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 DMAT 335 - Computational Linear Algebra earns 4 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
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).
RWU Course Catalog - DMAT 335 • Computational Linear Algebra
Course
DMAT 335
Course Title
Computational Linear Algebra
Transcript Title
Linear Algebra
Credits
4 Semester Credit Hours
Description
A 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, bases, rank, Eigenvalues and Eigenvectors, matrix decomposition and diagonalization.
Prerequisite
Successful completion (C- or higher) of 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.
DMAT 335 - 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
5. Eigenvalues and Eigenvectors
5.1 Diagonalization of a Matrix
5.2 Eigenvalues
5.3 Eigenvectors
5.4 Exponential of a Matrix
Legacy Course - DMAT 331 • Linear Algebra
In 2023, Distance Calculus introduced a new catalog of courses. New DMAT 335 = Old DMAT 331 = Old MATH 331
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. (3 credits)
Common Completion Timelines for DMAT 335 - Linear Algebra
Hours/Week
Math Skills
Dedication
Completion
Advisory
5-10 hrs/wk
Weaker
1-2 hrs/day
16 weeks
Reasonable
7-12 hrs/wk
Modest
2-3 hrs/day
12 weeks
Reasonable
10-15 hrs/wk
Stronger
3-4 hrs/day
8 weeks
Reasonable
15-20 hrs/wk
Strong
5-6 hrs/day
6 weeks
Stretched
20-25 hrs/wk
Strong
5-7 hrs/day
4 weeks
Stretched
25-35 hrs/wk
Strong
6-8 hrs/day
3 weeks
World's Record
Time commitments are important for success in an online Linear Algebra course for college credit from Distance Calculus. There are no
fixed due dates in the Distance Calculus online courses, so it is important that students instead set their schedules for a dedicated
amount of time towards the coursework.
It is also very important to consider that going faster through a course is DIRECTLY DEPENDENT upon your math skill level,
and your successful engagement of the course. We require that you complete the course in a Mastery Learning format.
If you are struggling with the course content, or trying to go too fast where the quality of your submitted work is suffering, then
the instructors will force a slow-down of your progress through the course, even if you have fixed deadlines.
Samples of Linear Algebra Lecture Movies
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.
Distance Calculus students have transferred course credits to these colleges and universities:
Agnes Scott College • Aiken Technical College • Albany College of Pharmacy and Health Science • Alma College • American Graduate University • American Public University • American University • Andrews University • Arizona State University • Armstrong Atlantic State Univeristy • Athens State University • Auburn University • Auburn University MBA Program • Augusta State University • Austin Peay State University • Azusa Pacific University • Babson College • Baruch College • Baylor University • Belmont University • Beloit College • Bentley University • Berklee College of Music • Berry College • Bethany College • Binghamton University • Bloomsburg University • Bluefield State College • Bluegrass Community and Technical College • Borough of Manhattan Community College • Boston Conservatory • Boston University • Bryant University • Buena Vista University • California Lutheran University • California Polytechnic State University, San Luis Obispo • California state University • California State 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Governor's State University • Green Mountain College • Griffith University • Grinnell College • Grove City College • Hamline University • Hampshire College • Hampton University • Harvard University, Kennedy School of Government • Harvard University: Kennedy School of Government, Medical Schools • Hillsdale College • Hillsdale University • Hiram College • Hofstra University • Howard University • Huntingdon College • Illinois Institute for Technology • Illinois Institute of Technology • Indiana University • Iowa State University • Jacksonville State University • James Madison University • Jeff State Community College • Johns Hopkins Univerisity • Johns Hopkins University • Kalamazoo College • Kansas State University • Kaplan University • Kennesaw State University • Kentucky State University • Kettering University • Kings College, University of London • La Sierra University • Lebanon Valley College • Lee University • LeTourneau University • Liberty University • Lincoln University of 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Michigan University • Northwest Nazarene University • Northwestern University • Oberlin College • Occidental College • Oglethorpe University • Oklahoma Baptist University • Old Dominion University • Olympic College • Orange Coast College • Oregon State University • Pacific Lutheran University • Penn State University • Pennsylvania State University • Pepperdine University • Pomona College • Portland State University • Princeton University • Purdue University • Quinnipiac University • Randolph-Macon College • Regent University • Regis University • Rensselaer Polytechnic Institute • Rhode Island School of Design • Rice University • Robert Morris University • Rochester Institute of Technology • Roger Williams Univerity • Roger Williams University • Roosevelt University • Rowan University • Rutgers University • Saint Anselm College • Saint Joseph's University • Saint Louis University • Saint Michael's College • Salve Regina University • Samford University • San Diego State University • Santa Fe