MAS 3105 : Applied Linear Algebra I

Role

Instructor of record, Summer 2025, responsible for classroom instruction, student mentoring, and assessment feedback. The course was coordinated across multiple sections, with a common departmental syllabus and shared assessments.

Course Overview

An applied introduction to linear algebra for students in mathematics, engineering, and the sciences, developing the theory of linear systems alongside the matrix factorizations that make them computationally useful.

Topics

• Systems of linear equations, row reduction, and vector and matrix equations
• Matrix algebra, inverses, and LU factorization
• Determinants
• Vector spaces, subspaces, basis, and dimension
• Eigenvalues, eigenvectors, and diagonalization
• Orthogonality, projections, least-squares problems, and QR factorization
• Symmetric matrices, quadratic forms, and the singular value decomposition

Grading

Component	Weight
Homework (in class and on Canvas)	25%
Midterm Exam 1	20%
Midterm Exam 2	20%
Final Exam	20%
Quizzes	15%

Course Materials

Lay, D. C., Lay, S. R., & McDonald, J. J. (2021). Linear algebra and its applications (6th ed.). Pearson.

Schedule

Week	Date	Topic	Materials
1	May 13	Course introduction and orientation Start of term
2–3	May 22 – May 31	Linear Equations in Linear Algebra Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.7
4	Jun 5	Midterm Exam 1 Assessment
5	Jun 13 – Jun 14	Matrix Algebra Sections 2.1, 2.2
6	Jun 17 – Jun 21	Linear Equations in Linear Algebra; Matrix Algebra Sections 1.10, 1.6, 1.8, 1.9, 2.3, 2.5, 2.7
7	Jun 24 – Jun 30	Matrix Algebra; Determinants Sections 2.8, 2.9, 3.1, 3.2, 3.3
8–9	Jul 2 – Jul 14	Midterm Exam 2 Assessment
10	Jul 17 – Jul 21	Vector Spaces Chapter 4
11	Jul 22 – Jul 25	Orthogonality and Least Squares; Symmetric Matrices and Quadratic Forms Sections 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 7.1
12	Jul 30 – Aug 3	Eigenvalues and Eigenvectors; Orthogonality and Least Squares Sections 5.1, 5.2, 5.3, 5.5, 5.7, 5.9, 6.8