Math 416: Daily Log of Material Covered and Assigned Homework

Week	Date	Topics covered	Homework assigned	Homework due
1	8/22	Section 1.1: Vector spaces	#1.1, 1.2, 1.4, 1.5 due 8/26
	8/24	Section 1.2: Linear combinations; Bases	#2.1, 2.3, 2.5 due 8/26
	8/26	Section 1.3: Linear transformations	#3.1, 3.2, 3.3 (a)(c) due 9/2	HW 1: Lectures 8/22, 8/24
2	8/29	Section 1.3: Matrix-vector multiplication Section 1.4: Linear transformations as a vector space	#3.4, 3.5, Additional problems A4.1, A4.2 due 9/2
	8/31	Section 1.5: Composition of linear transformations; Matrix multiplication	#5.1, 5.3, 5.5 due 9/2
	9/2	Section 1.6: Invertible transformations and matrices	#6.1, 6.2, 6.8, 6.9, 6.11 due 9/12	HW 2: Lectures 8/26, 8/29, 8/31
3	9/5	No lecture - Labor Day
	9/7	Section 1.6: Isomorphisms Section 1.7: Subspaces	#7.1, 7.2, 7.5 due 9/12 For 1 and 2, don't forget that a subspace must be non-empty.
	9/9	Section 1.7: Span, null space, column space Section 2.1: Different faces of linear systems Preview of Gauss-Jordan elimination	#2.1 (a) due 9/12	No HW due today
4	9/12	Section 2.2: Solution of a linear system; Echelon and reduced echelon forms	#2.1 (b)(e), 2.2 due 9/19	HW 3: Lectures 9/2, 9/7, 9/9
	9/14	Section 2.3: Analyzing the pivots	#3.1, 3.2, 3.3 (a), 3.4, 3.6 due 9/19
	9/16	Section 2.4: Finding A-1 by row reduction Elementary matrices	#4.1 first matrix only, Additional problems A4.1, A4.2 due 9/19	No HW due today
5	9/19	Review session (in class) with the practice midterm Extra review session 5-6 PM, room 143 Altgeld		HW 4: Lectures 9/12, 9/14, 9/16
	9/20	Extra office hours 4-5 PM
	9/21	Midterm 1: Covers up to lecture 9/16 Notes on some properties of matrices
	9/23	Section 2.5: Dimension Example about the column space and null space	#5.2, 5.4, 5.5, 5.6 (Hint: you can take the vectors in any order) due 9/30 Good practice: #5.1
6	9/26	Section 2.6: General solution of a linear system	#6.1, 6.2 , Additional problem A6.1 due 9/30
	9/28	Section 2.7: Fundamental subspaces of a matrix; Rank Notes on working in coordinates	#7.2, 7.3 second matrix (feel free to use this shortcut), 7.4, 7.8 due 9/30 Good practice: #7.1
	9/30	Section 2.8: Representation of a linear transformation in arbitrary bases	#8.2, 8.3, 8.4 due 10/7	HW 5: Lectures 9/23, 9/26, 9/28
7	10/3	Section 2.8: Change of coordinates; Similar matrices Notes on similar matrices	#8.5, 8.6, Additional problem A8.1 due 10/7
	10/5	Section 3.1: Introduction to determinants Section 3.2: Properties the determinant should have	#3.1, 3.2, 3.3, 3.4 due 10/7
	10/7	Section 3.3: Properties of the determinant	#3.5, 3.6, 3.7, 3.8 due 10/17	HW 6: Lectures 9/30, 10/3, 10/5
8	10/10	Section 3.4: Formal definition	#4.1, 4.2 (a)(b) due 10/17
	10/12	Section 3.5: Cofactor expansion Section 4.1: (Motivation for) Eigenvalues and eigenvectors	#5.2 due 10/17
	10/14	Section 4.1: Eigenvalues and eigenvectors	#1.2 second and third matrices, 1.3, 1.4 second and fourth matrices, 1.5 due 10/17	No HW due today
9	10/17	Review session (in class) with the practice midterm Extra review session 5-6 PM, room 143 Altgeld		HW 7: Lectures 10/7, 10/10, 10/12, 10/14
	10/18	Extra office hours 4-5 PM
	10/19	Midterm 2: Covers up to lecture 10/14
	10/21	Section 4.2: Diagonalization	#2.3, 2.4, 2.9 (a)(b)(c), 2.10 due 10/28
10	10/24	Section 5.1: Inner product in ℝn and ℂn; Inner product spaces	#1.1, 1.2, 1.4, 1.7, 1.8 due 10/28
	10/26	Section 5.2: Orthogonality	#2.1, 2.3 (a) due 10/28
	10/28	Section 5.2: Orthogonal and orthonormal bases Section 5.3: Orthogonal projection	#2.2, 2.3 (b)(c), 2.5, 3.7 due 11/4	HW 8: Lectures 10/21, 10/24, 10/26
11	10/31	Section 5.3: Gram-Schmidt orthogonalization Notes on Gram-Schmidt	#3.2, 3.3 (including "Can you describe..."), 3.4, 3.5, 3.8 due 11/4
	11/2	Section 5.4: Least squares Notes on least squares	#4.1, 4.3 due 11/4
	11/4	Section 5.5: Adjoint of a linear transformation	#5.2, 5.4, 5.5, 5.6 due 11/14	HW 9: Lectures 10/28, 10/31, 11/2
12	11/7	Section 5.6: Isometries and unitary operators	#6.1 first two matrices, 6.4, 6.5 due 11/14
	11/9	Section 5.6: Unitarily equivalent operators Section 6.1: Schur decomposition of an operator Notes on the Schur decomposition	#1.1, Additional problems A6.1.1, A6.1.2 due 11/14
	11/10	Extra office hours 4-5 PM
	11/11	Section 6.2: Spectral theorem for self-adjoint operators Extra review session 5-6 PM, room 141 Altgeld	#2.3, 2.4 (ignore "Find all square roots..."), 2.8, 2.9 due 11/14 Good practice: #2.1	No HW due today
13	11/14	Review session (in class) with the practice midterm		HW 10: Lectures 11/4, 11/7, 11/9, 11/11
	11/16	Midterm 3: Covers up to lecture 11/11
	11/18	Lecture canceled
14	11/21-25	Happy Thanksgiving! No lectures.
15	11/28	Section 6.5: Structure of orthogonal matrices Notes on orthogonal matrices and rotations	#2.13 from section 6.2; Additional problems A6.5.1, A6.5.2 due 12/7
	11/30	Section 6.6: Orientation	Additional problem A6.6.1 due 12/7
	12/2	Section 6.6: Continuous transformation of bases	#6.2, 6.3 due 12/7	No HW due today
16	12/5	Section 7.1: Bilinear and quadratic forms	#1.1, 1.2, 1.3 due 12/7
	12/7	Last lecture: Review session with the practice exam Extra review session 5-6 PM, room 145 Altgeld		HW 11: Lectures 11/28, 11/30, 12/2, 12/5
	12/9	No lecture
17	Wed 12/14	Extra office hours 3:30 - 5:30 PM
	Fri 12/16	Final exam, 1:30 - 4:30 PM in 142 Henry (usual room) Covers the whole semester

Exam results

Midterm 1

Midterm 2

Midterm 3

Final

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