MATH 2660: Topics in Linear Algebra
Section 110 by Minjae Park (MWF 11-11:50 in ACLC 102)
This page provides an outline of the topics, course content, and assignments for the semester. Please note that the schedule is subject to change and may be updated as the semester progresses.
| WEEK | DATE | TOPIC | MATERIALS | EXTRA | DUE |
|---|---|---|---|---|---|
| 1 | Wed, Jan 7 | Introduction | ๐ Syllabus ๐ฅ๏ธ Slides 01 ๐๏ธ Notes 01 |
๐ผ๏ธ Showcase :: Image Compression | |
| Fri, Jan 9 | Vectors and their operations (4.1) | ๐ฅ๏ธ Slides 02 ๐๏ธ Notes 02 |
๐ฅ 3Brown1Blue :: Essence of Linear Algebra | HW 0 due at 11:59 pm | |
| 2 | Mon, Jan 12 | Linear combinations (2.1) | ๐ฅ๏ธ Slides 03 ๐๏ธ Notes 03 |
๐ผ๏ธ Vectors in 2D ๐ผ๏ธ Vectors in 3D |
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| Wed, Jan 14 | Matrix multiplication (2.2) | ๐ฅ๏ธ Slides 04 ๐๏ธ Notes 04 |
๐งฎ MATLAB Online | ||
| Fri, Jan 16 | Linear transformations (4.7, 6.1) | ๐ฅ๏ธ Slides 05 ๐๏ธ Notes 05 |
๐ฅ 3Brown1Blue :: Linear transformations | HW 1 due at 11:59 pm | |
| 3 | Mon, Jan 19 | No class - M. L. King, Jr. Day | |||
| Wed, Jan 21 | Solving linear equations (1.1,1.2) | ๐ฅ๏ธ Slides 06 ๐๏ธ Notes 06 |
๐ Section 1.2 of Larsonโs e-book | ||
| Fri, Jan 23 | Inverse matrices (2.3) | ๐ฅ๏ธ Slides 07 ๐๏ธ Notes 07 |
๐ฅ 3Brown1Blue :: Matrix multiplication | HW 2 due at 11:59 pm | |
| 4 | Mon, Jan 26 | Elementary matrices (2.4) | ๐ฅ๏ธ Slides 08 ๐๏ธ Notes 08 |
๐ผ๏ธ Linear transformations in 2D ๐ผ๏ธ Linear transformations in 3D |
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| Wed, Jan 28 | Review for Quiz 1 | ๐ฅ๏ธ Slides 09 ๐๏ธ Notes 09 |
๐ Practice questions from WebAssign | Last day to drop with no grade/refund deadline | |
| Fri, Jan 30 | Quiz 1: Vector and matrices | ๐ฅ๏ธ Quiz 1 on WebAssign ๐ The access code will be given at the start of the quiz |
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| 5 | Mon, Feb 2 | Applications - Markov chains, LU decomposition (2.4, 2.5) | ๐ฅ๏ธ Slides 10 ๐๏ธ Notes 10 |
๐ฅ HarvardX :: Markov Chains ๐ผ๏ธ Markov Chains ๐ผ๏ธ Electric Circuits and LU decompositions |
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| Wed, Feb 4 | Vector spaces I (4.2) | ๐ฅ๏ธ Slides 11 ๐๏ธ Notes 11 |
๐ฅ 3Brown1Blue :: Abstract vector space | ||
| Fri, Feb 6 | Spanning sets (4.3) | ๐ฅ๏ธ Slides 12 ๐๏ธ Notes 12 |
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| 6 | Mon, Feb 9 | Vector spaces II (4.2, 4.3) | ๐ฅ๏ธ Slides 13 ๐๏ธ Notes 13 |
๐ผ๏ธ Subspaces in 3D | HW 3 due at 11:59 pm |
| Wed, Feb 11 | Linear independence and basis (4.4, 4.5) | ๐ฅ๏ธ Slides 14 ๐๏ธ Notes 14 |
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| Fri, Feb 13 | Lengths and angles from dot products (5.1) | ๐ฅ๏ธ Slides 15 ๐๏ธ Notes 15 |
๐ผ๏ธ Vectors in 2D ๐ผ๏ธ Vectors in 3D |
HW 4 due at 11:59 pm | |
| 7 | Mon, Feb 16 | Orthogonality and Gram-Schmidt process (5.2, 5.3) | ๐ฅ๏ธ Slides 16 ๐๏ธ Notes 16 |
๐ผ๏ธ Gram-Schmidt in 2D ๐ผ๏ธ Gram-Schmidt in 3D |
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| Wed, Feb 18 | Dot products II (5.1) | ๐ฅ๏ธ Slides 17 ๐๏ธ Notes 17 |
๐ฐ Decorrelating Features using the Gram-Schmidt Process | Early Alert Grade Deadline | |
| Fri, Feb 20 | Least squares approximations (5.4) | ๐ฅ๏ธ Slides 18 ๐๏ธ Notes 18 |
๐ฅ 3Brown1Blue :: Fourier transform ๐ฐ What are Filtering in Frequency Domain and Fourier Transform? ๐ผ๏ธ Fourier Transformation for Image Processing |
HW 5 due at 11:59 pm | |
| 8 | Mon, Feb 23 | Fundamental subspaces (4.6, 5.4) | ๐ฅ๏ธ Slides 19 ๐๏ธ Notes 19 |
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| Wed, Feb 25 | Determinants (3.1) | ๐ฅ๏ธ Slides 20 ๐๏ธ Notes 20 |
๐ผ๏ธ Geometric Proof of the 2ร2 Determinant ๐ผ๏ธ Orientation and Sign of Determinant | ||
| Fri, Feb 27 | Cofactor expansions (3.2) | ๐ฅ๏ธ Slides 21 ๐๏ธ Notes 21 |
