# Math 22: Linear Algebra with Applications

Fall 2015

## Syllabus

• The latest homework will always appear on top.

• If you are interested in learning to typeset mathematics here is a list of resources compiled by Prof. Weber on LaTex

Tutorials

Angelica Babei will be available for tutorials this term. The tutorials are Tuesdays, Thursdays and Sundays 7:00 - 9:00 PM. She will be in room KH 105.

Homework assignments

• Late Homework will not be accepted.
• Write the names of the people with whom you worked on the homework.
• Please make sure that what you turned in for homework is your own understanding of how to do the problems.

Week 10
 Friday, Nov. 20: Final Exam at 3PM in Dartmouth 105
 Monday, Nov. 16: Review Study for the final!

Week 9
 Friday, Nov. 13: Slides (For 10 Section): Image Compression An article on JPEG compression> "Image Compression: Seeing What's Not There" by D. Austin. Another cool article on JPEG compression Image Compression: How Math Led to the JPEG2000 Standard by Society for Industrial and Applied Mathematics. Study for the final!
 Thursday, Nov. 12: Slides (For 10 Section): Guest Lecture: Alin Popescu on Image Forgeries Alin Popescu Contact Info Study for the final!
 Wednesday, Nov. 11: Slides (For 10 Section): Singular Value Decomposition & Application Read: Section 7.4 Practice problems   7.4 # 5, 7, 9, 11, 13, 15
 Monday, Nov. 9: Slides (For 10 Section): Singular Value Decomposition Read: Section 7.4

Week 8
 Friday, Nov. 6: Slides (For 10 Section): Principal Component Analysis & Face Recognition Here is an article about Face Recognition: Eigenfaces for Recognition. Read: Section 7.5 and article on Eigenfaces Practice problems   7.5 # 1,3,7 Graded assignment  (for Wednesday, Nov. 11) 7.5 # 2,4,8,9 Additional Graded problems: PageRank Homework
 Thursday, Nov. 5: Read: Section 4.9 and article on PageRank Practice problems   4.9 # 2, 12 Graded assignment  (for Wednesday, Nov. 11) 7.1 # 28, 30, 32 4.9 # 10, 18, 19, 20
 Wednesday, Nov. 4: Slides (For 10 Section): Markov Chains and Pagerank algorithm Here is an article about PageRank: How Google Finds Your Needle in the Web's Haystack. Read: Section 4.9 Practice problems   6.4 # 17, 19 7.1 # 25, 26, 27 Graded assignment  (for Wednesday, Nov. 11) 6.4 # 6, 10, 12, 22 7.1 # 12, 18, 22
 Monday, Nov. 2: Slides (For 10 Section): Diagonalization of Symmetric Matrices Read: Section 7.1

Week 7
 Friday, Oct. 30: Slides (For 10 Section): Gram-Schmidt Read: Section 6.4 Practice problems   6.3 # 2, 21, 22, 23 Graded assignment  (for Thursday, Nov. 5) 6.3 # 6, 10, 12, 14, 18, 20, 24
 Thursday, Oct. 29: Slides (For 10 Section): Orthogonal Projections Read: Section 6.3 Practice problems   6.2 # 6, 23, 24, 27, 33 Graded assignment  (for Thursday, Nov. 5) 6.2 # 10, 12, 14, 16, 22, 26, 28
 Wednesday, Oct. 28: Slides (For 10 Section): Orthogonal Sets Read: Section 6.2 Practice problems   5.3 # 26, 29 6.1 # 6, 19, 20, 23, 25, 27 Graded assignment  (for Thursday, Nov. 5) 5.3 # 28 6.1 # 14, 24, 26, 28, 30, 31
 Monday, Oct. 26: Slides (For 10 Section): Inner Product Read: Section 6.1

Week 6
 Friday, Oct. 23: Slides (For 10 Section): Diagonalization Read: Section 5.2 & 5.3 Practice problems   5.2: # 2, 3, 6, 15, 17, 19, 21, 22 5.3: # 4, 21, 22, 23, 24, 25 Graded assignment  (for Wednesday, Oct. 28) 5.2: # 14, 18, 24 5.3: # 6, 12, 16, 18
 Thursday, Oct. 22: Slides (For 10 Section): Finding Eigenvalues Read: Section 5.2 Practice problems   5.1: # 2,4,6, 8, 19, 21, 22, 23, 31 Graded assignment  (for Wednesday, Oct. 28) 5.1: # 10, 14, 20, 25, 27, 29 5.2: # 12
 Wednesday, Oct. 21: Slides (For 10 Section): The Characteristic Equation Read: Section 5.1 and 5.2 Practice problems   4.6: # 13, 17, 18, 20, 27, 29 4.7: # 2, 11, 12 Graded assignment  (for Wednesday, Oct. 28) 4.6 # 14, 16 4.7 # 4, 6, 10, 14 Additional Graded problems: Range of a linear transformation
 Monday, Oct. 19: Slides (For 10 Section): Eigenvalues and Eigenvectors Read: Section 5.1

