Week 1: August 30 - September 3
Monday: Solving systems of linear equations
(
lecture,
tex file,
slides).
- Reading: Chapter One, Sections I and III.
- Practice problems: Chapter One, Section I: 1.17, 1.22, 1.27, 1.37
(challenge). (Note: do not turn in practice problems.)
- To do list for Wednesday.
Wednesday: Reduced row echelon form
(
lecture,
tex file,
slides).
- Reading: Chapter One, Sections I and III.
- Practice problems: Chapter One, Section I: 2.18, 2.21, 2.24, 2.29, 2.32
(challenge), 3.15, 3.18, 3.25; Section III: 1.8, 1.10, 1.14, 1.15, 2.11,
2.20, 2.24. (Note: do not turn in practice problems.)
- Attend the introduction to LaTeX session tonight on Zoom,
7–8 pm. The Zoom link can be found on our Moodle page.
Friday: Geometry of vectors in \(\mathbb{R}^2\) and \(\mathbb{R}^3\)
(
lecture,
tex file,
slides).
Interesting article:
What
is a clock?
Week 2: September 6 - 10
Monday: Labor Day (no class).
Tuesday: Turn in
Week 2 Tuesday
(
overleaf template)
homework by 3 p.m.
My
office hour today will be 12:30–1:25 p.m. today instead of
the usual 1–2 p.m.
Wednesday: Vector spaces.
(
lecture,
tex file,
slides).
- Reading: Chapter Two, Section I.
- Practice problems: Chapter Two, Section I: 1.18, 1.19, 1.22, 1.28, 1.29, 1.40.
Friday: Subspaces and spanning sets I.
(
lecture,
tex file,
slides).
- Reading: Chapter Two, Section I.2.
- Practice problems: Chapter Two, Section I.2: 2.20, 2.21, 2.29, 2.44.
-
Turn in: Week 2 Friday
(overleaf template) homework.
(From now on, it is understood that homework is due by 3 p.m. unless
otherwise stated.) [Recall: to prove that something is false, it is
almost always best to give a concrete counterexample.]
Week 3: September 13 - 17
Monday: Subspaces and spanning sets II.
(
lecture,
tex file,
slides).
- Reading: Chapter Two, Section II.1.
- Practice problems: Chapter Two, Section II.1: 21, 23 (b).
Tuesday: Turn in
Week 3
Tuesday
(
overleaf template).
Wednesday: Linear independence.
(
lecture,
tex file,
slides).
- Reading: Chapter Two, Section II.1.
- Practice problems: Chapter Two, Section II.1: 1.23 (c), 1.28, 1.29,
1.33 (ab).
- See our Moodle page for a video explaining the algorithm covered at
the end of today's lecture.
Friday: Bases.
(
lecture,
tex file,
slides).
Week 4: September 20 - 24
Monday: Dimension I. Exam 1 distributed after class today (due on Wednesday).
(
lecture,
tex file,
slides).
- Reading: Chapter Two, III.2.
- Practice problems: Chapter Two, III.2: 15, 17, 21.
Tuesday: No homework due today.
Wednesday: Dimension II. Exam 1 due before class today.
(
lecture,
tex file,
slides).
- Reading: Chapter Two, III.2.
- Practice problems: Chapter Two, III.2: 25, 26, 33.
Friday: Row and column spaces.
(
lecture,
tex file,
slides).
Week 5: September 27 - October 1
Monday: Linear transformations.
(
lecture,
tex file,
slides).
- Reading: Chapter Three, II.1.
- Practice problems: Chapter Three, Section II: 1.19, 1.20, 1.25, 1.28,
1.34, 1.36.
Tuesday: Turn in
Week 5
Tuesday
(
overleaf template).
Wednesday: Range and nullspace.
(
lecture,
tex file,
slides).
- Reading: Chapter Three, I.1 and I.2; Chapter Three, II.2.
- Practice problems: Chapter Three, Section II: 2.21, 2.23, 2.24, 2.26,
2.35, 2.37, 2.40.
Friday: Rank-nullity theorem; isomorphisms.
(
lecture,
tex file,
slides).
- Reading: Chapter Three, I.1 and I.2; Chapter Three, II.2.
- Practice problems: Chapter Three, Section I: 1.21, 1.23, 1.30, 1.37,
2.15, 2.19, 2.20.
- Turn in Exam 1 redo (see the email message from Saturday, September 25
for instructions).
-
No homework due today.
The homework that was scheduled to be turned in today has been postponed
until next Tuesday: Week 6 Tuesday
(overleaf template) homework.
Week 6: October 4 - 8
Monday: Matrices and linear transformations I.
(
lecture,
tex file,
slides).
- Reading: Chapter Three, Sections III.1 and III.2.
- Practice problems: Chapter Three, Section III: 1.16, 1.17, 1.21, 1.27,
2.12, 2.13, 2.15, 2.22.