๐ผ๏ธ Cofactor Expansion for 3ร3 Determinants ๐ผ๏ธ Cofactor Expansion for 4ร4 Determinants |
HW 6 due at 11:59 pm | |
| 9 | Mon, Mar 2 | Properties of determinants (3.3) | ๐ฅ๏ธ Slides 22 ๐๏ธ Notes 22 |
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| Wed, Mar 4 | Review for Quiz 2 | ๐ฅ๏ธ Slides 23 ๐๏ธ Notes 23 |
๐ฐ A worked example ๐ Practice questions from WebAssign |
Deadline for request to move finals to Associate Deans | |
| Fri, Mar 6 | Quiz 2: Vector spaces and determinants | ๐ฅ๏ธ Quiz 2 on WebAssign ๐ The access code will be given at the start of the quiz |
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| 10 | Mon, Mar 9 | No class - Spring break | |||
| Wed, Mar 11 | No class - Spring break | ||||
| Fri, Mar 13 | No class - Spring break | ๐ Happy Pi Day! ๐ฅ 3Brown1Blue :: Why colliding blocks compute ฯ |
Mid-semester Feedback | ||
| 11 | Mon, Mar 16 | Post Spring Break Review | ๐ฅ๏ธ Slides 24 ๐๏ธ Notes 24 |
๐ฅ KoothBrush :: All of linear algebra | |
| Wed, Mar 18 | Applications of determinants (3.4, 5.5) | ๐ฅ๏ธ Slides 25 ๐๏ธ Notes 25 |
๐ฅ 3Brown1Blue :: Cross products | ||
| Fri, Mar 20 | Eigenvalues I (7.1) | ๐ฅ๏ธ Slides 26 ๐๏ธ Notes 26 |
๐ผ๏ธ Eigenvectors and eigenvalues | HW 7 due at 11:59 pm | |
| 12 | Mon, Mar 23 | Eigenvalues II (7.1, 7.3) | ๐ฅ๏ธ Slides 27 ๐๏ธ Notes 27 |
๐ฅ 3Brown1Blue :: Eigenvectors and eigenvalues | |
| Wed, Mar 25 | Diagonalizing a matrix (7.2, 7.3) | ๐ฅ๏ธ Slides 28 ๐๏ธ Notes 28 |
๐ผ๏ธ Matrix Diagonalization | ||
| Fri, Mar 27 | Solving linear differential equations (7.4) | ๐ฅ๏ธ Slides 29 ๐๏ธ Notes 29 |
HW 8 due at 11:59 pm | ||
| 13 | Mon, Mar 30 | Complex matrices (8.1, 8.3) | ๐ฅ๏ธ Slides 30 ๐๏ธ Notes 30 |
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| Wed, Apr 1 | Singular value decompositions | ๐ฅ๏ธ Slides 31 ๐๏ธ Notes 31 |
๐ Cleve Moler :: Eigenvalues and singular values with Matlab ๐ผ๏ธ Singular Value Decomposition in 2D ๐ผ๏ธ Singular Value Decomposition in 3D |
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| Fri, Apr 3 | Applications of SVD | ๐ฅ๏ธ Slides 32 ๐๏ธ Notes 32 |
๐ผ๏ธ Digit Recognition | HW 9 due at 11:59 pm | |
| 14 | Mon, Apr 6 | Principal value analysis | ๐ฅ๏ธ Slides 33 ๐๏ธ Notes 33 |
๐ฐ Analytics Vidhya :: The Math of PCA ๐ฐ Explained Visually :: PCA |
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| Wed, Apr 8 | Review for Quiz 3 | ๐ฅ๏ธ Slides 34 ๐๏ธ Notes 34 |
๐ฐ Quiz 3 review questions ๐ Further practice questions from WebAssign |
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| Fri, Apr 10 | Quiz 3: Eigenvalues and eigenvectors | ๐ฅ๏ธ Quiz 3 on WebAssign ๐ The access code will be given at the start of the quiz |
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| 15 | Mon, Apr 13 | Image processing: hands-on | ๐ฅ๏ธ Slides 35 ๐๏ธ Notes 35 |
โจ๏ธ Matlab Demo | |
| Wed, Apr 15 | Balancing equations | ๐ฅ๏ธ Slides 36 ๐๏ธ Notes 36 |
โจ๏ธ Matlab Demo ๐ฅ Veritasium :: Spring Paradox |
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| Fri, Apr 17 | Gradient decent | ๐ฅ๏ธ Slides 37 ๐๏ธ Notes 37 |
โจ๏ธ Matlab Demo ๐ฅ 3Brown1Blue :: Gradient Descent |
Last day to withdraw with a โWโ | |
| 16 | Mon, Apr 20 | Final Review I | ๐ฅ๏ธ Slides 38 ๐๏ธ Notes 38 |
๐ผ๏ธ Overview | AU eValuate opens |
| Wed, Apr 22 | Final Review II | ๐ฅ๏ธ Slides 38 ๐๏ธ Notes 38 |
๐ฐ Final review questions | ||
| Fri, Apr 24 | Final (1/2): Comprehensive exam | ๐ฅ๏ธ Final (1/2) on WebAssign ๐ The access code will be given at the start of the exam |
HW 10 due at 11:59 pm | ||
| 17 | Mon, Apr 27 | Final Exam | ๐๏ธ Handwwritten exam (10:30 am โ 12:30 pm) in the same classroom | AU eValuate closes | |
| Wed, Apr 29 | Deadline for all assignments |
Bonus 1 due at 11:59 pm Bonus 2 due at 11:59 pm |
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| Fri, May 1 | Final letter grade review by May 3 (Sun) |