| lecture | week | date | reading, reminders | daily topics | section 1 resources | section 2 resources | practice problems from book |
|---|---|---|---|---|---|---|---|
| #1 | 0 | June 23 F | website, 1.1 | Systems of linear equations | solnsets worksheet | lecture01.pdf | 5, 7, 9, 11, 13, 21, 27 |
| #2 | June 24 Sa | 1.2 | Row reduction, echelon forms | row reduction, echelon form examples; echform worksheet |
lecture02.pdf
1;4205;0c classwork02.pdf |
3, 5, 13, 15, 19, 21(ans:ffttf), 31 | |
| #3 | 1 | June 26 M | 1.3 | Vector equations, linear combinations, span | span worksheets: from class, another | lecture03.pdf | 7, 9, 11, 15, 21, 22, 23(ans:ffttf) |
| #4 | June 28 W | 1.4, 1.5 | The matrix equation Ax=b, solution sets | matvec | lecture04.pdf | 1.4: 3, 9, 15, 19, 23(ans:ftfttt) 1.5: 7, 15, 23(ans:tffft), 27, 31 |
|
| #5 | June 30 F | 1.6, 1.7, HW1 Due | Linear independence, Applications: network flow | lecture05.pdf | 1.6: 11, 12 1.7: 5, 13, 17, 21(ans:fftt), 25, 27, 33, 37, 39 |
||
| X-hour | Resources on proofs | doing proofs | methods of proof | lectureX01.pdf | |||
| #6 | 2 | July 3 M | 1.8 | Introduction to linear transformations |
lecture06.pdf
classwork06.pdf classwork06ans.pdf linxform |
lecture06.pdf
classwork06.pdf classwork06ans.pdf |
7, 9, 11, 13, 17, 19, 21(ans:tffft), 27 |
| #7 | July 5 W | 1.9 | The matrix of a linear transformation | onto and 1-1 |
lecture07.pdf
classwork07.pdf classwork07ans.pdf |
3, 9, 15, 17, 23(ans:ttfff)), 25, 35. | |
| #8 | July 7 F | 1.10, 2.1 | HW2 Due. Applications: difference equations, matrix operations | matrix multiplication | lecture08.pdf | 1.10: 9. 2.1: 3,5,9,15(ans:ffttf),16(ans:ftfft),17,21(tricky),23. | |
| X-hour | Resources on proofs |
more critical thinking about proofs
No X-hour for section 2 this week (they are welcome in section 1) |
1x1 lin sys proofs, Is it a proof? | ||||
| #9 | 3 | July 10 M | 2.2 | The inverse of a matrix | basic inverse computation | lecture09.pdf | 7, 10(ans:ftttf), 13, 17, 19, 21, 31, 35 |
| #10 | July 12 W | 2.3 | Characteristics of invertible matrices | (exercise proving p.114 of book) | lecture11.pdf | 3,7,11(ans:ttftt),15,17,22,27,33. | |
| #12 | July 14 F | 4.1, HW3 Due | Vector spaces and subspaces | subspace | lecture12.pdf | 2,3,7,9,15,17,31 | |
| X-hour (#11) | 3.1, 3.2 | Extra lecture (a one-off): Determinants and their properties (for section 2: X-hr is Tuesday so lecs #10 and #11 swapped) | det via row red. | lecture10x.pdf | 3.1: 5,9,11,35,37; 3.2: 7,23,27(ans:tftf),29,31,33,39 | ||
| #13 | 4 | July 17 M | 4.2 | Null and column spaces | lecture13.pdf | 3, 7, 11, 17, 21, 23, 25(ans:tftftt). [For some harder ones: 31, 35] | |
| #14 | July 19 W | 4.3 | Bases, spanning set theorem | lecture14.pdf | 3,5,11,13,15,19,21(ans:tftff),23,25(be careful & see prac prob 3!) | ||
| Midterm 1: Wednesday July 19, 6:00pm - 8:00pm, Kemeny 008 (solutions) | |||||||
| #15 | July 21 F | 4.4, HW4 Due | Coordinate systems and isomorphism | basis for Col A |
lecture15.pdf classwork15.pdf |
3,7,11,13,15(ans:tff),21,23,27 | |
