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:
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University Channel Islands • California State University, Dominguez Hills • California State University, Sacramento • Carleton College • Carnegie Mellon University • Cedarville University • Central Michigan University • Central Washington University • Champlain College • Chapman University • Charter Oak State College • Chicago State University • Clark University • Clarkson University • Clemson University • Cleveland State University • Coastal Carolina University • College of Santa Fe • College of William & Mary • Colorado Mesa University • Colorado State University • Columbia University • Columbia University School of Business • Cornell Univeristy • Cornell University • Covenant College • CUNY Medgar Evers College • Denison University • DePaul University • Drexel University • Duke University - Fuqua School of Business • Duke University School of Law • Duke University, Durham NC • Duke University, Fuqua School of Business, Law School, Graduate Programs • East Stroudsburg University • Eastern Illinois University • Eastern Kentucky University • Eastern Mennonite University • Eastern Nazarene College • Elon University • Embry Riddle Aeronautical University • Embry Riddle University • Endicott College • Evangel University • Excelsior College • Fairifield University • Fairleigh Dickenson University • Ferris State University • Florida A & M University • Florida Agricultural and Mechanical University • Florida Atlantic University • Florida Institute of Technology • Florida International University • Florida State College, Jacksonville • Florida State University • Fordham University • Fox Valley Technical College • Franklin University • Freed-Hardamen University • Fresno State University • Friends University • Gannon University • George Mason university • George Washington University • George Washington University School of Business • Georgetown University • Georgia Institute of Technology • Georgia State • Georgia State University • Georgia Tech • Gordon College • 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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 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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
Andris H.★★★★★
Posted: May 3, 2020
Courses Completed: Applied Calculus
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
Ian M.★★★★★
Posted: May 18, 2025
Courses Completed: Multivariable Calculus
Distance Calculus was a life saver! I needed an accredited program to complete multi-variable calculus for grad school and at the time was an American living in England. Being able to take the course on my own timeline, from my own home, was amazing! The content was thorough and the visualization exercises were very helpful for comprehension and understanding. This was an exceptionally, affordable, thorough, and convenient course that I found a lot of value in and I’m thankful it was available to me!
Transferred Credits To: Air Force Institute of Technology
M M.★★★★★
Posted: Feb 8, 2026
Courses Completed: Precalculus, Calculus I
The courses were excellent. Very flexible and engaging and the platform offers a lot of upper-level courses. Dr. Curtis is an outstanding professor and very responsive. I would take again.
Transferred Credits To: None yet
Tanja B.★★★★★
Posted: Jan 28, 2026
Courses Completed: Calculus I
After two failed attempts at my university, this course helped me understand Calculus. The live maths tool along with Dr. Curtis were especially helpful, allowing me to visualize concepts and expand my understanding. The explanations were clear, the examples practical, and I could learn at my own pace, which built my confidence. Thank you.
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.