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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 Course Syllabus Topics

  1. Vectors
    1. Geometry of Vectors
    2. Perpendicular Frames
    3. Curves in 2D: Change of Frames/Basis
    4. Dot Products
    5. Cross Products
    6. Ellipses and Ellipsoids
    7. Area and Volume
  2. Matrices
    1. Basics
    2. Transforming Curves
    3. Matrix Arithmetic
    4. Translations and Rotations
    5. Shears
    6. Linear Transformations
    7. Inverses
    8. Determinants
    9. Transposes
    10. Matrix Decomposition: Singular Value Decomposition
    11. Rank
    12. Projections
    13. Higher Dimensions
  3. Linear Systems
    1. Conversion to Matrix Notation
    2. Gaussian Elimination
    3. Vector Spaces and Subspaces
    4. Numerical Considerations
    5. Applications: Least Square Fit
    6. Spanning Sets; Basis
    7. Linear Independence
    8. Pseudo Inverses
    9. Approximate Solutions
    10. Null Space and Image Space
  4. Eigenvalues and Eigenvectors
    1. Diagonalization of a Matrix
    2. Eigenvalues
    3. Eigenvectors
    4. Exponential of a Matrix

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: May 3, 2020
Review by: Andris H.
Courses Completed: Applied Calculus
Review: I found out from my MBA program that I needed to finish calculus before starting the MBA. They told me 3 weeks before term started! I was able to finish Applied Calculus from Distance Calculus. Definitely a great class. Thanks Distance Calculus!
Transferred Credits to: SUNY Stony Brook

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Date Posted: Dec 20, 2019
Review by: Bill K.
Courses Completed: Calculus I, Calculus II, Multivariable Calculus, Linear Algebra
Review: I took the whole calculus series and Linear Algebra via Distance Calculus. Dr. Curtis spent countless hours messaging back and forth with me, answering every question, no matter how trivial they might seem. Dr. Curtis is extremely responsive, especially if the student is curious and is willing to work hard. I don't think I ever waited much more than a day for Dr. Curtis to get a notebook back to me. Dr. Curtis would also make videos of concepts if I was really lost. The course materials are fantastic. If you are a student sitting on the fence, trying to decide between a normal classroom class or Distance Calculus classes with Livemath and Mathematica, my choice would be the Distance Calculus classes every time. The Distance Calculus classes are more engaging. The visual aspects of the class notebooks are awesome. You get the hand calculation skills you need. The best summary I can give is to say, given the opportunity, I would put my own son's math education in Dr. Curtis's hands.
Transferred Credits to: None

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Date Posted: Jan 12, 2020
Review by:
Courses Completed: Calculus I, Calculus II
Review: I needed to brush up on my high school calculus and finally take Calc II before starting a graduate program that needed them as prereqs. This was perfect choice to fit in that summer. Got done at fast pace that I wanted and needed. Also had added bonus of one on one feedback and help when needed. Video lessons were better than many on campus instructors in large lecture settings. Recommend for anyone needing to satisfy prereqs at home institution.
Transferred Credits to: University of Michigan

Frequently Asked Questions

Yes, most definitely. Linear Algebra is one of the core courses needed for starting any degree program in Data Science

Yes, Calculus II is the prequisite for the Linear Algebra course, but interestingly no Calculus is used in the Linear Algebra course!

4-6 Weeks is a very fast but reasonable pace to finish the Linear Algebra course.

Anytime - Enrollment for Distance Calculus courses is on-going - enroll and start the course on the same day

Linear Algebra is quite different from Calculus, but it is not a harder course than Calculus II. Some students find Linear Algebra to be easier than Calculus, while other students find Linear Algebra to be more challenging than Calculus.