8 | Distance, Standard Deviation | Slides | Video Recording | 3.2, 3.3 |
| 6 | Th September 10 | Angles, Cauchy-Schwartz, Complexity | Slides | Video Recording | 3.4, 3.5 |
| 7 | Tu September 15 | Linear Independence, Bases | Slides | Video Recording | 5.1, 5.2. Also see chapter 2 of this book for vector space material. |
| 8 | Th September 17 | More on Vector Spaces, Orthonormal Vectors | Slides | Video Recording | 5.3, 5.4 and previous notes on vector spaces above |
| 9 | Tu September 22 | More on Vector Spaces, Gram-Schmidt | Slides | Video Recording | 5.4 and previous notes on vector spaces above |
| 10 | Th September 24 | Gram-Schmidt | Slides | Video Recording | 5.5 |
| 11 | Tu September 29 | Review on Vector Spaces, Subspaces, Linear Independence, Basis | Slides | Video Recording | Chapter 4.1 and 4.3 of this book |
| 12 | Th October 1 | Review on Basis, Orthogonality, Coordinate systems, Orthogonal Projections | Slides, Slides | Video Recording | Chapters 4.4, 4.5, 6.1 and 6.2 of this book |
| 13 | Tu October 6 | Orthogonal Decomposition, Gram Schmidt | Slides | Video Recording | Chapters and 6.2-6.4 of this book |
| 14 | Th October 8 | Review | Video Recording | ||
| 15 | Tu October 13 | Matrices | Slides | Video Recording | Chapters 6.1-6.3 of textbook |
| 16 | Th October 15 | Matrices, continued | Slides | Video Recording (Unfortunately, I only hit "record" mid way through lecture. Luckily, the first 20-30 mins are covered extensively in chapter 6.4 of the textbook) | Chapters 6.4 of textbook |
| 17 | Tu October 20 | Matrix examples and operations | Slides | Video Recording | Chapters 7.1 of textbook and 2.1,2.2 of this book |
| 18 | Th October 22 | Vector Valued Linear Functions, Linear Systems | Slides | Video Recording | Chapter 8 of textbook |
| 19 | Tu October 27 | Matrix Multiplication, Paths in Directed Graphs, QR factorization | Slides | Video Recording | Chapter 10 of textbook |
| 20 | Th October 29 | Matrix Inverses | Slides | Video Recording | Chapters 11.1,11.2 of textbook |
| 21 | Tu November 3 | Matrix Inverses contd. Solving Systems of Linear Equations | Slides | Video Recording | Chapters 11.2-11.5 of textbook |
| 22 | Th November 5 | Row equivalence, echelon form, column space, rank, nullspace | Slides | I did not hit "record" this lecture, I apologize. See math book instead | Chapters 1.1-1.2 and 2.8-2.9 of this book |
| 23 | Tu November 10 | Determinants | Slides | Video Recording | Chapters 3.1-3.2 of this book |
| 24 | Th November 12 | Determinants, contd. | Slides | Video Recording | Chapters 3.3-3.4 of this book |
| 25 | Tu November 17 | Eigenvectors and Eigenvalues | Slides | Video Recording | Chapters 5.1-5.2 of this book |
| 26 | Th November 19 | Eigenvectors and Eigenvalues, contd. | Slides | Video Recording | Chapters 5.2-5.3 of this book |
| 27 | Tu November 24 | Review session | Slides | Video Recording | |
| 28 | Th November 26 | No Class, Thanskgiving | |||
| 29 | Tu December 1 | Complex eigenvalues and eigenvectors | Slides | Video Recording | Chapters 5.5 of this book |
| 30 | Th December 3 | Review For Final | Video Recording |
| Homework # | Due | Homework Solutions |
|---|---|---|
| HW0 | TBD | Solutions |
| HW1 | TBD | - |
| HW2 | TBD | - |
| HW3 | TBD | - |
| HW4 | TBD | - |
| HW5 | TBD | - |
| Homework |
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| There will be weekly homework. |
| Students are encouraged to collaborate, but each homework has to be turned in individually by each student . |
| There are *ABSOLUTELY NO LATE HOMEWORKS* accepted. Instead, I will be dropping the lowest two homework grades. |
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Please do not forget to cite your collaborators and sources (you will get a zero if you use material from elsewhere and do not cite the source!) |
| Exams |
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| There will be two midterms and a Final exam in the "take-home exam" format. More details to come. |
| Grading |
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| 60% homeworks, 15% each midterm, and 20% final exam. |
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Chapters 1-5: "Vectors" |
- We will start with "basic" Notation and terminology. Vector operations. Vector Spaces. Inner product. Linear functions, Taylor approximation and regression model. Complex numbers and vectors. Norm, distance, and angle. Linear independence, basis, orthonormal vectors, and Gram–Schmidt algorithm. |
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Chapters 6-11: "Matrices"
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- Notation and terminology. Matrix operations. Matrix inverses. Orthogonal matrices. QR factorization, Diagonalization. Linear equations. |
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Chapter 12-19: "Least Squares"
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- Least squares data fitting. Multi-objective least squares. Constrained least squares. Nonlinear least squares. |
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Not in the Book: "Eigenvalues and Eigenvectors"
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- Matrix Spectra. Eigendecomposition. Eigenvalues and Eigenvectors. |