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Algebraic Geometry Online Course for Academic Credit

Algebraic Geometry introduces the study of algebraic curves, varieties, and computational techniques using Mathematica.

Clebsch Diagonal Cubic
Heart Surface
Course
DMAT 362 - Introduction to Algebraic Geometry
Credits
4 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Double Folium Curve
Double Folium Curve

RWU Course Catalog - DMAT 362 • Introduction to Algebraic Geometry
Course
DMAT 362
Course Title
Introduction to Algebraic Geometry
Transcript Title
Algebraic Geometry
Credits
4 Semester Credit Hours
Description
An introduction to the study of Algebraic Geometry from elementary formulations, historical perspectives, and modern visualizations of algebraic curves and surfaces, providing tangible examples to give first presentations of groups, rings, and fields. Topics include classical real and complex conics, projective geometry, links to number theory, cubic and elliptic curves, an introduction to groups, higher degree curves and surfaces, and the Riemann-Roch Theorem.
Prerequisite
Successful completion with grade B or higher in Linear Algebra and Multivariable Calculus or equivalent, or consent of instructor.
E-Textbook
Algebraic Geometry - A Problem Solving Approach by Garrity et al.
Software
Mathematica and LiveMath

DMAT 362 - Learning Outcomes

  1. To understand the general topic of Algebraic Geometry from first principles and examples
  2. To understand the historical aspect of Algebraic Geometry leading to its modernization in the 1970s
  3. To understand affine and projective geometry
  4. To understand polynomial equations, their algebra and methods of analysis
  5. To understand singular points
  6. To understand the geometric notion of duality
  7. To understand cubic curves and their natural group structure
  8. To understand introductory group, ring, and field theory
  9. To understand the initial connections between curves and surfaces and group and quotient group structures
  10. To understand and utilize visualization tools such as computer algebra systems

DMAT 362 - 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. Conics
2.1 Conics over the Reals
2.2 Changes of Coordinates
2.3 Conics over the Complex Numbers
2.4 The Complex Projective Plane
2.5 Projective Change of Coordinates
2.6 The Complex Projective Line
2.7 Ellipses, Hyperbolas, and Parabolas as Spheres
2.8 Links to Number Theory
2.9 Degenerate Conics
2.10 Tangents and Singular Points
2.11 Conics via Linear Algebra
2.12 Duality
2.13 Visualization of Real and Complex Curves
3. Cubic Curves and Elliptic Curves
3.1 Cubics in Complex Plane
3.2 Inflection Points
3.3 Group Law
3.4 Normal Forms of Cubics
3.5 Group Law for Smooth Cubic in Canonical Form
3.6 Cross-Ratios and the j-Invariant
3.7 Torus as a Quotient Group of Complex Line
3.8 Mapping Torus Quotient Group to a Cubic
3.9 Cubics as Tori
3.10 Visualization of Real and Complex Curves
4. Higher Degree Curves
4.1 Higher Degree Polynomials and Curves
4.2 Higher Degree Curves as Surfaces
4.3 Bezout Theorem
4.4 The Ring of Regular Functions and Function Fields
4.5 Divisors
4.6 The Riemann-Roch Theorem
4.7 Blowing Up
4.8 27 Lines on a Cubic Surface
4.9 Visualization of Real and Complex Surfaces
Barth Sextic
Tanglecube
Tanglecube

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 Pennsylvania • Lipscomb University • Loma Linda University • London School of Economics • Loyola Marymount University • Luther College • Macon State College • Marian University • Marquette University • Mars Hill College • Marshall University • Mary Baldwin College • Massachusetts Maritime Academy • McHenry County College • Mercer University • Mercyhurst College • Meredith College • Mesa State College • Messiah College • Miami University • Michigan State University • Michigan Technological University • Middle Tennessee State University • Middlebury College • Millersville University • Missouri University of Science and Technology • Montana State University • Montana Tech • Montclair University • Morehead State University • Murray State University • Naval Post Graduate School • New Mexico Military Institute • New Mexico State University • New York University • North Carolina Agricultural and Technical State Univerisity • Northeastern University • Northern Arizona University • Northern 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
Chair Surface
Goursat Surface





Distance Calculus - Student Reviews

Sean Metzger★★★★★
Posted: Aug 23, 2020
Courses Completed: Differential Equations
A lifesaver. When I found out I needed a course done in the last weeks of summer I thought there was no way i'd find one available, but this let me complete the course as quickly as I needed to while still mastering the topics. Professor always got back to me very quickly and got my assignments back to me the next day or day of. Can't recommend this course enough for students in a hurry or who just want to learn at their own pace.
Email: seanmetzger78@gmail.com
Transferred Credits To: Missouri University of Science and Technology
Chester F.★★★★
Posted: May 21, 2020
Courses Completed: Calculus I, Calculus II
I did not enjoy Calculus I at my school. I retook Calculus I, and then Calculus II, over the summer via Distance Calculus and it was awesome. I started my sophomore year back on track and ready for my physics classes. I struggled with the MathLive software but I guess it was alright.
Transferred Credits To: University of North Carolina
Douglas Z.★★★★★
Posted: Jun 6, 2020
Courses Completed: Multivariable Calculus, Differential Equations, Linear Algebra, Probability Theory
I loved these courses. So in depth and comprehensive. The mix of software and math curriculum was tremendously helpful to my future studies and career in engineering. I highly recommend these courses if you are bored of textbook courses.
Transferred Credits To: University of Massachusetts, Amherst
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.
Julia★★★★★
Posted: Jun 24, 2026
Courses Completed: Calculus I
As a full-time business owner completing an Executive MBA, I needed to satisfy a calculus prerequisite without putting my work on hold. Distance Calculus made that possible. The fully self-paced structure let me work early mornings and weekends around an unpredictable schedule, which a fixed-semester classroom course never would have allowed.
The course covered the core business calculus material thoroughly — derivatives, optimization, integration techniques including u-substitution, the Fundamental Theorem of Calculus, improper integrals, and numerical methods. The LiveMath computer algebra environment was central to the experience: it forced me to build each step explicitly rather than just arriving at an answer, which actually deepened my understanding of the mechanics.
Communication through the student portal was responsive when I had questions. For working professionals who need a rigorous, accredited calculus course on a flexible timeline, I'd recommend it.
Transferred Credits To: MIT Ebma
Barth Sextic (alternate view)
 
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