Course ePortfolio

Introduction to Linear Algebra

This collection contains the California Open Educational Resources Council (CA OER) list of peer-reviewed textbooks for Linear Algebra (common course-id MATH 250), one of the top 50 college courses identified for inclusion in the Southern University Online Library for Education (SUOLforEd).

See LA Master Course Matrix

http://www.regents.la.gov/page/master-course-articulation-matrix

General Course Description - MATH 250:

This course develops the techniques and theory needed to solve and classify systems of linear equations. Solution techniques include row operations, Gaussian elimination, and matrix algebra. Investigates the properties of vectors in two and three dimensions, leading to the notion of an abstract vector space. Vector space and matrix theory are presented including topics such as inner products, norms, orthogonality, eigenvalues, eigenspaces, and linear transformations. Selected applications of linear algebra are included.

Minimum units: 3.0

Any rationale or comment: None

Date Added to MERLOT:

August 3, 2016

Created by:

SUOL4ed subr

License:

Derived from

Prerequisites

Prerequisites: Calculus I (C-ID MATH 210, MATH 211 OR MATH 900S)

Corequisites: None

Advisories/Recommendations: A year of college calculus. Prior or concurrent course work with vector calculus or vector-intensive physics would be helpful.

Pedagogical Approach & Learning Outcomes

Pedagogical Approach

None

Learning Outcomes

Upon successful completion of the course, students will be able to:

Find solutions of systems of equations using various methods appropriate to lower division linear algebra;
Use bases and orthonormal bases to solve problems in linear algebra;
Find the dimension of spaces such as those associated with matrices and linear transformations;
Find eigenvalues and eigenvectors and use them in applications; and
Prove basic results in linear algebra using appropriate proof-writing techniques such as linear independence of vectors; properties of subspaces; linearity, injectivity and surjectivity of functions; and properties of eigenvectors and eigenvalues.

Assessment & Other Information

Assessment

Tests,
examinations,
homework or
projects

where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems and proofs.

Other Information

None

Course Resources

A First Course in Linear Algebra (Open (Access) Textbook)

A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically... More

A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.
Linear Algebra (Open (Access) Textbook)

From the author’s description of the book: The approach is developmental. Although the presentation is focused on... More

From the author’s description of the book: The approach is developmental. Although the presentation is focused on covering the requisite material by proving things, it does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.
Linear Algebra Done Wrong (Open (Access) Textbook)

Brown University has two introductory linear algebra courses. This text is used in the honors course that emphasizes... More

Brown University has two introductory linear algebra courses. This text is used in the honors course that emphasizes proofs. The book’s title suggests that it is not the typical approach to linear algebra even among those books that are more theoretical. For example, the concept of a basis is treated as more fundamental than the concept of linear independence, and linear transformations are introduced before solving systems of linear equations.