Peter Blomgren
San Diego State University
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Math 254 – Introduction to Linear Algebra Fall 2018
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Evolving Schedule (topics arranged by "target week.")

Week # Monday Wednesday
-
Video: Teaching Center!!!
1 Aug-27-2018
0.1 First Meeting
[Notes #0.1]
Aug-29-2018
1.1 Intro to Linear Systems
[Notes #1.1] [with Supplements]
Movie(s): Supplemental Material
  • Metacognitive Reflection
  • Row-reductions revisited
  • Problem Statements for Suggested Problems
  • ☛ Lab-1.1 ☚ (Labs are 101.3% experimental)
2 Sep-03-2018
Labor Day
Sep-05-2018
1.2 Matrices, Vectors, and Gauss-Jordan Elimination
[Notes #1.2] [with Supplements]
FIRST i-Clickers Session
Bring your i-Clickers
Optional: REEF Polling by i-clicker app
[iTunes] [Google Play]

Supplemental Material
  • [Computer Science] perspective on a Matrix.
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems

Recommended Video(s)
3 Sep-10-2018
1.3 Solutions of Linear systems; Matrix Algebra
[Notes #1.3] [with Supplements]

Supplemental Material
  • [Additional discussion] Statements (and contra-positive statements) regarding rank(A).
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems

Schedule adjustment deadline.
(11:59 p.m. deadline.)
Sep-12-2018
1.4 Matrix--Vector Fundamentals Wrapup
[Notes #1.4] [with Supplements]

Supplemental Material
  • Metacognitive Reflection
4 Sep-17-2018
2.1 Linear Transformation and Their Inverses
[Notes #2.1] [with Supplements]
Movie(s): Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
Sep-19-2018
2.2 Linear Transformations in Geometry
[Notes #2.2] [with Supplements]
Movie(s): Supplemental Material
  • [Math] Challenge Question
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems

Recommended Video(s)
5 Sep-24-2018
2.3 Matrix Products
[Notes #2.3] [with Supplements]

Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems

Recommended Video(s)
Sep-26-2018
2.4 The Inverse of a Linear Transformation
[Notes #2.4] [with Supplements]

Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
6 Oct-01-2018
MIDTERM #1 (1.1 – 2.4)
[study_guide]
[midterm-01-practice]
[OLD TESTS]
Oct-03-2018
3.1 Image and Kernel of a Linear Transformation
[Notes #3.1] [with Supplements]
Movie(s): Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
  • [Math] Bonus Proof and discussion — Properties of im(T)
7 Oct-08-2018
3.2 Subspaces of ℜn; Bases and Linear Independence
[Notes #3.2] [with Supplements]

Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
Oct-10-2018
3.3 The Dimension of a Subspace of ℜn
[Notes #3.3] [with Supplements]

Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems

Recommended Video(s)
8 Oct-15-2018
3.4 Coordinates
[Notes #3.4] [with Supplements]
Movie(s): Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
  • [Math] Beyond Vectors & Matrices — Linear Spaces
Oct-17-2018
MIDTERM #1 Solutions
[MT#1 Statistics (Spring 2018)]
9 Oct-22-2018
Examples & Discussion / Buffer
REVIEW#2 (1.1 – 3.4)
Oct-24-2018
MIDTERM #2 (1.1 – 3.4)
[study_guide]
[midterm-02-practice]
[OLD TESTS]
10 Oct-29-2018
5.1 Orthogonal Projections and Orthonormal Bases
[Notes #5.1] [with Supplements]

Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
  • [Application] MPEG-4 Video Compression
Oct-31-2018
5.2 Gram-Schmidt Process and QR Factorization
[Notes #5.2] [with Supplements]

Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
  • [Application] Solving the "Unsolvable" (Keywords: Minimum Residual, Least Squares, Linear Regression)
11 Nov-05-2018
5.3 Orthogonal Transformations and Orthogonal Matrices
[Notes #5.3] [with Supplements]

Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
  • [Application] Least Squares Data Fitting;
  • [Math] Bonus Theory and Proofs — Orthongonal Transformations and Orthonormal Bases; Linear Spaces; ker(ATA), ker(A), invertibility of (ATA)
Nov-07-2018

MIDTERM #2 Solutions
[MT#2 Statistics (Spring 2018)]
12 Nov-12-2018



Veterans Day: Honoring All Who Served
Nov-14-2018
6.1 Introduction to Determinants
[Notes #6.1] [with Supplements]
Movie(s): Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
  • [Additional Discussion] Determinants of Block Matrices
  • [Math] The 7D Cross Product, Quarternions, Octonions, and other nonsense!
  • [Example] Computation of det(A) for a 4×4 matrix with many zeros (sparse matrix) using the combinatorial (pattern) method.
13 Nov-19-2018
6.2 Properties of Determinants (.)
[Notes #6.2] [with Supplements]

