Honors Linear Algebra Online Course for Academic Credit
Honors 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.
Nationally, "Honors" courses usually are centered on a mathematically rigorous development of the concepts of
calculus, bringing many advanced topics from upper division courses such as Advanced Calculus and Real Analysis
into the freshman honors calculus courses. While this may be a worthwhile approach for students who seek to
become mathematics majors, it creates, for many students, an inflated level of course difficulty of questionable benefit to
related fields of study.
Our approach to Honors courses is built upon a distinctly different educational philosophy:
Freshman & Sophomore Calculus is NOT the correct math level to increase rigor
We believe that mathematical rigor is learned after exposure to the calculus, in the upper division,
after some time and maturing of mathematical thought is allowed to organically develop. No student ever understood
the concept of a derivative because the natural numbers were first axiomatically developed.
Honors means DEEPER, not just HARDER
In mathematics, the potential for making any course harder is a rather simple proposition. Work SMARTER, not HARDER
mandates that an honors course should not be more difficult just to say it is. A true honors student wants to go deeper into the
topics, not flirt with academic demoralization via some mathematical bootcamp experience.
Technical Writing Curriculum
While axiomatic development has its place in upper division math, core improvement of technical writing skills
will benefit all students in all disciplines with immediate effect. If calculus is supposed to be mathematical preparation for
science, technology, and engineering related fields, then development of technical writing skills should be
as important as computational prowess.
Course Term Paper
Each Honors course student will write a 10-20 page term paper on a topic chosen in collaboration with the course instructor,
empowering the student to simultaneously improve technical writing skills and deepen knowledge in the student's chosen academic field
via a uniquely creative exercise that will transcend the traditional course boundaries.
In summary, our Honors courses go deeper and broader in the curriculum,
offer a notch more challenging course work set, and featuring a technical writing curriculum that truly prepares the student
for further academics in the sciences.
Completion of DMAT 336 - Honors Computational Linear Algebra earns 5 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
Elementary Row Operations
Elementary Row Operations on a Matrix
Samples of Linear Algebra Lecture Movies
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).
An honors-level first course in matrix algebra and linear spaces with emphasis on computational software techniques and geometrical analysis. Topics include matrices, solutions of systems of linear equations, determinants, linear spaces and transformations, inner products, higher dimensional spaces, inverses and pseudoinverses, rank, Singular Value Decomposition, change of basis, Eigenvalues and Eigenvectors, matrix decomposition and diagonalization, dynamical systems and the Spectral Theorem. Honors courses will include greater breadth and depth of topics, and develop technical writing skills, culminating in a mathematical term paper on an approved topic.
Prerequisite
Successful completion with grade B or higher in Calculus II or equivalent, or consent of instructor.
E-Textbook
Matrices, Geometry & Mathematica by Davis/Porta/Uhl
To understand the core connection between matrix algebra and a study of systems of linear equations
To understand and compute measurements of vectors and their geometry
To understand and compute core matrix algebra operations and their geometrical interpretations
To understand and compute the fundamental properties of determinants and inverses of matrices, both for square and non-square generalizations
To understand and compute Singular Value Decomposition
To understand and compute the core concept of rank and its variations
To understand and compute Gaussian elimination and other strategies for finding solutions or approximate solutions to systems of linear equations
To understand and compute bases, change of bases, spanning and linear independence, kernel and image sets
To understand and compute the diagonalization of a matrix, both with Singular Value Decomposition, and Eigenvalue - Eigenvector constructions.
Honors Topics:
* To understand and compute interpolating polynomials and Fourier fitting and analysis
* To understand and compute the Gram-Schmidt process in relation to Singular Value Decomposition
* To understand and compute the diagonalization of a matrix when Eigenvalues are repeated and/or complex.
* To understand and compute the relationship of matrix diagonalization and dynamical systems of differential equations
* To understand and compute the Spectral Theorem
* To develop mathematical technical writing skills, culminating in a term paper on an approved topic
DMAT 336 - Syllabus of Topics
1. Getting Started
1.1 Email and Chat
1.2 Learning About the Course
1.3 Required Hardware
1.4 Software Fundamentals
2. Vectors
2.1. Geometry of Vectors
2.2. Perpendicular Frames
2.3. Curves in 2D: Change of Frames/Basis
2.4. Dot Products
2.5. Cross Products
2.6. Ellipses and Ellipsoids
2.7. Area and Volume
3. Matrices
3.1 Basics
3.2 Transforming Curves
3.3 Matrix Arithmetic
3.4 Translations and Rotations
3.5 Shears
3.6 Linear Transformations
3.7 Inverses
3.8 Determinants
3.9 Transposes
3.10 Matrix Decomposition: Singular Value Decomposition
3.11 Rank
3.12 Projections
3.13 Higher Dimensions
4. Linear Systems
4.1 Conversion to Matrix Notation
4.2 Gaussian Elimination
4.3 Vector Spaces and Subspaces
4.4 Numerical Considerations
4.5 Applications: Least Square Fit
4.6 Spanning Sets; Basis
4.7 Linear Independence
4.8 Pseudo Inverses
4.9 Approximate Solutions
4.10 Null Space and Image Space
4.11* Interpolating Polynomials and Trigonometric Functions: Fourier Fit
4.11* Undetermined Coefficients in Differential Equations Systems
5. Eigenvalues and Eigenvectors
5.1 Diagonalization of a Matrix
5.2 Eigenvalues
5.3 Eigenvectors
5.4 Exponential of a Matrix
6.* Honors Topics
6.1* Gram-Schmidt Process and Singular Value Decomposition
6.2* 4D Projections
6.3* Non-Real Eigenvalue and Eigenvectors
6.4* Applications to Dynamical Systems
6.5* Spectral Theorem
7.* Mathematical Writing
7.1* Cogent writing
7.2* Mathematical Presentation
7.3* Term Paper Topic and Research
3D Linear Transformation
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.
