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
☛ Friday ☚
Linear independence.
Homework due Friday
Week 3
☛ Monday ☚
Linear independence.
Homework due Monday
☛ Wednesday ☚
Bases.
Homework due Wednesday
☛ Friday ☚
Dimension.
Homework due Friday
Week 4
☛ Monday ☚
Row rank = column rank; dimension of solution space.
Homework due Monday
☛ Wednesday ☚
Linear transformations.
Homework due Wednesday
☛ Friday ☚
Range space and null space.
Homework due Friday
Week 5
☛ Monday ☚
Isomorphisms.
Homework due Monday
☛ Wednesday ☚
Lines, planes, and hyperplanes: equations and parametrizations.
Homework due Wednesday
☛ Friday ☚
Matrices.
Homework due Friday
Week 6
☛ Monday ☚
The ring of square matrices. Matrix inversion.
Homework due Monday
☛ Wednesday ☚
Matrices and linear transformations.
Homework due Wednesday
☛ Friday ☚
Matrices and linear transformations.
Homework due Friday
Week 7
☛ Monday ☚
Matrices and linear transformations: examples. Change of basis.
Homework due Monday
☛ 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
☛ Friday ☚
Determinants.
Homework due Friday
Week 8
☛ Monday ☚
\(\det(A)=\det(A^t)\).
Homework due Monday
☛ 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
☛ Friday ☚
Finish permutation expansions. Laplace expansion. Existence and uniqueness of the determinant.
Homework due Friday
Week 9
☛ Monday ☚
Geometric interpretation of the determinant.
Homework due Monday
☛ Wednesday ☚
Eigenvalues.
Homework due Wednesday
☛ Friday ☚
Eigenvalues, continued.
Homework due Friday
Week 10
☛ Monday ☚
Diagonalization.
Homework due Monday
☛ Wednesday ☚
Algebraic and geometric multiplicity. Jordan form.
Homework due Wednesday
☛ Friday ☚
Counting walks in graphs.
Homework due Friday
Week 11
☛ Monday ☚
Differential equations.
Homework due Monday
☛ Wednesday ☚
Inner products.
Homework due Wednesday
☛ Friday ☚
Length, distance, components, projections, angles.
Homework due Friday
Week 12
☛ Monday ☚
Gram-Schmidt.
Homework due Monday
☛ 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
☛ Wednesday ☚
Markov chains I.
Homework due Wednesday
☛ Friday ☚
Markov chains II. Pagerank I.
Homework due Friday
Week 14
☛ Monday ☚
Pagerank II.
Homework due Monday
☛ Wednesday ☚
Pagerank III.
Homework due Wednesday
☛ Friday ☚
No class.