Math 201
Fall 2017, Sections 01 and 02
Instructor:
David Perkinson (
schedule)
General info: Course description, office hours, grading, etc.
Text:
Linear Algebra, by Jim Hefferon
Handouts:
mathematical writing
LaTeX:
getting
started;
Sage:
getting
started
Math 201 study sessions: Monday and Thursday nights, 7–8pm, L204.
General drop-in tutoring: SMTWTh, 7–9 pm, L389.
Midterm 1:
solutions.
Midterm 2: review
sheet,
solutions.
Final exam: The final exam with be a 3-hour take-home exam. It will be
available for pick-up at noon on Monday, December 11 and will be due on Thursday,
December 14 by 5pm.
Review session 7–9 pm Sunday, December 10,
L204. Here are some
practice problems,
and
solutions.
Collected lecture notes, homework, and handouts: :
Math 201,
Week 1
☛ Monday ☚
Solving systems of linear equations.
Homework due Monday
- Reading: Chapter One, Sections I and III.
- Practice problems: Chapter One, Section I: 1.17, 1.22, 1.27, 1.37
(challenge).
☛ Wednesday ☚
Reduced row echelon form. Wikipedia link:
Gaussian elmination.
Homework due Wednesday
- 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.
☛ Friday ☚
Vector spaces.
Homework due Friday
- Reading: Chapter One, Section II.1, Chapter Two, Section I.
- Practice problems: Chapter Two: 1.18, 1.19, 1.22, 1.28, 1.29, 2.20,
2.21, 2.26, 2.29, 2.44.
- Turn in: H01F
(tex file: H01F.tex,
solutions: H01Fsol).
Week 2
☛ Monday ☚
No class: Labor Day
☛ Wednesday ☚
Subspaces and spanning sets.
Homework due Wednesday
- Reading: Chapter Two, Section I.2.
- Practice problems: Chapter Two, Section I.1: 1.18, 1.19, 1.22, 1.29,
1.30.
- Turn in at the beginning of class today: H02T (tex file: H02T.tex,
solutions:
H02Tsol ).
Here are some examples demonstrating the correct
style for a solution to the second problem in the above homework:
supplement.
☛ Friday ☚
Linear independence.
Homework due Friday
- Reading: Chapter Two, Section II.1.
- Practice problems: Chapter Two, Section II.1: 1.20, 1.21, 1.23 (b).
- Turn in:
H02F
(tex file: H02F.tex,
solutions: H02Fsol).
Week 3
☛ Monday ☚
Linear independence.
Homework due Monday
- Reading: Same as last Friday: Chapter Two, Section II.1.
- Practice problems: Same as last Friday: Chapter Two, Section II.1: 1.20, 1.21, 1.23 (b).
- Turn in by 2 pm on Tuesday in the folder outside my office: H03T (tex file: H03T.tex,
solutions: H03Tsol).
☛ Wednesday ☚
Bases.
Homework due Wednesday
- Reading: Chapter Two, III.1.
- Practice problems: Chapter Two, III.1: 18, 19, 20, 21, 23, 29.
☛ Friday ☚
Dimension.
Homework due Friday
- Reading: Chapter Two, III.2.
- Practice problems: Chapter Two, III.2: 16, 18, 22, 26, 27, 34.
- Turn in:
H03F
(tex file: H03F.tex,
(solutions: H03Fsol).
Week 4
☛ Monday ☚
Row rank = column rank; dimension of solution space.
Homework due Monday
- Reading: Chapter Two, III.3.
- Practice problems: 3.17, 3.20, 3.21, 3.23, 3.29.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H04T (tex file: H04T.tex
solutions: H04Tsol).
☛ Wednesday ☚
Linear transformations.
Homework due Wednesday
- Reading: Chapter Three, II.1.
- Practice problems: Chapter Three, II.1, 1.18, 1.19, 1.22, 1.26, 1.28,
1.32, 1.35, 1.37.
☛ Friday ☚
Range space and null space.
Homework due Friday
- Reading: Chapter Three, I.1, I.2, II.2.
- Practice problems: Chapter Three, Section II: 2.21, 2.23, 2.24, 2.26,
2.35, 2.37, 2.40.
- Turn in: Midterm 1 due at the beginning of class. To review
for the midterm, please read through all of the lecture notes up through
and including last Monday's, and review the homework problems given up
through last Friday—the solutions are available through our
moodle. The midterm is closed-book/computers/etc. You should not
consult others about your solutions. You have two hours to complete it
once you have started.
Week 5
☛ Monday ☚
Isomorphisms.
Homework due Monday
- Reading: Chapter Three, Sections I.1, I.2, II.2.
- Practice problems: Chapter Three, Section I: 1.21, 1.23, 1.30, 1.37,
2.15, 2.19.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H05T (tex file: H05T.tex,
solutions: H05Fsol).
☛ Wednesday ☚
Lines, planes, and hyperplanes: equations and parametrizations.
Homework due Wednesday
- Reading: Chapter One, II.1
- Practice problems: Chapter One, II.1: 1, 2, 3, 4, 5, 6.
☛ Friday ☚
Matrices.
Homework due Friday
- Reading: Chapter Four, IV.1 and IV.2.
- Practice problems: IV.1: 1.8, 1.11; IV.2: 2.14, 2.15, 2.16.
- Turn in:
H05F
(tex file: H05F.tex,
solutions: H05Fsol
).
Week 6
☛ Monday ☚
The ring of square matrices. Matrix inversion.
