East Carolina University
Department of Computer Science

CSCI 3584
Computational Linear Algebra
Standard Syllabus

Catalog entry

May not count toward MATH major or minor. P: Calculus course. Introduces vectors, matrices, and determinants. Special emphasis on application of linear algebra to solution of practical problems.

Course summary

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. In this course, we will take an application and computation oriented ``matrix approach'' to the subject instead of the more theoretical ``abstract approach'' to the subject. There are several areas in computer science and programming where the concepts, techniques and theorems of linear algebra are used. So, this is arguably the most useful math course in CS curriculum.

Course topics

• Systems of Linear Equations
• Vectors
• The Equation Ax=b
• Solution Sets of Linear Systems
• Linear Independence
• Linear Transformation
• Applications of Linear Systems
• Basic Matrix Operations
• Inverse of a Matrix
• The Invertible Matrices Theorem
• Concepts of Vector Space
• Column Space and Null Space of a Matrix
• Determinants
• Eigenvalues and Eigenvectors
• Diagonalization
• Discrete Dynamical Systems

Student learning outcomes

• Given a system of linear equations, determine whether a solution exists and if so, find all solutions.
• Model diverse applications as Linear Systems.
• Given a bunch of vectors, determine whether they are linearly independent or not.
• Given a transformation, determine whether it is a linear transformation or not. If so, figure out the standard matrix of the linear transformation.
• Add, subtract and multiply matrices.
• Determine whether a given matrix has an inverse and if so, compute it using few different techniques.
• Compute the determinant of a matrix using few different techniques.
• Give a geometric interpretation of determinants and apply it to solve problems.
• Determine the Null Space and Column Space of a matrix.
• Determine the eigenvalues and eigenvectors of a matrix.
• Diagonalize symmetric matrices.
• Apply the concept of eigenvalues and eigenvectors to discrete dynamical systems.

Textbook

Linear Algebra and Its Applications by David C. Lay, Steven R. Lay and Judi J. McDonald, Pearson Education Inc., Fifth Edition, 2016.

This is a popular text book written with the intent to modernize the linear algebra curriculum. I will be sticking to the book closely in this course. Earlier editions of the same book (third and higher) might also suffice. We would be focusing primarily on chapters Chapters 1 thorough 5.

Other required material

All students will be required to have an account in Pearson's MyMathLab System. This system will be used for web based assignments

Grading

Your grade in this course will be based on your performance in assignments and examinations. The examinations will count for two third of your grade and the assignments will count for one third of your grade.

Assignments must be taken seriously and must be submitted in time. There will not be any programming assignments in this course. Most of the assignments will be done using the web based ``Pearson's MyMathLab'' System (that will be auto-graded) and the remaining assignments will be traditional paper based assignments (homework) that are graded manually.

There will be two regular examinations during the semester and a final comprehensive examination at the end of the semester.

Grade meanings