Week 5
 Friday, Oct. 16: Slides (For 10 Section): Change of Coordinates Read: Section 4.7 Practice problems   4.5: # 7, 8, 9, 19, 20, 21, 23, 25, 29, 30, 31 Graded assignment  (for Wednesday, Oct. 21) 4.5 # 22, 24, 26, 32 4.6 # 2, 4, 8, 12
 Thursday, Oct. 15: Read: Section 4.6 Practice problems   4.4: # 10, 11, 15, 16, 17, 19, 21, 28, 31 Graded assignment  (for Wednesday, Oct. 21) 4.4 # 14, 23, 24, 32 4.5 # 6, 12, 14
 Wednesday, Oct. 14: Slides (For 10 Section): Rank Read: Section 4.5 Practice problems   4.3: # 3, 5, 19, 21, 22, 23, 25, 29, 30 Graded assignment  (for Wednesday, Oct. 21) 4.3 # 14, 31, 32 4.4 # 4, 8, 10, 12
 Monday, Oct. 12: Slides (For 10 Section): Dimension Read: Section 4.4

Week 4
 Friday, Oct. 9: Slides (For 10 Section): Coordinates Read: Section 4.3 Practice problems   4.2: # 5, 7, 18, 25, 26, 33 Graded assignment  (for Wednesday, Oct. 14) 4.2 # 4, 10, 28, 30, 32 4.3 # 4, 10, 16
 Thursday, Oct. 8: Slides (For 10 Section): Basis Read: Section 4.2 and 4.3 Practice problems   4.1: # 2, 13, 23, 24 Graded assignment  (for Wednesday, Oct. 14) 3.2 # 33, 36 4.1 # 8, 12, 14, 22, 32
 Wednesday, Oct. 7: Slides (For 10 Section): Null Space (Kernel), Column Space, Kernel and Linear Transformations Read: Section 4.2 Practice problems   3.1: # 4, 11, 22, 39, 40 3.2: # 2, 4, 6, 15, 19, 27, 28, 33 Graded assignment  (for Wednesday, Oct. 14) 3.1: # 14 3.2: # 8, 22, 24, 29, 31, 32
 Monday, Oct. 5: Slides (For 10 Section): Vector Spaces and Subspaces Read: Section 4.1

Week 3
 Friday, Oct. 2: Slides (For 10 Section): Determinants Read: Section 3.1 and 3.2 Practice problems   2.2: # 7, 9, 10, 25, 21, 26, 37 2.3: # 3, 4, 5, 11, 12, 17 Graded assignment  (for Wednesday, Oct. 7) 2.2: # 22, 24, 32 2.3: # 6, 16, 18, 20
 Thursday, Oct. 1: Slides (For 10 Section): Characterization of Invertible Matrices Read: Section 2.2 and 2.3 Practice problems   2.1: # 4,7,8,12,15,16, 17-21 2.2: # 3, 7, 9, 10, 13 Graded assignment  (for Wednesday, Oct. 7) 2.1: # 6, 10, 22, 26, 33 2.2: # 6, 16
 Wednesday, Sept. 30: Slides (For 10 Section): Inverse of a Matrix Read: Section 2.1 and 2.2 Practice problems   1.9: # 2, 7, 9, 17, 23, 24, 36 Graded assignment  (for Wednesday, Oct. 7) 1.9: # 4, 8, 16, 19, 27, 35, 38
 Monday, Sept. 28: Slides (For 10 Section): Matrix Operations Read: Section 2.1

Week 2
 Friday. Sept. 25: Slides (For 10 Section): The Matrix of a Linear Transformation Read: Section 1.8 and 1.9 Practice problems   1.8: # 2, 7, 17, 21, 22, 23 Graded assignment  (for Wednesday, Sept. 30) 1.8: # 4,10, 12, 19, 30, 31, 34
 Thurs. Sept. 24: Slides (For 10 Section): Intro to Linear Transformations Read: Section 1.7 and 1.8 Practice problems   1.7: # 9, 15-24, 27, 31, 33-37 Graded assignment  (for Wednesday, Sept. 30) 1.5: # 28, 30 1.7: # 1, 6, 28, 36, 38
 Wed. Sept. 23: Slides (For 10 Section): Linear Independence Read: Section 1.4, 1.5 and 1.7 Practice problems   1.4: # 6, 8, 12 23-26, 29, 30 1.5: # 4, 14, 23, 24, 26, 34, 35 Graded assignment  (for Wednesday, Sept. 30) 1.4: # 14, 16, 20, 22, 32 1.5: # 6, 18, 25
 Mon. Sept. 21: Slides (For 10 Section): The Matrix Equation Ax=b and Solution Sets of Linear Equations Read: Section 1.4 and 1.5

Week 1
 Fri. Sept. 18: Slides (For 10 Section): Vector Equations Read: Section 1.3 Practice problems   1.3: # 10, 23, 25, 29 Graded assignment  (for Wednesday, Sept. 23) 1.3: # 12, 14, 16, 21
 Thurs. Sept. 17: Slides (For 10 Section): Row Reduction and echelon forms Read: Section 1.2 Practice problems   1.2: # 5, 11, 16, 19, 21, 22, 23 Graded assignment  (for Wednesday, Sept. 23) 1.2: # 4, 11, 24, 26, 28, 29
 Wed. Sept. 16: Slides (For 10 Section): Systems of Linear Equations Read: Section 1.1 Practice problems   1.1: # 19, 23, 24, 27, 28, 29 Graded assignment  (for Wednesday, Sept. 23) 1.1: # 12, 16, 25, 26

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