Supplemental Material
  • Metacognitive Reflection
  • Problem Statements for Suggested Problems
Nov-21-2018
Pre-Thanksgiving
(No Classes Nov. 21nd)
Campus "open" [#GhostTown]
14 Nov-26-2018
6.3 Geometrical Interpretations of the Determinant; Cramer's Rule
[Notes #6.3] [with Supplements]

Supplemental Material
  • Problem Statements for Suggested Problems
  • [Application] Variation of Parameters for Ordinary Differential Equations (ODEs)
Nov-28-2018
MIDTERM #3 (1.1 – 6.2)
[study_guide]
[midterm-03-practice]
[OLD TESTS]
15 Dec-03-2018
7.1 Diagonalization
[Notes #7.1] [with Supplements]
Movie(s): Supplemental Material
  • Problem Statements for Suggested Problems
  • Complex Analysis: Essentials for Linear Algebrax
Dec-05-2018
7.2 Finding Eigenvalues of a Matrix
[Notes #7.2] [with Supplements]

Supplemental Material
  • Problem Statements for Suggested Problems
  • Complex Eigenvalues
16 Dec-10-2018
7.3 Finding Eigenvectors of a Matrix
[Notes #7.3] [with Supplements]

Supplemental Material
  • Problem Statements for Suggested Problems
  • Complex Eigenvectors, Complex Diagonalization, Block-Diagonalization
Dec-12-2018
MIDTERM #3 Solutions
[MT#3 Statistics (Spring 2018)]
Movie(s):
SAME
WEEK
Dec-10-2018
FRIDAY FINAL!!!
Dec-14-2018
FINAL (1.1 – 7.3) 1:00pm – 2:00pm.
[final-practice]
[study_guide]
[OLD TESTS]
[Final Statistics (Spring 2018)]

Mandatory (WeBWork) Homework will be assigned.

HIGHLY "Recommended" Problems

  • Topic 1 : Linear Systems
    • 1.1 — 1, 3, 7, 14, 19, 21, 42
    • 1.2 — 1, 3, 9, 11, 18, 21, 34
    • 1.3 — 1, 2, 3, 7, 13, 22, 23, 37, 46, 55
  • Topic 2 : Linear Transformations
    • 2.1 — 1, 2, 3, 4, 5, 7, 8, 13, 14, 16, 17, 41, 42
    • 2.2 — 1, 6, 7, 9, 12, 13, 17, 26
    • 2.3 — 1, 3, 5, 7, 13, 17, 19, 27, 28, 33, 37
    • 2.4 — 1, 3, 9, 16, 17, 29, 31, 35
  • Topic 3 : Subspaces of Rn
    • 3.1 — 1, 7, 11, 14, 15, 17, 23, 24, 29, 39
    • 3.2 — 1, 3, 7, 11, 17, 25, 27, 32, 34
    • 3.3 — 1, 3, 19, 23, 25, 27
    • 3.4 — 1, 3, 7, 17, 19, 23, 37
  • (Topic 4 : Linear Spaces (Generalization)) — Partially "Absorbed" into the other topics
    • 4.1 — 1, 3, 5, 6, 8, 17, 20, 25, 32, 37
    • 4.2 — 1, 9, 13, 17, 18, 33, 51, 53, 63
    • 4.3 — 1, 5, 7, 9, 13, 15, 21, 25, 37, 41, 51, 55, 61
  • Topic 5 : Orthogonality, Gram-Schmidt, and QR-Factorization
    • 5.1 — 7, 10, 11, 15, 17, 27, 28
    • 5.2 — 3, 7, 13, 31, 32, 33, 35, 39
    • 5.3 — 1, 2, 5, 6, 13, 15, 17, 19, 28, 32, 33, 36, 41
  • Topic 6 : Determinants (A Minimal Introductions)
    • 6.1 — 1, 5, 11, 13, 23, 25, 27, 31, 43, 45
    • 6.2 — 1, 5, 7, 9, 11, 12, 13, 15
    • 6.3 — 1, 3, 5, 7, 9, 11, 13, 19-20-21
  • Topic 7 : Eigenvalue and Eigenvectors
    • 7.1 — 1, 3, 5, 7, 15, 17, 21
    • 7.2 — 1, 3, 5, 11, 15, 17, 19, 23
    • 7.3 — 1, 3, 5, 9, 13, 17, 23, 27, 31, 35
    • (7.4 — 1, 5, 11, 25, 35, 37, 39, 41, 43, 47)
    • (7.5 — 13, 15, 17, 21, 23)

Copyright © 2018 Peter Blomgren.