Math 201

Linear Algebra, Spring 2021 (Sections S01, S02)

Instructor: Kyle Ormsby
Text: Linear Algebra (4th ed.), by Hefferon
Course Information & Syllabus
For details on attending the following, see our Moodle page:
  • Office Student hours: MWTh 15-16, and by appointment.
  • Problem sessions: Tu 19-20, Th 18-19.
  • Drop-in tutoring: SuMTuWTh 19-21.
Exams:
  • Exam 1: distributed Monday 15 February, due Wednesday 17 February.
  • Exam 2: distributed Monday 22 March, due Wednesday 24 March.
  • Final Exam: distributed Monday 10 May, due Wednesday 12 May.
Lecture notes
Current week
Week 1: 25 January - 29 January
Monday: Welcome and warm up.
  • Reading: Syllabus.
  • Notes: day01.
  • Homework due: Syllabus contract.
Wednesday: Solving systems of linear equations.
  • Reading: One.I. (Note: Readings are all from Hefferon. "One.I" refers to Chapter One, Section I.)
  • Notes: day02.
  • Sage worksheet: day02. (Click the green "Open with one click!" button to see the 3D renderings.)
Friday: Reduced echelon form.
  • Reading: One.III.
  • Notes: day03.
  • Sage worksheet: day03.
Week 2: 1 February - 5 February
Monday: Vector spaces.
  • Reading: One.II.1, Two.I.1.
  • Notes: day04.
Wednesday: Subspaces and spanning sets.
  • Reading: Two.I.2.
  • Notes: day05.
Friday: Linear independence.
  • Reading: Two.II.1.
  • Notes: day06.
  • Sage worksheet: day06.
  • Homework due: week02. (Change .pdf to .tex in the URL to get a \(\LaTeX\) template from which to start your solutions.)
Week 3: 8 February - 12 February
Monday: Linear independence.
  • Reading: Two.II.1.
  • Notes: day07.
Wednesday: Bases.
Friday: Dimension.
  • Reading: Two.III.2.
  • Notes: day09.
  • Homework due: week03.
Week 4: 15 February - 19 February
Monday: ❄ SNOW DAY ❄
  • Exam 1 distributed via Slack.
Wednesday: ❄ SNOW DAY ❄
Friday: Row space & column space.
  • Reading: Two.III.3.
  • Notes: day10.
  • Exam 1 due via Gradescope by 23:00.
  • Homework due: none.
Week 5: 22 February - 26 February
Monday: Linear transformations.
  • Reading: Three.II.1.
  • Notes: day11.
  • Visualization: MatVis.
Wednesday: Image, kernel, & rank-nullity.
  • Reading: Three.I.1-2, Three.II.2.
  • Notes: day12.
Friday: Isomorphisms.
  • Reading: same as Wednesday.
  • Notes: day13.
  • Homework due: week05.
Week 6: 1 March - 5 March
Monday: Lines, planes, & hyperplanes.
  • Reading: One.II.1.
  • Notes: day14.
Wednesday: Matrices.
  • Reading: Three.IV.1-2.
  • Notes: day15.
Friday: Matrix inversion.
  • Reading: Three.IV.4.
  • Notes: day16.
  • Homework due: week06.
Week 7: 8 March - 12 March
Monday: Matrices and linear transformations I.
  • Reading: Three.III.2.
  • Notes: day17.
Wednesday: NO CLASS.
Friday: Matrices and linear transformations II.
  • Reading:Three.III.2.
  • Notes: day18.
  • Homework due: week07.
Week 8: 15 March - 19 March
Monday: Change of basis.
  • Reading: Three.V.1-2.
  • Notes: day19.
  • Sage worksheet: day19.
Wednesday: Determinants.
  • Reading: Four.I.1-2.
  • Notes: day20.
Friday: \(\det(A)=\det(A^\top)\).
  • Reading: same as Wednesday.
  • Notes: day21.
  • Homework due: week08.
Week 9: 22 March - 26 March
Monday: Permutation expansion.
  • Reading: Four.I.3.
  • Exam 2 distributed via Slack.
  • Notes: day22.
Wednesday: NO CLASS.
  • Exam 2 due via Gradescope by 23:00.
Friday: Laplace expansion + \(\exists ! \det\).
  • Reading: Four.III.1.
  • Notes: day23.
  • Homework due: none.
Week 10: 29 March - 2 April
Monday: Eigenvectors & eigenvalues.
  • Reading: Five.II.3.
  • Notes: day24.
Wednesday: Diagonalization.
  • Reading: Five.II.3.
  • Notes: day25.
Friday: Eigenspaces. REST.
Week 11: 5 April - 9 April
Monday: Algebraic and geometric multiplicity.
  • Reading: None.
  • Notes: day26.
Wednesday: Walks on graphs.
  • Reading: None.
  • Notes: day27.
Friday: Linear differential equations.
Week 12: 12 April - 16 April
Spring Break. 🌱🌈🌞
Week 13: 19 April - 23 April
Monday: Inner product spaces.
  • Reading: None.
  • Notes: day29.
Wednesday: Length, projections, angles.
  • Reading: None.
  • Notes: day30.
Friday: Gram-Schmidt orthonormalization.
Week 14: 26 April - 30 April
Monday: Orthogonal complements & projections.
  • Reading: None.
  • Notes: day32.
Wednesday: Determinants & volume.
  • Reading: None.
  • Notes: day33.
Friday: Review.
  • Reading: None.
  • Homework due: week14.
\(\LaTeX\) resources
  • \(\LaTeX\) (getting started in \(\LaTeX\))
  • short guide
  • Change .pdf to .tex in the URL of (nearly) any file accessed from this page to get the \(\LaTeX\) source code.