MAT 350 – Applied Linear Algebra

Draft Fall 2025 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 the basic concepts and skills, students will use their knowledge of linear algebra to model a selection of applied mathematics problems in business, economics, science, computer science, and engineering.

Course Timeline and Notebooks

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

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