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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.

2D Linear Transformation
2D Linear Transformation
Course
DMAT 336 - Honors Computational Linear Algebra
Credits
5 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced

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
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).


RWU Course Catalog - DMAT 336 • Honors Computational Linear Algebra
Course
DMAT 336
Course Title
Honors Computational Linear Algebra
Transcript Title
Honors Linear Algebra
Credits
5 Semester Credit Hours
Description
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
Software
Mathematica

DMAT 336 - Learning Outcomes

  1. To understand the core connection between matrix algebra and a study of systems of linear equations
  2. To understand and compute measurements of vectors and their geometry
  3. To understand and compute core matrix algebra operations and their geometrical interpretations
  4. To understand and compute the fundamental properties of determinants and inverses of matrices, both for square and non-square generalizations
  5. To understand and compute Singular Value Decomposition
  6. To understand and compute the core concept of rank and its variations
  7. To understand and compute Gaussian elimination and other strategies for finding solutions or approximate solutions to systems of linear equations
  8. To understand and compute bases, change of bases, spanning and linear independence, kernel and image sets
  9. To understand and compute the diagonalization of a matrix, both with Singular Value Decomposition, and Eigenvalue - Eigenvector constructions.
  10. Honors Topics:
  11. * To understand and compute interpolating polynomials and Fourier fitting and analysis
  12. * To understand and compute the Gram-Schmidt process in relation to Singular Value Decomposition
  13. * To understand and compute the diagonalization of a matrix when Eigenvalues are repeated and/or complex.
  14. * To understand and compute the relationship of matrix diagonalization and dynamical systems of differential equations
  15. * To understand and compute the Spectral Theorem
  16. * 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
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.

Sample Curriculum PDFs

MGM.01.B5 - 3D Perpendicular Frames
sample curriculum pdf MGM.01.B5 View PDF
MGM.02.T1 - Hitting with a 2D Matrix
sample curriculum pdf MGM.02.T1 View PDF

Help Movies


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.

Copy/Paste Workflow in Mathematica
Copy/Paste Workflow in Mathematica


Distance Calculus Referenced Colleges & Universities (29 Years - 393+ Institutions)

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 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 • 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 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Distance Calculus - Student Reviews

Carl Conners★★★★★
Posted: Feb 23, 2020
Courses Completed: Multivariable Calculus, Differential Equations, Linear Algebra
After a really rough first year of calculus, I completed all of the second year calculus courses with Distance Calculus. It was like night and day the difference. My first year was so boring and monotonous. Multivariable Calculus, Differential Equations, and Linear Algebra through Distance Calculus were just so much different - so not boring at all. I thoroughly enjoyed these courses. So engaging.
Transferred Credits To: Michigan State University
Cristian Mojica★★★★★
Posted: Jan 8, 2021
Courses Completed: Probability Theory
A fantastic course! I was able to complete it in about half a year (with a few gaps) alongside other coursework I was completing. There are no deadlines except the one-year mark after registering, so you work at your own rate and schedule.

Probability Theory is required for me to apply to Master's programs in Statistics, so I was glad when I found Distance Calculus. While the course was slightly less difficult than I originally expected, there were parts that definitely slowed me down and made me think. (Also, although calculus is not everywhere in the course, it is everywhere in normal and exponential variables and beyond, so make sure to review derivatives and integrals (single and double)!) I used Mathematica for my software, and it helped speed along calculations and proved to be the perfect stage and tool for this material. I think visual learners will absolutely revel in how the material is presented in this course. (I know I did!) As there is plenty of writing and calculation to do, you have many opportunities to develop and strengthen your voice as a mathematician. The modern format of 80% electronic notebook work and 20% handwritten work is an excellent mixture for studying probability theory and grasping its core ideas. Dr. Curtis is clear in his answers to any questions and concerns you may have and is highly responsive to email and chat, and to responses you leave in your notebooks. He truly wants to help you and to see you succeed, and he is always on your side.

I highly recommend Probability Theory with Distance Calculus!
Email: comojica@ucdavis.edu
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
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.
Transferred Credits To: University of Namibia
Henry F.★★★★★
Posted: Dec 18, 2025
Courses Completed: Differential Equations
Transferred Credits To: Saint Joseph High School
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