Community College • Shepherd University • Smith College • South Dakota School of Mines and Technology • Southern Adventist University • Southern Methodist University • St. Anselm College • St. John's College • St. Mary's College of Maryland • Stanford University • Stanford University, MBA • State University at Buffalo Law School • State University at Buffalo, Law School • State University of New York • Stevens Institute of Technology • Strayer University • SUNY Binghamton • Swarthmore College • Syracuse University • Texas A&M University • Texas A&M • Texas A&M University • Texas Tech University • The Art Institute of Atlanta • The Catholic University of America • The Citadel • The Citadel, Military College of South Carolina • The College of New Jersey • The College of St. Scholastica • The George Washington University • The Master's College • The New England Institute of Art • The Ohio State Universtity • The University of Alabama • The University of South Carolina • The University of Texas at Austin • The University of Virginia • Thomas Edison State College • Trinity University • TUI University • Tulane University • Union University • United States Air Force Academy • United States Military Academy • Univeristy of Puget Sound • University of Alabama, Huntsville • University of Arizona • University of Arkansas, Little Rock • University of Auckland, New Zealand • University of California, Berkeley • University of California, Los Angeles • University of California, Santa Barbara • University of California, Santa Cruz • University of Central Florida • University of Central Oklahoma • University of Central Texas • University of Chicago • University of Cincinnati • University of Colorado • University of Colorado, Boulder • University of Colorado,Colorado Springs • University of Connecticut • University of Dallas • University of Findlay • University of Florida • University of Georgia • University of Hartford • University of Hawai'i-Manoa • University of Illinois • University of Kentucky • University of La Verne • University of Maine • University of Maryland • University of Massachusetts • University of Massachusetts, Amherst • University of Memphis • University of Michigan • University of Michigan: MBA, Medical Schools, Graduate Programs • University of Minnesota • University of Minnesota, School of Public Health • University of Minnesota, Twin Cities • University of Minnesota-Twin Cities • University of Mississippi • University of Missouri • University of Missouri, Columbia • University of Montana • University Of Mount Union • University of Nebraska • University of Nevada • University of New Hampshire Law School • University of New Haven • University of New Orleans • University of North Carolina • University of North Carolina at Chapel Hill • University of North Carolina, Chapel Hill • University of North Carolina, MBA • University of North Dakota • University of North Texas • University of Northern Iowa • University of Notre Dame • University of Oklahoma • University of Otago • University of Pennsylvania • University of Pennsylvania Architectural School • University of Pennsylvania, Wharton School of Business • University of Phoenix • University of Pittsburgh • University of Portland • University of Redlands • University of Richmond • University of San Francisco • University of South Carolina • University of Southern California • University of Southern Indiana • University of Sussex • University of Tampa • University of Tennessee • University of Texas • University of Texas at Austin • University of Texas, Arlington • University of Texas, Austin • University of Texas, Brownsville • University of Texas, Dallas • University of Texas, Houston • University of Utah • University of Virginia • University of Warwick • University of West Alabama • University of West Florida • University of West Georgia • University of Wisconsin • University of Wisconsin, Madison • University of Wyoming • University West Florida • US Air Force Academy • Utah State University • Utah Valley University • Valdosta State University • Valley Forge Military College • Vanderbilt University • Villanova University • Virginia Military Institute • Virginia Tech • Walla Walla University • Washing State University • Washington and Lee University • Washington State University • Webster University • West Chester University • West Virginia University • West Virginia Wesleyan College • Western Governors University • Western Kentucky University • Western Michigan University • Westminster College • Wharton School of Business, University of Pennsylvania • Wheaton College • Wheaton College (IL) • Wheaton College Illinois • Whitman College • Whittier College • Widener University • William and Mary • William Jewell College • Winthrop University • Woodbury University • Wright State University • Yale University • Yeshiva University • Yonsei University
Distance Calculus - Student Reviews
Samuel H.★★★★☆
Posted: Jun 2, 2021
Courses Completed: Linear Algebra
Nothing but praise for Dr. Curtis. He's an excellent professor who is very responsive and knowledgeable. I did this course at night while working full-time, and I often skyped him late in the evening with questions. He never took long to respond, regardless of when it was. I finished this course in about a month and a half, and I worked for it. For those looking for an easy A, this is not it. You will have to put in serious work, but you will come out of the course with a good understanding of the material, especially if you apply yourself throughout the entirety of the course.