Tuesday: Turn in
Week 6
Tuesday
(
overleaf template).
Wednesday: Matrices and linear transformations II: rank.
(
lecture,
tex file,
slides).
- Reading: Chapter Three, Section III.2.
- Practice problems: Chapter Three, Section III: 2.22, 2.26, 2.29, 2.33.
Friday: Matrices and linear transformations III: composition.
(
lecture,
tex file,
slides).
- Reading: Chapter Three, Sections IV.2 and IV.3.
- Practice problems: Chapter Three, Section IV: 2.14, 2.17, 2.26, 2.33, 3.24.
-
Turn in: Week 6 Friday
(overleaf template) homework.
Week 7: October 11 - 15
Monday: Matrix inversion.
(
lecture,
tex file,
slides).
- Reading: Chapter 3, IV.4.
- Practice problems: Chapter 3, IV.4: 15, 17, 18, 20, 22, 28, 33, 35.
Tuesday: Turn in:
Week 7
Tuesday
(
overleaf template).
Wednesday: Change of basis.
(
lecture,
tex file,
slides).
- Reading: Chapter Three, V.1 and V.2.
- Practice problems: Chapter Three, V.1: 1.7, 1.9, 1.10; V.2: 2.16, 2.17.
Friday: Determinants.
(
lecture,
tex file,
slides).
Week 8: October 25 - 29
Monday: The determinant of the transpose.
(
lecture,
tex file,
slides).
- Reading: Chapter Four, I.1 and I.2.
- Practice problems: Chapter Four, I.1: 1.6, 1.7, 1.8, 1.9.
Tuesday: Turn in:
Week 8
Tuesday
(
overleaf template).
Wednesday: Permutation expansion of the determinant.
(
lecture,
tex file,
slides).
- Reading: Course lecture notes.
- Practice problems: Chapter Four, I.3: 3.20, 3.21.
Friday: Laplace expansion. Existence and uniqueness of the determinant.
(
lecture,
tex file,
slides).
Week 9: November 1 - 5
Monday: The space of all \(k\)-dimensional subspaces of a vector space.
Exam 2 distributed after class today (due on Wednesday).
- Reading: None.
- Practice problems: None.
Tuesday: No homework due today.
Wednesday: Determinants and volume. Exam 2 due before class today.
(
worksheet,
tex file;
lecture,
tex file).
- Reading: Chapter Four, Section II.1.
- Practice problems: 1.9, 1.12, 1.16, 1.21, 1.27.
Friday: Eigenvectors and eigenvalues.
(
lecture,
tex file,
slides).
Week 10: November 8 - 12
Monday Diagonalization algorithm.
(
lecture,
tex file,
slides).
- Reading: Chapter Five, II.3.
- Practice problems: Chapter Five, II.3: 21, 22, 23.
Tuesday: Turn in:
Week 10 Tuesday
(
overleaf template).
Wednesday Eigenspaces.
(
lecture,
tex file,
slides).
- Reading: Chapter V, II.3.
- Practice problems: Chapter V, II.3: 24, 25, 28, 29
Friday: Algebraic and geometric multiplicity. Jordan form.
(
lecture,
tex file,
slides).
Week 11: November 15 - 19
Monday Walks on graphs.
(
lecture,
tex file,
slides).
- Reading: today's lecture notes.
- Practice problems: None.
Tuesday: Turn in:
Week 11 Tuesday
(
overleaf
template).
Wednesday Inner product spaces.
(
lecture,
tex file,
slides).
- Reading: today's lecture notes.
- Practice problems: None.
Friday: Length, distance, components, projections, angles.
(
lecture,
tex file,
slides).
Week 12: November 22-26
Monday Gram-Schmidt.
(
lecture,
tex file,
slides).
- Reading: today's lecture notes.
- Practice problems: None.
Tuesday: Turn in:
Week 12 Tuesday
(
overleaf template).
Wednesday Orthogonal complements and orthogonal projections.
(
lecture,
tex file,
slides).
- Reading: today's lecture notes.
- Practice problems: None.
- Here is a nice
webpage supplementing the last example in today's lecture.
Friday: Thanksgiving break. No class today.
Week 13: November 29 - December 3
Monday Systems of linear differential equations.
(
lecture,
tex file,
slides).
- Reading: today's lecture notes.
- Practice problems: None.
Tuesday: Turn in:
Week 13 Tuesday
(
overleaf template).
Wednesday Cross products.
(
lecture,
tex file,
slides).
- Reading: today's lecture notes.
- Practice problems: None.
Friday: Spectral theorem.
Note: We meet in Physics 240A today.
(
lecture,
tex file,
slides).
Week 14: December 6 - 8
Monday Presentations.
Tuesday: No homework due today.
Wednesday Presentations.
Friday: Reading period. No class today.
Note: Please remember to fill out the course evaluation forms! Links
were sent to you by email.
The \(\LaTeX\) document preparation system