Geometry is one of the richest areas for mathematical exploration. The visual aspects of the subject make exploration and experimentation natural and intuitive. At the same time, the abstractions developed to explain geometric patterns and connections make the subject extremely powerful and applicable to a wide variety of physical situations. In this book [and course] we give equal weight to intuitive and imaginative exploration of geometry, and to abstract reasoning and proof.This course is a practical introduction Non-Euclidean geometry from an experimental viewpoint. It is also a thorough review of axiomatic and analytical Euclidean geometry, as well as a gentle introduction to complex numbers. It also serves as an introduction to rigorous proofs and good mathematical exposition. While experience with plane vectors (MA 241) and symbolic logic (MA 347) are recommended, motivated students may complete supplementary lessons to learn these techniques early in the term. The course may be taken for 3 or 4 credit hours.From the Introduction of Hvidsten't text
To pursue these twin goals quoted above, we use a balanced mixture of contemporary online and classical learning techniques. All lessons are held in a computer equipped classroom. Hvidsten's temporarily out of print textbook is online together with extensive notes, explanations, examples, tutorials and exercises. We use a custom edition of his geometric drawing software, Geometry Explorer (GEX), which downloads to all platforms. Students have the opportunity to learn and use LaTeX, the universal scientific and technical typesetting tool, with our custom webtool texWins. Students also keep a hand-written journal of what they have learned, which may be used during tests. We use the ATLAS Moodle for online consultation, discussion, and submission of homework. Daily work (30%), tests(40%) and the final (30%) are announced in the online syllabus.