Algebraic Geometry Online Course for Academic Credit
Algebraic Geometry introduces the study of algebraic curves, varieties, and computational techniques using Mathematica.
Course
DMAT 362 - Introduction to Algebraic Geometry
Credits
4 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
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
Syllabus PDF
DMAT 362 - Learning Outcomes
- To understand the general topic of Algebraic Geometry from first principles and examples
- To understand the historical aspect of Algebraic Geometry leading to its modernization in the 1970s
- To understand affine and projective geometry
- To understand polynomial equations, their algebra and methods of analysis
- To understand singular points
- To understand the geometric notion of duality
- To understand cubic curves and their natural group structure
- To understand introductory group, ring, and field theory
- To understand the initial connections between curves and surfaces and group and quotient group structures
- 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
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 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Distance Calculus - Student Reviews
Posted: May 17, 2025
Courses Completed: Linear Algebra
Online learning for math is certainly a different way of learning than most are used to in school - However, Distance Calculus does a great job of providing valuable feedback and tips on each assignment, and the professor is always available for detailed instruction and help. Tools like Mathematica provide an environment for learning with a lot more freedom and opportunity for exploration of concepts than the regular classroom setting.
Transferred Credits To: Chaminade University of Honolulu
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
Posted: May 3, 2018
Courses Completed: Calculus I, Calculus II
I needed to finish the Business Calculus course very very very fast before my MBA degree at Wharton started. With the AWESOME help of Diane, I finished the course in about 3 weeks, allowing me to start Wharton on time. Thanks Diane!
Transferred Credits To: Wharton School of Business, University of Pennsylvania
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
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
Posted: Dec 18, 2025
Courses Completed: Differential Equations
Transferred Credits To: Saint Joseph High School
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