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Linear Algebra Online Course for Academic Credit

Linear Algebra is technically part of the undergraduate Calculus sequence, usually taken the sophomore year, but there is almost no Calculus in the course! Linear Algebra is usually considered a more difficult course, especially in a classroom/textbook format. Our Linear Algebra via Distance Calculus is a beautiful course, with masterful use of Mathematica that brings together the topics in a highly visual way, giving the student both theoretical and computational understanding of the very important topics of Linear Algebra, especially for economics, data science, computer science, engineering, and financial mathematics.

Completion of Math 331 - Linear Algebra earns 3 academic credit semester hours with an official academic transcript from Roger Williams University, in Providence, Rhode Island, USA, which is regionally accredited by the New England Commission of Higher Education (NECHE), facilitating transfer of credits nationwide to other colleges and universities.

Linear Algebra Introductory Videos

Linear Algebra Course Introduction

Linear Algebra is a sophomore-level introductory course to the subject.

Traditional approaches to the subject include learning tedious manual computations on matrices, followed by an introduction to a more abstract approach to looking at a class of examples called linear spaces.

Our approach in this course is not a traditional one. In the words of the authors of the curriculum, "This is not your mother's (or father's) linear algebra course", referring to the fact that someone who took an introductory linear algebra course years ago would not recognize much similarity with this course.

Leveraging the high-powered computer algebra and graphing system Mathematica™ by Wolfram Research, the course curriculum Matrices, Geometry, & Mathematica by Davis/Porta/Uhl bypasses the traditional manual calculation tedium, and leapfrogs to a computationally-based, geometric, experimentation-centered approach to the subject. Instead of learning manual computations that are today easily completed by any computer algebra system, this course races into topics that are seldom found in any linear algebra textbook - a quite unique, fresh, and powerful approach to the subject.

Students completing this Matrices, Geometry, & Mathematica curriculum will have a thorough understanding of the geometry of linear algebra, the solutions of linear systems of equations, and the theoretical investigation of the generalized linear spaces concept (although only lightly dabbling in "proofs" - just the right amount for this course level).

Roger Williams University Course Catalog Listing: Math 331 - Linear Algebra

MATH 331: Linear Algebra [3 credit hours]

Course Description: Presents matrices, determinants, vector spaces, linear transformations, eigenvectors and eigenvalues, diagonalization, solution of systems of linear equations by the Gauss-Jordan method, and applications.

Prerequisite: Calculus II
Detailed Course Syllabus in PDF

Linear Algebra Examples of the Curriculum

Below are some PDF "print outs" of a few of the Mathematica™ notebooks from Matrices, Geometry, & Mathematica by Davis/Porta/Uhl. Included as well is an example homework notebook completed by a student in the course, demonstrating how the homework notebooks become the "common blackboards" that the students and instructor both write on in their "conversation" about the notebook.

That Looks Like Programming Code!

Yes, Mathematica™ is a syntax-based computer algebra system - i.e. the instructions to generate the graphs and computations look like a programming language code (which it is).

This course is not a course on programming. We do not teach programming, nor do we expect the students to learning programming, or even to know anything about programming. The mathematics is what is important in this course, not the code.

With that tenet in mind, the authors of the Matrices, Geometry, & Mathematica courseware have designed the explanation notebooks (Basics & Tutorials) and the homework notebooks (Give It a Try) in such a way as to make it easy to Copy/Paste from the explanations into the homework notebooks, and make minor changes (obvious ones) to produce the desired similar (but different) output. In this way, we are able to stick strickly to the mathematics at hand, and deal with the programming code as minimally as possible.

sample mathematica notebook

Distance Calculus - Student Reviews

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Date Posted: Feb 28, 2020
Review by: Teddy M.
Courses Completed: Precalculus, Calculus I
Review: Pros: once you get going, you can go really fast. The visual textbook is pretty cool. The instructors were very responsive. Cons: the movies are great, but the software crashes more than it should. Sometimes it is just a hassle doing things in the software instead of on paper, but once I got used to the software, it was ok.
Transferred Credits to: Texas Christian University

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Date Posted: Mar 17, 2020
Review by: Rebecca M.
Courses Completed: Calculus II, Multivariable Calculus
Review: Fantastic courses! I barely made it through Cal 1, and halfway through Cal 2 I found this program. I took Cal 2 and then Multivariable and I just loved it! SOOOOOOO much better than a classroom+textbook class. I highly recommend!
Transferred Credits to: Tulane University

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Date Posted: Jan 12, 2020
Review by: Anonymous
Courses Completed: Calculus I
Review: This course is amazing! I took it as a requirement for admission to an MBA program, and couldn't have been happier with the quality and rigor of the course. I previously took calculus two times (at a public high school and then a large public university commonly cited as a "public ivy"), this course was by far the best and *finally* made the concepts click. Previously I had no idea what was going on because terrible PhD students were teaching the course and saying stuff like "a derivative is the slope of a tangent line" - ??? but what does that mean ???, but the instructors in the Shorter University course explain everything in ways where it FINALLY made sense (e.g., "imagine a roller coaster hitting the top of a hill, there's a moment where it shifts momentum and you're not accelerating or decelerating, that's what a 0 rate of change is - that's when the derivative would be zero"). They explain everything in multiple ways and relate it to other concepts. It all made perfect sense when I finally had a good instructor. Really recommend this class
Transferred Credits to: The Wharton School, UPenn