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Online Courses in Geometry
The following geometry courses are commonly offered online.
- Calculus and Analytic Geometry Course: The level I course covers analytic geometry, continuity, limits and functions, as well as differentiation and integration and their applications. Topics in level II include integration techniques, conic sections, polar coordinates, infinite series and two- and three-dimensional vectors.
- Geometry Course: This undergraduate geometry course studies parallel postulates systematically, looking at both Euclidean and non-Euclidean geometry. Prerequisites for this course are linear algebra and calculus I and II.
- Introduction to Differential Geometry Course: Students learn about two- and three-dimensional surfaces and curves using linear algebra, multi-variable calculus and differential equations. The Frenet frame and Gauss's 'Remarkable Theorem' (Theorema Egregium) are among topics examined in the course.
- Axiomatic Geometry Course: Students learn how the axiomatic approach is used in the development of Euclidean and hyperbolic geometry. Linear algebra is a prerequisite to the course.
- Introduction to Arithmetic Geometry Course: Arithmetic geometry is a mathematical field that combines number theory with algebraic geometry. The course presents a modern take on classical theories, such as Diophantine problems.
- Geometry and Quantum Theory Course: This online course covers the relationship between geometric concepts and quantum field theory. An advanced course, lessons look at classical field theory, quantum theories, and Feynman diagrams in order to allow students to become conversant in topics related to quantum fields and string theory.
- Introduction to Topology Course: Topology is a field that grew out of geometry and explores similar issues of space and shape. Students in an online topology course will learn about continuous functions, connectedness, topological spaces, metrization theorems, and other topics.
- Geometric Combinatorics Course: Combinatorial geometry is a somewhat specialized online course in geometry. The course focuses on computational geometry and discrete geometry, and also covers various important problems in the field, both solved and unsolved.
Students will find a variety of online geometry courses through universities that have online offerings. Many are required college credit courses for both online and on-campus bachelor's and master's degree programs in mathematics. Some online geometry courses necessitate the use of specific operating systems, such as Windows, to execute mathematical tasks.
There are also a number of Open Courseware classes in geometry that students can take at any time by accessing video lectures. These are college-level courses, but they do not give college credit and are free.
Online courses in geometry are a great way to learn about topics covering the entire field of geometry, from introductory and general geometry topics to advanced or specialized topics, like quantum theory. These courses are available on their own, and some are available for free to those interested.