Linear Algebra

MATH2076-007, Spring semester, 2023

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: French Hall 4302.
Office Hours: by appointment.
Class meeting in hybrid mode: in-person lectures MW 12:20-1:15pm, Braunstein 309, and a pre-recorded third lecture via Canvas.

Textbook

• Linear Algebra and its applications, 6th edition (Pearson online).

Course description

See tentative schedule below.

Grades

• Grading: Pearson HW 30%, Canvas HW 20%, midterms 30%, final 20%.
• Letter grades: A (90), A- (85), B+ (80), B (75), B- (70), etc.

There are two types of HWs.

• Canvas->MyLab: via Pearson MyLab, where your solutions will be graded right away by the online system.
• Canvas->Assignment: where I will post weekly HWs (should be 1 or 2 questions only) and where you submit a PDF scan of your solutions, I grade them, and also I leave some comments for you if I see mistakes/issues.

Tentative Schedule

• Week 1 (Aug 21, Mon): Sections 1.1 Systems of linear equations, 1.2 Row reduction and echelon forms, 1.3 Vector equations.
• Week 2 (Aug 29): Sections 1.4 The matrix equation, 1.5 Solution sets of linear systems, 1.7 linear independence.
• Week 3 (Sep 4): No class on Labor Day, Monday Sep 4. Sections 1.8 Introduction to linear transformations, 1.9 The matrix of a linear transformation.
• Week 4 (Sep 11): Sections 2.1 Matrix operations, 2.2 The inverse of a matrix, 2.3 Characterizations of invertible matrices.
• Week 5 (Sep 18): Exam 1, regular time in classroom on Fri. Sections 2.8 Subspaces of $\mathbb R^n$, 2.9 Dimension and rank.
• Week 6 (Sep 25): Sections 4.1 Vector spaces and subspaces, 4.2 Null spaces, column spaces, row spaces and linear transformations, 4.3 Linearly independent sets; bases.
• Week 7 (Oct 2): Sections 4.4 Coordinate systems, 4.5 The dimension of a vector space, 4.6 Change of basis.
• Week 8 (Oct 9): Fall Reading Days, no class on Mon Oct 9. Sections 3.1 Introduction to determinants, 3.2 Properties of determinants.
• Week 9 (Oct 16): Sections 5.1 Eigenvectors and eigenvalues, 5.2 The characteristic equations, 5.3 Diagonalization.
• Week 10 (Oct 23): Exam 2, regular time in classroom on Fri. 5.4 Eigenvectors and linear tranformations.
• Week 11 (Oct 30): Sections 6.1 Inner product, length and orthogonality, 6.2 Orthogonal sets, 6.3 Orthogonal projections.
• Week 12 (Nov 6): Veterans Day Holiday, no class on Nov 10, Fri. Sections 6.4 The Gram-Schmidt process, 6.5 Least-squares problems.
• Week 13 (Nov 13): Sections 7.1 Diagonalization of symmetric matrices, 7.2 Quadratic forms.
• Week 14 (Nov 20): Section 7.4 The singular value decomposition. Thanksgiving Weekend Holiday, no class on Nov 24, Fri.
• Week 15 (Nov 27): Review.
• Week 16 (Dec 4): Final, Dec 4, Mon, 10:15am-12:15pm, usual classroom.

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