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Applied Linear Algebra | Welcome

MAT 350 – Applied Linear Algebra

Spring 2024 Syllabus

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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