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.
Distance Calculus students have transferred course credits to these colleges and universities:
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Distance Calculus - Student Reviews
Hannah J.★★★★★
Posted: Apr 30, 2020
Courses Completed: Probability Theory
Probability Theory was a great course. Very very thorough. I thought it would never end :). I was very prepared for my coursework in economics. Excellent refereshher of derivatives and integrals - really forced me to remember that stuff from freshman cal.
Transferred Credits To: Boston University
Benjamin T.★★★★★
Posted: Apr 10, 2020
Courses Completed: Calculus I
This course provided an excellent chance to learn about Calculus...again. I took calculus in high school, but I learned so much more with this course!
It does take a good amount of time to do all the lessons, so definitely keep on top of them, but all the exercises helped me to really understand the material. And the nice thing is you can do it on your own time at home.
Transferred Credits To: Western University of Health Sciences: College of Optometry
Harlan E.★★★★★
Posted: Apr 29, 2020
Courses Completed: Calculus I, Calculus II
I did not do well in AP Calculus during my senior year in high school. Instead of trying to cram for the AP exam, I decided to jump ship and go to Distance Calculus to complete Calculus I. This was awesome! I finished Calculus I in about 6 weeks, and then I kept going into Calculus II. I started as a freshman at UCLA with both Calculus I and II done!
Transferred Credits To: University of California, Los Angeles
Ryan★★★★★
Posted: Aug 28, 2026
Courses Completed: Finite Math
I will preface this review by saying that if you are looking to take the easiest course possible, cheat through it, and learn as little as possible, this is not the course for you. Below, I will provide my uncensored opinions to this course:
First, this course uses software called LiveMath. This software can be a little bit challenging to get the hang of, but once you do get the hang of it, it's super easy. Remember that for all new things, it takes a bit to get used to it. Overall, I was highly satisfied with this course. I thought that the instructions were extremely detailed, including a video and a textbook explaining every different concept. In addition, this course offered exposure to a lot of different aspects of finite math. I think that many would agree with me on the following, that, you know, when a teacher is passionate about what they are teaching, it is so much more enjoyable, and you can definitely see that in this course. This course can be challenging at times. Maybe it'll be easy for you, maybe it'll be hard, but I think it's important to remember that the things that challenge us are, you know, the things that make us learn and the things that make us better. There's also a math chat option for if you need help or if you have any questions. Overall, I would recommend this course. I actually initially went into this course looking for an easy course to just help me get the credit requirements, but it ended up being an amazing learning experience and completely shifted my perspective on math overall. And another thing that I thought was great in this course is throughout so many different lectures, the professor would explain how each different thing can be applicable in life. And I think that, you know, that is a lot of what people think about when they are learning something. They're like, will I ever use this? Do I need to learn this? And a lot of this actually is really applicable. And I think that even if, you know, you may not be doing these math equations in your future, I think that, you know, the psychology behind these and the rules can be applied to so many different fuacets of life.
Transferred Credits To: GWU
Aiden B.★★★★★
Posted: Jul 29, 2026
Courses Completed: Calculus II, Multivariable Calculus, Differential Equations, Linear Algebra
After completing all the math offered by my highschool, I switched over to Roger Williams for Calculus II and onward. Overall, it has been a pretty great way to understand the topics online, with transferrable college credits. The exams are not terrible, and the courses cover the vast majority (if not all) of topics covered by traditional courses, with some unique ones added to. So far, I have taken four courses, with another one or two before I graduate.
The only problem with the course is the lack of pen and paper work. This shouldn't come as a crazy surprise with an online course, but there is not much emphasis on symbolic computation. Mathematica or other software does most of the heavy computation for you. The lectures usually show how to solve the problems through paper, but those skills are rarely put into practice. Literacy Sheets act as a way to do some of that (especially with the Calculus II & III course).
All in all, this isn't a huge issue. I just memorize and practice things like double integration, Laplace, ODE solving, matrix diagonalized form, row operations, etc. With a little outside work, this resolves itself. Without Roger WIlliams, I probably would not have been able to take any of these math courses in highschool.
So overall, a great choice for highschool advanced math, especially with transferrable credits.
Email: abarger@protonmail.com
Lucas L.★★★★★
Posted: Jun 25, 2026
Courses Completed: Multivariable Calculus
The professor as well as the TAs give great feedback when you need help with problems and the videos are great at explaining concepts. Return time on work is good and the work is not too much to handle.