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Projective Geometry
BY
Udemy
Gain a practical understanding of the essential concepts of projective geometry to gain the knowledge needed to prepare ...Read more
Online
₹ 455 3499
Quick Facts
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Medium of instructions
English
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Mode of learning
Self study
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Mode of Delivery
Video and Text Based
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Course overview
Projective geometry is an application of Euclidean geometry, in which there is no notion of length or degree measurement. It can logically be defined as containing just coordinates and line segments. Projective Geometry online certification is created by Dr. Michael Sun - a professional mathematician, which is presented by Udemy and is designed for applicants who wish to learn about one of mathematics' most stunning achievements.
Projective Geometry online focuses on assisting applicants in understanding the majority of the concepts developed with construction, perspectives theories, and presenting 3D objects on a 2D plane. Projective Geometry online classes include almost 40.5 hours of video-based content, 14 downloadable resources, 16 articles, and assignments that cover topics such as duality, axiomatic method, Desargues theorem, and Pappus' theorem, among others.
The highlights
- Certificate of completion
- Self-paced course
- 40.5 hours of pre-recorded video content
- 16 articles
- 14 downloadable resources
- Assignments
Program offerings
- Online course
- Learning resources. 30-day money-back guarantee
- Unlimited access
- Accessible on mobile devices and tv
Course and certificate fees
Fees information
₹ 455 ₹3,499
certificate availability
Yes
certificate providing authority
Udemy
What you will learn
Mathematical skill
After completing the Projective Geometry certification course, candidates will acquire a deep understanding of the fundamentals theorem of projective geometry in the mathematics discipline. Candidates will explore the methodologies associated with geometry like duality, projective and axiomatic methods. Candidates will learn how to work with homogeneous coordinates, harmonic sets, quadrangular sets, and harmonic quads using various approaches.
The syllabus
Introduction
Chapter 1: Projectivities
- Perspectivities
- ABCD ^ BADC (Theorem 1.63)
- Example of Projectivity
- Another example
- 1.6 Exercise 1
Chapter 2: Complete quads
- 2.1 Axioms
- 2.1 Exercise 2
- 2.2 Exercise 1
- 2.4 Quadangular sets
- 2.4 Exercise 1
- 2.4 Exercise 2
- 2.5 Harmonic sets (plus Ex 5)
- 2.5 Exercise 1
- 2.5 Exercises 2 and 3
- 2.5 Exercise 6
Chapter 3
- Intro
- Dual of Desargues' Theorem
- 3.1 Exercise 1
- 2D Axioms and Duality
- 3.3 Harmonic lines from harmonic points
- 3.5 Harmonic nets
Chapter 4: Fundamental Theorem of Projective Geometry
- Axiom 2.18 is the Fundamental Theorem
- 4.22 When Projectivity is Perspectivity
- Desargues' Theorem
- Pappus' Theorem
Euclidean geometry interlude
- Summary without proof
- Polar of a point w.r.t circle
- H(AB;CF) ^ H(CB;AF)
- Cross ratio -1 means Harmonic
- Harmonic Quads (parallel tangents)
- Harmonic Quads (intersecting tangents)
- 2010 IMO Shortlist G1
Missing cross ratio proofs
- Elementary correspondence preserves ratio
- Cyclic ratio well-defined
- Perspective cyclic quads
- 2010 IMO 4 G2
- 2010 IMO 2 G4
- 5 mins later (G4)
- Pascal's Theorem proved projectively
- Projective Butterfly Theorem
Further projective geometry
- Chapter 5-12 Overview
- 5.4 Involutions with a fixed point
- 6.41 Correlation projective on one range/pencil
- 7.11 Polarities one
- 7.11 Polarities two
- 7.13 Projectivity from a Polarity
- 8.1 Conic from a polarity
- 8.2 Polarity from a conic
Ch 12: Homogeneous Coordinates
- 12.1 Exercise
- Determinant calculations
- 12.2 Definitions and determinants
- 12.2 Exercises 1-6
- 12.3 live
- 12.3 Exercise 9 Cross Ratios
- 12.8 part 1 of 3
Ch 5 in detail
- 5.1 Parabolic P
- Understood 5.1 and 5.2
- 5.3 Involutions generate 1D projectivities
Assignments
- Emailed
Chapter 6 in detail
- 6.11 Projective Collineations
- 6.12 then 3
- 6.1 Exercise
- 6.2 Homology and Elation
- 6.24 onward
- 6.3 Involutary collineations
- 6.42 Correlations on quads
Ch 10: Finite projective Geometry
- 10.1 How many points?
- 10.1 Exercise 2 How many triangles?
- 10.3 Exercise 2 Fano labels
- PG(2,3)
- 10.2 Exercises
- 10.2 PG(2,5)
- 10.3 all but last axiom
- 10.3 Last axiom
- 10.6 part 1 of 3
- 10.6 part 2 of 3
- 10.6 part 3 of 3
Steiner's Theorem (Ch8 completed)
- 8.31 Seydewitz Theorem
- 8.32 Steiner's Theorem
- Degenerate cases in Steiner's Theorem
- Steiner's Theorem explained
- Pascal's Theorem
- Braickenridge Maclaurin construction
- 11.1 Circle is a conic
Ch12 continued
- 12.4 part 2
- 12.4 part 3
- 12.4 end
- 12.5 polarities
- 12.5 end
- 12.6 conics
- 12.6 end
- 12.7 PG(2,5) coordinates
- 12.8 part 2 of 3
- 12.8 part 3 of 3
Skipped chapters
- Extension/Appendix
Instructors
Dr Michael Sun
Instructor
Freelancer
Articles
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