↩

Schedule

Table of Contents

Week 1 ✓

TUE 09-03 Lecture 1

THU 09-05 Lecture 2

FRI/MON 09-06/09 Discussion 1

  • Topics:
    • Set up your Python environment (with help from the TF/TAs)
    • Practice with SymPy
  • Material:

Week 2 ✓

TUE 09-10 Lecture 3

THU 09-12 Lecture 4

FRI/MON 09-13/16 Discussion 2

  • Topics: Practice solving linear systems
  • Practice Problems:
    • Linear Algebra and Its Applications (LAA) 1.2:
      • 3, 13, 19, 21, 22, 23-26

Week 3 ✓

TUE 09-17 Lecture 5

THU 09-19 Lecture 6

FRI/MON 09-20/23 Discussion 3

  • Topics:
    • Practice with vectors, spans, and matrix-vector multiplication
  • Practice Problems:
    • LAA 1.3:
      • 19, 23, 24, 30
    • LAA 1.4:
      • 15, 23, 24, 35

Week 4 ✓

TUE 09-24 Lecture 7

  • Title: Linear Independence
  • Topics:
    • Introduce notion of linear independence as a way to understand if the span of a set of vectors is "as large as possible"
    • Examine the relationship between linear independence and systems of linear equations (in particular, look at what the shape of a matrix says about the linear dependences of its columns)
  • Material:

THU 09-26 Lecture 8

FRI/MON 09-27/30 Discussion 4 (CANCELLED)

We will not hold these discussion sections due to the BU presidential inauguration.

  • Practice Problems:
    • LAA 1.7:
      • 5, 8, 21, 22, 27, 28
    • LAA 1.8:
      • 3, 8, 21, 22

Week 5 ✓

TUE 10-01 Lecture 9

THU 10-03 Lecture 10

FRI/MON 10-04/07 Discussion 5

  • Topics:
    • Practice with linear transformations and matrix multiplication
  • Practice Problems:
    • LAA 1.8:
      • 6, 16, 21, 22, 31
    • LAA 1.9:
      • 1-16, 23, 24

Week 6 ✓

TUE 10-08 Lecture 11

THU 10-10 Lecture 12

  • Title: Invertible Matrix Theorem + Algebraic Graph Theory
  • Topics:
    • Review matrix inversion
    • Connect everything we've seen so far in the case of square matrices (one theorem to rule them all…)
    • See how matrices can be used to represent graphs (a.k.a. networks)
    • See how matrix operations can be interpreted as operations on graphs
    • Set up the conceptual framework for Markov chains and PageRank
  • Material:
  • Reminders:
    • Homework 5 is due
    • Homework 6 is assigned

FRI/TUE 10-11/15 Discussion 6

  • Topics:
    • Practice with matrix inversion
  • Practice Problems:
    • LAA 2.2:
      • 3, 5, 7, 12, 16, 17
    • LAA 2.3:
      • 3, 4, 8, 11, 12, 16, 17
  • Reminders:
    • The discussion section normally held on Monday will be held on Tuesday because of Indigenous People's Day

Week 7 ✓

THU 10-17 Lecture 13

FRI/MON 10-18/21 Discussion 7

  • Topics:
    • Go over last year's midterm exam and review

Week 8 ✓

TUE 10-22 Midterm Exam

  • The midterm will be held during lecture
  • See Piazza for details about the exam

THU 10-24 Lecture 14

FRI/MON 10-25/28 Discussion 8

  • Topics:
    • Practice with Markov Chains
  • Practice Problems:
    • LAA 4.9
      • 4-11
    • LAA 2.5
      • 5, 19, 21

Week 9 ✓

TUE 10-29 Lecture 15

THU 10-31 Lecture 16

FRI/MON 11-01/04 Dicussion 9

  • Topics:
    • Help with Homework 8

Week 10 ✓

TUE 11-05 Lecture 17

THU 11-07 Lecture 18

FRI/MON 11-08/11 Discussion 10

  • Topics:
    • Practice with the rank theorem and eigenvalues
  • Practice Problem:
    • LAA 2.9
      • 2, 10, 17, 18, 23, 24
    • LAA 5.1
      • 2, 13, 21, 22, 24, 25

Week 11 ✓

TUE 11-12 Lecture 19

THU 11-14 Lecture 20

FRI/MON 11-15/18 Discussion 11

  • Topics:
    • Make sure you understand how to diagonalize a matrix!

Week 12

TUE 11-19 Lecture 21

THU 11-21 Lecture 22

  • Title: Orthogonal Projection
  • Topics:
    • Introduce orthogonal projection as a way of finding the "shadow" of a vector in a subspace
    • Connect orthogonality to matrices and linear transformations
  • Material:
  • Reminders:
    • Homework 10 is due
    • Homework 11 is assigned

FRI/MON 11-22/25 Discussion 12

  • Topics:
    • Practice with orthogonality
    • Practice with orthogonality in NumPy
  • Material:
  • Reminders:

Week 13

TUE 11-26 Lecture 23

  • Title: Least Squares
  • Topics:
    • Introduce the least squares method as a way of giving "approximate" solutions to systems of linear equations
    • Demonstrate the relationship between orthogonal projection and least squares solutions
  • Material:
  • Reminders:
    • There is no class on Thursday because of the Thanksgiving recess

Week 14

TUE 12-03 Lecture 24

  • Title: Linear Models
  • Topics:
    • Look at applications of linear algebra in machine learning
  • Material:
  • Reminders:
    • There will be no discussion section on Monday because of the Thanksgiving recess

THU 12-05 Lecture 25

  • Title: Symmetric Matrices
  • Topics:
  • Material:
  • Reminders:
    • Homework 11 is due
    • Homework 12 is assigned (it is shorter than usual)

FRI/MON 12-06/09 Discussion 13

  • Topics:
  • Material:
  • Reminders:

Week 15

TUE 12-10 Lecture 26

  • Title: Singular Value Decomposition (SVD)
  • Topics:
  • Material:
  • Reminders:
    • Homework 12 is due
    • Last day of class (!)

Week 16

??? ??-?? Final Exam

  • The final exam will be held during finals week
  • More information TBA