Linear Algebra

Things to be Working On: 

• Study for the final Celebration of Knowledge.  Study guide available here 
• Have a wonderful summer!

Course Documents: 

• Homework Assignments
• In Class Examples
• In Class Python Example
• Syllabus

• Email: <emcnicho>
• Office Hours:  
  • Office Hours: https://sites.google.com/willamette.edu/emcnicholas/home (In addition to the office hours posted on the website, I’m also available by appointment for in-person or Zoom meetings)
• Math Tutoring:
  • Sunday, Monday, Wednesday, and Thursday nights 7-9pm in the Math Hearth (2nd floor Ford) 
• Class Meetings: 
  • Tu/Th 1:10-2:40 pm, Ford 204;  Final Exam Time: Tu May 7, 9-11am

1

1/15-1/19

Vectors & Linear Equations: Lines, Planes, Hyperplanes, Systems of Linear Equations, and Matrices

Ch. 1.1-1.3

• Before the first class: Join the class discord channel, and review vectors and dot products (Section 1.1-1.2) by looking over the text of watching the Perusall videos from the first assignment and trying out the Extra Credit WeBWorK Assignment #0

• Class Prep Questions:

  • Review the definition of vector norm, dot product, orthogonal, and unit vector, and the rules for vector addition and scalar multiplication
  • What defines a line?
  • How do you tell if two vectors or two lines are parallel? perpendicular?
  • What defines a plane?
  • What is a linear combination?

• Perusall Assignment #1: Syllabus, Intro to Linear Algebra, and Vector Review (EC) (due Wednesday 1/17) 

2

1/22-1/26

Systems of Linear Equations: Lines, Planes, Hyperplanes, Systems of Linear Equations, and Matrices

Ch. 1.3-2.2

• Perusall Assignment #2: 3b1b Span (due Monday 1/22) 
• Computational WeBWorK Assignment #1: Extra Credit Assignment #0 and Assignment #1 (due Monday 1/22 Wednesday 1/24)
• Theoretical Assignment #1: due Saturday 1/20 Friday 1/26
• Week 2 Survey: Please complete by Monday 1/29

3

1/29-2/2

Matrix Algebra: Operations

3.1-3.2

• Perusall Assignment #3: Elementary Row Operations & Gauss-Jordan Elimination, a choose your own adventure Perusall assignment (due Monday 1/29) 
• Computational WeBWorK Assignment #2: Set 2 Systems of Linear Equations and Augmented Matrices (due Wednesday 1/31)
• Applied Assignment #1: Cubic Splines, Part I due Friday 2/2, Part II due Monday 2/5

4

2/5-2/9

Matrix Algebra: Inverses, Elementary Matrices, Subspaces & Span

3.3-3.4

• Applied Assignment #1: Cubic Splines, Part I due Friday 2/2, Part II due Monday 2/5
• Computational WeBWorK Assignment #3: Set 3 Matrix Algebras (due Wednesday 2/7)
• Theoretical Assignment #2: due Friday 2/9

5

2/12-2/16

Matrix Algebra: Subspaces & Linear (In)Dependence

3.4

Group Exam 1

• Perusall Assignment #4: Matrix Multiplication as a Linear Transformation (due Monday 2/12)
• Computational WeBWorK Assignment #4: Set 4a Matrix Inverses and Vector Spaces (due Wednesday 2/14)
• Study for Group Exam Thursday 2/15 Study Guide

6

2/19-2/23

Geometry of Solutions Sets and Linear Transformations

3.5 & Ch. 6

• Perusall Assignment #5: Linear Transformations (due Monday 2/19) 
• Computational WeBWorK Assignment #5: Set 4b Linear Dependence/Independence (due Wednesday 2/21) 
• Applied Programming Assignment #2: Part I due Friday 2/23, Part II due Monday 2/26

7

2/26-3/1

Linear Transformations

Ch. 6

• Computational Assignment #6: (You should do these problems before the first individual celebration of knowledge - I will not be collecting them) 6.1/ 3, 14, 15, 35, 37, 39; 6.2/ 9, 11, 25, 30; 6.3/ 7, 11, 19, 21; 6.4/ 9, 19
• Study for Individual Celebration of Knowledge (happening Tuesday 3/5) Study Guide 
• Theoretical Assignment #3: due Monday 3/4

8

3/4-3/8

Midterm Bases & Dimension

Ch. 7.1-7.2

• Perusall Assignment #6: Inverse Matrices, Column Space, and Null Space (due Monday 3/4) 
• Study for Individual Celebration of Knowledge (happening Tuesday 3/5) Study Guide 
• Applied Programming Assignment #3: Part I due Friday 3/8, Part II due Wednesday 3/13

3/11-3/15

Bases & Determinants 

Ch. 4.1-4.2

• Applied Programming Assignment #3: Part I due Friday 3/8, Part II due Wednesday 3/13
• Perusall Assignment #7: Determinants (due Monday 3/11) 
• Test Corrections due Thursday 3/14

10

3/18-3/22

• Computational WeBWorK Assignment: Set 5 S24 Bases, Independence, and Determinants (due Wednesday 3/20)
• Theoretical Assignment #4: due Friday 3/22

11

3/25-3/29

12

4/1-4/5

Eigenvectors & Eigenvalues

4.4 

• Perusall Assignment #8: Cramer’s Rule (due Monday 4/1) 
• Computational WeBWorK Assignment: Set 6 S24 Determinants Continued - Cramer’s Rule and Cofactor Expansion (due Wednesday 4/3)
• Week 12 Survey: https://forms.gle/SPBtTYft2YUkE5pz7 Please complete the week 12 survey by Friday 4/5
• Applied Assignment #4: Graphics (due Monday 4/8)

13

4/8-4/12

Linear Isometries & Orthogonal matrices

Chapter 6.2 Revisited

Group Exam 2

• Perusall Assignment #9: Abstract Vector Spaces (due Monday 4/8)  
• Computational WeBWorK Assignment: Set 7 S24 Eigenvalues & More Linear Transformations (due Wednesday 4/10)
• Study for Group Exam Study guide available here

14

4/15-4/19

Fundamental Spaces of a Matrix, Rank, Dimension, and Pivot Theorems

Ch.7.3-7.7

• Perusall Assignment #10: Bases & Eigenbases (due Monday 4/15)  
• Computational WeBWorK Assignment: Set 8 S24 Fundamental Subspaces (due Friday 4/19)
• Theoretical Assignment #5: due Monday 4/22

15

4/22-4/26

Projection, Change of Basis, and Diagonalization

Ch.7.7-8.1

• Computational WeBWorK Assignment: Set 9 S24 (due Friday 4/26)
• Applied Assignment #5: SVD due Tuesday 4/30
• Perusall Extra Credit Assignments:  due Tues 4/30  

16

4/29-5/3

• Study for the final Celebration of Knowledge.  Study guide available here 
• Have a wonderful summer!

17

5/6-5/10

Related Websites:

3blue1brown Essence of Linear Algebra - Excellent video series explaining many of the concepts covered in class from a geometric perspective, complete with very illuminating graphics!

Colin Starr's Glossary of Common Mathematical Terms - these are terms that get thrown around a lot, but not always clearly defined (like "map", "unique", "respectively")

Important Dates

Week 1: 1/16 (Tu) First day of classes

Week 4: 1/29 (M) Add/Drop Deadline

Week 10: 3/19 (Tu) Withdraw Deadline

Week 11: 3/25-3/29 Spring Break

Week 13: 4/8-4/11  Registration for Fall

Week 14: 4/17 (W) SSRD No Classes

Week 16: 4/30 (T) Last Day of Classes

Week 17: Final Exams