Math 22: Lecture schedule and practice problems - FALL 2016

Note: X-hour dates are shown for Section 1 (Barnett); Section 2 (Tanabe) has the X-hr on Thursday not Tuesday.

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)

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)