| X-hour |
m22matlab.m m22sage-notebook sage-quickref.pdf sage-for-linear-algebra.pdf |
||||||
| #16 | 5 | July 24 M | 4.5 | Dimension of a vector space or subspace | dimension of subspaces of R3 worksheet | lecture16.pdf | 5,7,11,13,19(ans:ttfft),21,23,29(ans:ttt),31 (ie T cannot grow the dim!) |
| #17 | July 26 W | 4.6 | The rank theorem | abstract V.S. review, rank and bases worksheet | lecture17.pdf | 4.6: 1,5,9,15,17(ans:tftft),19,27,29,33 | |
| #18 | July 28 F | 5.1, HW5 Due | Eigenvectors and eigenvalues | eigen worksheet | lecture18.pdf | 5.1: 7,9,15,17,20,21(ans:ftttf),23,26(note that A may not be the zero matrix),27,31(find both eigenvalues) | |
| X-hour | Resources | Linear algebra on the computer, MATLAB | No X-hour for section 2 | ||||
| #19 | 6 | July 31 M | 5.2 | The characteristic equation | (Quiz 2 for section 1). char eqn (use for practise) | lecture19.pdf | 5.2: 3,7,11,15,18,22bcd(ans:ftf),23,25(see Ex.5) |
| #20 | Aug 2 W | 5.3 | Diagonalization | diagonalization | lecture20.pdf | 5.3: 5,7,9,13,21(ans:ttff),23,25,27,28 | |
| #21 | Aug 4 F | 4.9, Resources, HW6 Due | Applications: Markov chains, Google PageRank | evolve.m |
lecture21.pdf
PageRank2x2 PageRank3x3 PageRank4x4 |
4.9: 1,5,9,11,19, & writing the A and G matrices for any small web. | |
| X-hour | mathematical language grammar worksheet, mid2 prac qus | (Quiz for section 2) | |||||
| #22 | 7 | Aug 7 M | 6.1 | Inner products, orthogonality | lecture22.pdf | 6.1: 1,5,9,13,19(ans:tttft),24,28,30. | |
| Midterm 2: Tuesday August 8, 6:00pm - 8:00pm, Kemeny 008 (solutions) | |||||||
| #23 | Aug 9 W | 6.2 | Orthogonal sets | orthog sets worksheet | lecture23.pdf | 6.2: 9,11,13,21,23(ans:ttftf),25,28(key),29,33. | |
| #24 | Aug 11 F | 6.3, HW7 Due | Orthogonal projections | lecture24.pdf | 6.3: 3,7,13,15,17(good),19,22(ans:tttff),23,24 | ||
| X-hour | |||||||
| #25 | 8 | Aug 14 M | 6.4 | Constructing orthogonal bases: Gram-Schmidt | Guest lecture: Lizzie Tripp |
Guest lecture: Emma Hartman
classwork25.pdf |
6.4: 3,7,9,13,17(ans:ttt),18(ans:ttt),19,21,22. |
| #26 | Aug 16 W | 6.5 | Least-squares problems | least sq worksheet | lecture26.pdf | 6.5: 1,5,9,13,17(ans:ttftt),19(lovely; note b has a vector 0 that should be a scalar 0),20,21,25. | |
| #27 | Aug 18 F | 7.4, HW8 Due | Singular value decomposition (SVD) |
lecture27.pdf
SVD2x2 |
7.4: 3,7,11,13,14(1st row of V^T),18,19,21. | ||
| X-hour | Guest lecture: Lizzie Tripp (7.1 and trace formula for graphs) | ||||||
| #28 | 9 | Aug 21 M | 7.4, 7.5 | Applications of SVD: fundamental spaces, low rank approximation, principal component analysis (PCA) | lowrankapprox.m demo, needs mystery.jpg | lecture28.pdf | |
| X-hour | Guest lecture: Emma Hartman | ||||||
| #29 | Aug 23 W | HW9 Due | Review | review diag/orthog |
lecture29.pdf
classwork29.pdf classwork29ans.pdf |
||
| Final Exam (Section 1): Monday August 28, 8:00am-11:00am, location Kemeny 008 (solutions) | |||||||
| Final Exam (Section 2): Sunday August 27, 8:00am-11:00am, location Kemeny 006 (solutions) | |||||||
