week | date | reading | daily topics | worksheets, links, demos | practice problems from book |
---|---|---|---|---|---|
1 | Sep 12 M | website, 1.1 | Systems of linear equations. | solnsets | 5,7,9,11,13,21,27. |
13 Tu X-hr | Resources on proofs | doing proofs. | proofs | ||
14 W | 1.2 | Row reduction, echelon forms (slides, more) | echform | 3,5,13,15,19,21(ans:ffttf),31. | |
16 F | 1.3 | Vector equations (lin combos, span) | span | 7,9,11(ans is wrong!),15,21,22, 23(ans:ffttf) | |
2 | 19 M | 1.4-1.5 | The matrix equation Ax=b, solution sets. | matvec | 1.4: 3,9,15,19,23(ans:ftfttt); 1.5: 7,15,23(ans:tffft),27,31. |
20 Tu X-hr | Resources on proofs | more critical thinking about proofs. | proofsrecap, proofs2 | ||
21 W | 1.6 (last 2 pp), 1.7 | HW1 due. App: network flow. Linear independence. | paramsoln | 1.6: 12(ans:80),13; 1.7: 5,13,17,21(ans:fftt),25,27,33,37,39. | |
23 F | 1.8 | Intro to linear transformations | linxform | 1.8: 7,9,11,13,17,19,21(ans:tffft),27. | |
3 | 26 M | 1.9 | The matrix of a linear transformation. | onto | 1.9: 3,9,15,17,23(ans:ttfff),25,35. |
27 Tu X-hr | 1.10 (last 2 pp), 2.1 | extra lecture. App: difference eqns. Matrix operations. | matmat | 1.10: 9. 2.1: 3,5,9,15(ans:ffttf),16(ans:tftft),17,21,23. | |
28 W | 2.2 | HW2 due. The inverse of a matrix. | inverse | 2.2: 7,10(ans:ftftt),13,17,19,21,31,35. | |
30 F | 2.3 | Characteristics of invertible matrices. | prove stuff on p.112 | 2.3: 3,7,11(ans:ttftt),15,17,22,27,33. | |
4 | Oct 3 M | 3.1-3.2 | Determinants and their properties. | detred | 3.1: 5,9,11,35,37; 3.2: 7,23,27(ans:tttf),29,31,33. |
4 Tu X-hr | Resources | linear algebra on the computer, MATLAB | code | ||
5 W | 4.1 | HW3 due. Vector spaces and subspaces (not this!) | subspace | 4.1: 2,3,7,9,15,17,31; go over mini quiz 1. | |
7 F | 4.2 | Null and column spaces. | 4.2: 3, 7, 11, 17, 21, 23, 25(ans:tftftt). [For some harder ones: 31, 35] | ||
5 | 10 M | 4.3 | Bases, spanning set theorem. | basisColA | 4.3: 3,5,11,13,15,19,21(ans:tftff),23,25(be careful & see prac prob 3!) |
Midterm 1: Monday Oct 10, 6-8pm, Steele 006. (Topics: up to Sec 2.3) (solutions) | |||||
12 W | 4.4 | HW4 due. Coordinate systems and isomorphism. | coordsys | 4.4: 3,7,11,13,15(ans:tff),21,23,27. | |
14 F | 4.5 | Dimension of a vector space or subspace. | dimV | 4.5: 5,7,11,13,19(ans:ttfft),21,23,29(ans:ttt),31. | |
6 | 17 M | 4.6 | The Rank Theorem. | rankbases | 4.6: 1,5,9,15,17(ans:tftft),19,27,29,33. |
19 W | 5.1 | HW5 due. Eigenvectors and eigenvalues. | eigen | 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). | |
21 F | 5.2 | The characteristic equation. | chareqn | 5.2: 3,7,11,15,18,22bcd(ans:ftf),23,25(see Ex.5). | |
7 | 24 M | 5.3 | Diagonalization. | diagonalization | 5.3: 5,7,9,13,21(ans:ttff),23,25,27,28. |
25 Tu X-hr | - | practice problem session. | xhrmid2prac | ||
26 W | 4.9, this | HW6 due. App: Markov chains. App: Google PageRank (see links in Resources) | code to evolve chain | 4.9: 1,5,9,11,19, & writing the A and G matrices for any small web. | |
Midterm 2: Wednesday Oct 26, 6-8pm, Silsby 028. [make-up slot is Thurs 1-3pm, Haldeman 041] (Topics: Sec. 3.1-5.2) (solutions) | |||||
27 Th | (4:30pm: colloquium on linear algebra accessible to undergrads) | ||||
28 F | 6.1 | Inner product, orthogonality. | 6.1: 1,5,9,13,19(ans:tttft),24,28,30. | ||
8 | 31 M | 6.2 | Orthogonal sets. | orthog | 6.2: 9,11,13,21,23(ans:ttftf),25,28(key),29,33. |
Nov 2 W | 6.3 | HW7 due. Orthogonal projections. | 6.3: 3,7,13,15,17(good),19,22(ans:tttff),23,24. | ||
4 F | 6.4 | Constructing orthogonal bases: Gram-Schmidt. (no lecture for Barnett) | 6.4: 3,7,9,13,17(ans:ttt),18(ans:ttt),19,21,22. | ||
9 | 7 M | 6.5 | Least-squares problems. | leastsq | 6.5: 1,5,9,13,17(ans:ttftt),19(lovely),20,21,25. |
8 Tu X-hr | (Barnett make-up lecture for 6.5) | ||||
9 W | 7.4 | HW8 due. Singular value decomposition (SVD). | 7.4: 3,7,11,13,14(1st row of V^T),18,19,21. | ||
11 F | 7.4 (7.5 opt) | Apps of SVD: fundamental spaces, low rank approximation, principal component analysis (PCA). | lowrankapprox.m, image | ||
10 | 14 M | - | Review. | old exams | end-of-chapter review probs, make list of topics and problem types, concept maps... |
15 T | HW9 due 8pm (note: not Wed). | ||||
Final: Friday Nov 18, 11:30am-2:30pm ("joint math" slot), LSC 100. (solutions) |