Email: samuel.howell@g.fmarion.edu
Transferred Credits To: Francis Marion University
Daniel Marasco★★★★★
Posted: Jan 13, 2020
Courses Completed: Multivariable Calculus
This course was more affordable than many, and the flexible format was terrific for me, as I am inclined to work very diligently on tasks on my own. It could be dangerous for a person who requires external discipline more, but it works well for self-starters, allowing you to prioritize when you have other pressing work. I was a full time teacher adding a math certification, and this course allowed me to master the math while working around my teaching schedule and fitting work into moments here and there when I had time. I was able to transfer the credits to Montana State University, Bozeman for my teaching internship program without a hitch. The instructors were all very helpful and patient, even when I failed to see a ridiculously simple solution on one problem after 20 emails back and forth. Overall, I was more pleased with my experience in this class than I was with any of my other 9 courses.
Transferred Credits To: Montana State University, Bozeman
Chris M.★★★★★
Posted: May 7, 2025
Courses Completed: Multivariable Calculus, Differential Equations, Linear Algebra, Probability Theory
I've taken Multivariable Calculus, Linear Algebra, Differential Equations, and Probability Theory through Distance Calculus. All four courses were awesome. Dr. Curtis and the TA's were very responsive and helpful.
The biggest advantage of these courses, compared to taking a traditional course, is that in addition to the theory, I was forced to also think computationally. I have become quite adept at using LiveMath and Mathematica for doing calculations and plots.
All of the courses were accepted for credit transfer (Johns Hopkins University)
Email: chrismillermd@me.com
Transferred Credits To: Johns Hopkins University
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.
Transferred Credits To: University of Wisconsin
Hari K.★★★★☆
Posted: Jun 24, 2026
Courses Completed: Linear Algebra
This course gives a perspective on Linear algebra that no traditional course does. I’d say i gained much more intuition for this subject from the DC course than my friends who took traditional courses elsewhere. As a cs major, this version of learning with visualization has helped me a lot in understand ML models. However the course doesn’t have videos for the last 2 chapers so i had to self learn with the mathematica notebooks. Response times are a little slow but since it’s a remote class, i guess it’s justified. Overall amazing course and definitely take this over traditional lin alg classes.
Yes, most definitely. Linear Algebra is one of the core courses needed for starting any degree program in Data Science
Does Linear Algebra Require Calculus II?
Yes, Calculus II is the prerequisite for the Linear Algebra course, but interestingly no Calculus is used in the Linear
Algebra course!
How Fast Can I Complete Linear Algebra?
4-6 Weeks is a very fast but reasonable pace to finish the Linear Algebra course.
When Can I Enroll in Linear Algebra?
Anytime - Enrollment for Distance Calculus courses is on-going - enroll and start the course on the same day
Is Linear Algebra Hard?
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.