Homework due Monday
- Reading: Chapter 3, IV.4.
- Practice problems: Chapter 3, IV.4: 4.15,Chapter 3, IV.4: 4, 17, 18,
20, 22, 28, 33, 35,
- Turn in by 2 pm on Tuesday in the folder outside my office:
H06T (tex file: H06T.tex,
solutions: H06Tsol).
☛ Wednesday ☚
Matrices and linear transformations.
Homework due Wednesday
- Reading: Chapter Three, III.2.
- Practice problems: 2.12, 2.15.
☛ Friday ☚
Matrices and linear transformations.
Homework due Friday
- Reading: Chapter Three, III.2.
- Practice problems: 2.12, 2.15.
- Turn in:
H06F
(tex file: H06F.tex,
solutions: H06Fsol).
Week 7
☛ Monday ☚
Matrices and linear transformations: examples. Change of basis.
Homework due Monday
- Reading: Chapter Three, V.1 and V.2.
- Practice problems: V.1: 1.7, 1.9, 1.10; V.2: 2.15, 2.16.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H07T (tex file: H07T.tex
solutions: H07Tsol).
☛ Wednesday ☚
Determinants.
Note: Substitute the following definition of the determinant for the
one given in the book:
determinant.
(The definition given in the book
does not work in a field where 1+1=0.)
Homework due Wednesday
- Reading: Chapter Four, I.1 and I.2.
- Practice problems: I.1: 1.1, 1.2, 1.3.
☛ Friday ☚
Determinants.
Homework due Friday
- Reading: Chapter Four, I.1 and I.2.
- Practice problems: I.1: 1.6, 1.7, 1.8, 1.9.
- Turn in:
H07F
(tex file: H07F.tex
solutions: H07Fsol.)
Week 8
☛ Monday ☚
\(\det(A)=\det(A^t)\).
Homework due Monday
- Reading: Chapter 3, end of IV. (elementary matrices).
- Practice problems: None.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H08T (tex file: H08T.tex
solutions: H08Tsol).
☛ Wednesday ☚
Permutation expansion of the determinant.
Note: We will have a
second midterm, handed out next Wednesday, then
collected in class the following Friday. It will cover everything we have
done up through and including determinants.
Homework due Wednesday
- Reading: lecture notes.
- Practice problems: Chapter Four, I.3: 3.20, 3.21.
☛ Friday ☚
Finish permutation expansions. Laplace expansion. Existence and uniqueness
of the determinant.
Homework due Friday
- Reading: Chapter Four, III.1.
- Practice problems: Chapter 4, III.1: 1.14
- Turn in:
H08F
(tex file: H08F.tex
solutions: H08Fsol).
Week 9
☛ Monday ☚
Geometric interpretation of the determinant.
Homework due Monday
- Reading: None.
- Practice problems: None.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H09T (tex file: H09T.tex
solutions: H09Tsol).
☛ Wednesday ☚
Eigenvalues.
Homework due Wednesday
- Reading: Chapter Five, II.3.
- Practice problems: 3.21, 3.22, 3.23.
☛ Friday ☚
Eigenvalues, continued.
Homework due Friday
- Reading: Chapter Five, II.3.
- Practice problems: 3.21, 3.22, 3.23.
- Turn in: Midterm 2.
Solutions.
Week 10
☛ Monday ☚
Diagonalization.
Homework due Monday
- Reading: Chapter V, II.3.
- Practice problems: 3.24, 3.25, 3.28, 3.29.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H10T (tex file: H10T.tex
solutions: H10Tsol).
☛ Wednesday ☚
Algebraic and geometric multiplicity. Jordan form.
Homework due Wednesday
- Reading: Lecture notes.
- Practice problems: None.
☛ Friday ☚
Counting walks in graphs.
Homework due Friday
- Reading: Lecture notes.
- Practice problems: None.
- Turn in:
H10F
(tex file: H10F.tex
solutions: H10Fsol).
Week 11
☛ Monday ☚
Differential equations.
Homework due Monday
- Reading: Lecture notes.
- Practice problems: None.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H11T (tex file: H11T.tex
solutions: H11Tsol).
☛ Wednesday ☚
Inner products.
Homework due Wednesday
- Reading: Lecture notes.
- Practice problems: Notes.
☛ Friday ☚
Length, distance, components, projections, angles.
Homework due Friday
- Reading: Lecture notes.
- Practice problems: None.
- Turn in:
H11F
(tex file: H11F.tex
solutions: H11Fsol).
Week 12
☛ Monday ☚
Gram-Schmidt.
Homework due Monday
- Reading: Lecture notes.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H12T (tex file: H12T.tex
solutions: H12Tsol).
☛ Wednesday ☚
Orthogonal complements and orthogonal projections.
Homework due Wednesday
☛ Friday ☚
Thanksgiving break. No class today, and no homework due.
Week 13
☛ Monday ☚
Least squares.
Homework due Monday
- Reading: Lecture notes.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H13T (tex file: H13T.tex
solutions: H13Tsol).
☛ Wednesday ☚
Markov chains I.
Homework due Wednesday
☛ Friday ☚
Markov chains II. Pagerank I.
Homework due Friday
Week 14
☛ Monday ☚
Pagerank II.
Homework due Monday
- Reading: Lecture notes and Pagerank.
- Turn in by 2 pm on Tuesday in the folder outside my office:
H14T (tex file: H14T.tex
solutions: H14Tsol.)
☛ Wednesday ☚
Pagerank III.
Homework due Wednesday
☛ Friday ☚
No class.