Math 201, Fall 2018

Math 201: Linear Algebra, Fall 2018

F02: MWF 11:00-11:50am, Lib 389
F03: MWF 12:00-12:50pm, Lib 389

Office Hours: MWF 2:45-4:15pm in Lib 306

Drop-in tutoring: SuTWTh 7-9pm, Lib 204

Problem session: MTh 7:30-8:30pm, Physics 123

Text: Linear Algebra (3rd ed.) by Jim Heffron (freely available online)

201syllabus.pdf / 201syllabus.tex

Cumulative notes [pdf]

Week 1: August 27-31

M: Welcome and warmup. Solving systems of linear equations (One.I & One.III). Notes.
W: Syllabus. Reduced echelon form (One.I & One.III). Notes.
F: Vector spaces (One.II.1 & Two.I.1). HW1F due. Notes.

Week 2: September 3-7

M: Labor Day holiday. No class and no problem session.
T: HW2T due.
W: Subspaces and spans (Two.I.2). Notes.
F: Linear independence (Two.II.1). HW2F due. Notes.

Week 3: September 10-14

M: More linear independence (Two.II.1) and Bases (Two.III.1). Notes.
T: HW3T due.
W: Dimension (Two.III.2). Notes.
F: Application: Condorcet's voting paradox (Two.Topic: Voting Paradoxes; optional: The voter's paradox, spin, and the Borda count by W.S. Zwicker). HW3F due. Notes.

Week 4: September 17-21

M: The rank of a matrix (Two.III.3). Notes.
T: HW4T due.
W: Linear transformations (Three.II.1). Notes.
F: Kernel and image (Three.II.2). HW4F due. Notes. Exam 1 distributed in class; due at the start of class on Monday, Sept 24.

Week 5: September 24-28

M: Isomorphisms (Three.I.1-2 & II.2). Exam 1 due at the start of class. Notes.
T: HW5T due.
W: Visualizing linear transformations. Notes.
F: Matrices (Three.IV.1-2). HW5F due. Notes.

Week 6: October 1-5

M: The ring of square matrices; matrix inversion (Three.IV.4). Notes.
T: HW6T due.
W: Matrices and linear transformations (Three.III.2). Notes.
F: More matrices and linear transformations (Three.III.2). HW6F due. Notes.

Week 7: October 8-12

M: Duals, double duals, dual transformations, and transpose matrices. Notes.
T: HW7T due.
W: Annihilators. Notes.
F: Determinants (Four.I.1 & Four.I.2). HW7F due. Notes.

Fall break: October 15-19

Week 8: October 22-26

M: Determinants and transpose matrices (Three.IV.3 [especially elementary matrices]). Notes.
T: HW8T due.
W: Permutation expansion of the determinant. Notes.
F: Laplace expansion of the determinant (Four.III.1). HW8F due. Notes. Exam 2 distributed in class; due at the start of class on Monday, Oct 29.

Week 9: October 29 - November 2

M: Geometrix interpretation of the determinant. Exam 2 due at the start of class. Notes.
T: HW9T due.
W: Eigenvalues (Five.II.3). Notes.
F: More eigenvalues (Five.II.3). HW9F due. Notes.

Week 10: November 5-9

M: Loose ends: adjugates, inverses, and determinants over $\mathbb{R}$.
T: HW10T due.
W: Algebraic and geometric multiplicity of eigenvalues. Notes.
F: Counting walks on graphs. HW10F due. Notes.

Week 11: November 12-16

M: Differential equations. Notes.
T: HW11T due.
W: Inner product spaces. Notes.
F: Length, distance, components, projections, angles. HW11F due. Notes.

Week 12: November 19-23

M: Gram-Schmidt. Notes.
T: HW12T due.
W: Orthogonal complements and orthogonal projections. Notes.
F: No class or HW. Thanksgiving holiday.

Week 13: November 26-30

M: Least squares. Notes.
T: HW13T due.
W: Pincipal component analysis I. Notes.
F: PCA II. See also this writeup on PCA and this blog post on eigenfaces. Course evaluations. HW13F due. Notes.

Week 14: December 3-7

M: Spectral theorem I. Notes (see also this writeup).
T: HW14T due.
W: Spectral theorem II.
F: No class or HW. Reading period.

Final exam: Tuesday 11 December 1-4pm in PAB 320

Comprehensive exam with an emphasis on material covered after fall break.
One page (front and back) of notes allowed; no other resources.

The $\LaTeX$ document preparation system

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$\LaTeX$ at Reed.
A short guide [pdf] to writing mathematics with $\LaTeX$.
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