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MAT 350 – Applied Linear Algebra

Textbook Cover and Link

Draft Syllabus (Subject to Change)

Course Description: This is a first course in linear algebra and matrices. Topics include systems of linear equations, linear independence, matrices of linear transformations, matrix algebra, determinants, vector spaces, eigenvalues, and eigenvectors. After mastering basic concepts and skills, students will use their knowledge of linear algebra to model a selection of applied mathematics problems in business, science, computer science, and economics.




Course Timeline and Notebooks

Below will is a tentative timeline for our course. It includes a detailed set of notes corresponding to each class meeting and assignments following each class meeting. Note that assignments are all available on MyOpenMath.

Class Meeting Before Class During Class After Class
1 Review Syllabus
Set Up Google Colab		 Introduction and What to Expect
$\S$ 1.1 - What Can We Expect?
(Slides)		 Week 1 Assignment
Homework 0
2 3Blue1Brown: Vectors Vector Arithmetic and Operations
(Slides)		 Homework 1
3   Matrix Arithmetic and Operations
(Slides)		 Homework 1 (Cont’d)
4   $\S$ 1.2 - Finding Solutions to Linear Systems
(Slides)		 Homework 2
5   $\S$ 1.3 - Computation with Python
(Slides)		  
6   $\S$ 1.4 - Pivots and their Influence on Solution Spaces
(Slides)		 Homework 3
7   Row-Reduction Workshop
(Slides)
Initial Row-Reduction Gateway Exam		  
8 3Blue1Brown: Linear Combinations, Spans, and Bases $\S$ 2.1 - Vectors and Linear Combinations
(Slides)		 Homework 4
9 3Blue1Brown: Linear Transformation $\S$ 2.2 - Matrix Multiplication and Linear Combinations
(Slides)		 Homework 4 (Cont’d)
10   $\S$ 2.3 - The Span of a Set of Vectors
(Slides)		 Homework 5
11   $\S$ 2.4 - Linear Independence
(Slides)		 Homework 5 (Cont’d)
12 3Blue1Brown: Matrix Multiplication $\S$ 2.5 - Matrix Transformations
(Slides)		 Homework 6
13 3Blue1Brown: 3D Transformations $\S$ 2.6 - The Geometry of Matrix Transformations Homework 6 (Cont’d)
14   Group Exam I  
15   Individual Exam I  
16 3Blue1Brown: Inverse Matrices, Rank, and Null Space $\S$ 3.1 - Invertibility
(Slides)		 Homework 7
17 3Blue1Brown: Change of Basis $\S$ 3.2 - Bases and Coordinate Systems
(Slides)		 Homework 8
18   $\S$ 3.3 - Image Compression
(In-Class Version)		  
19 3Blue1Brown: Determinants $\S$ 3.4 - Determinants
(Slides)		 Homework 9
3Blue1Brown: Cramer’s Rule
20   $\S$ 3.5 - Subspaces
(Slides)		 Homework 10
21 3Blue1Brown: Eigenvalues and Eigenvectors $\S$ 4.1 - An Introduction to Eigenvectors and Eigenvalues
(Slides)		 Homework 11
22   $\S$ 4.2 - Finding Eigenvalues and Eigenvectors
(Slides)		 Homework 11 (Cont’d)
23   Group Exam II  
24   Individual Exam II  
25   $\S$ 4.3 - Diagonalization, Similarity, and Powers of a Matrix
(Slides)		 Homework 12 (Optional)
26   $\S$ 4.4 - Dynamical Systems
(In-Class Version)		 Homework 13 (Optional)
27   $\S$ 4.5 - Markov Chains and Google’s PageRank Algorithm Homework 14 (Optional)
28   Review  
29   Final, Part I (Required)  
30   Final, Part II (Optional)  





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