Math 2.0

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The Geometry of Möbius Transformations 4JZNJ3FFNJ

URIm2://res/4JZNJ3FFNJ
Kindcourse
CreatorsKrishnendu Gongopadhyay (instructor)
Date2026-07-01
Scopein

Expressions

e1: edition

Languageen
Date2026-07-01
Contents
  • part 1: Week 1
  • session 1: Introduction
  • session 2: Complex numbers
  • session 3: Euler's forumula
  • session 4: Orthogonal matrices
  • session 5: Euclidean isometries
  • session 6: Classification of isometries
  • part 2: Week 2
  • session 7: An example
  • session 8: Complex differentiability-I
  • session 9: Complex differentiability-II
  • session 10: Cauchy-Riemann Eqn
  • part 3: Week 3
  • session 11: Cauchy-Riemann revisited
  • session 12: Complex logarithm
  • session 13: Complex Integration
  • session 14: Cauchy Integral Formula
  • part 4: Week 4
  • session 15: Power Series Expansion
  • session 16: Zeros of holomorphic fn
  • session 17: Open Maping thm
  • session 18: Singularity
  • part 5: Week 5
  • session 19: Poles
  • session 20: Essential singularities
  • session 21: Residues
  • session 22: The residue theorem
  • part 6: Week 6
  • session 23: The Riemann Sphere
  • session 24: Meromorphic functions
  • session 25: Rational functions
  • session 26: degree of rational functions
  • session 27: degree theorem and orders
  • part 7: Week 7
  • session 28: Mobius transformation
  • session 29: Mobius transformation-II
  • session 30: anti-automorphism
  • session 31: Generators of Mobius group
  • part 8: Week 8
  • session 32: Circles on Riemann Sphere
  • session 33: Mobius transformation & circles
  • session 34: Cross Ratios
  • session 35: Permutation and cross ratios
  • session 36: Circles and Cross Ratios
  • part 9: Week 9
  • session 37: Group action
  • session 38: Stabiliser of a disc & circle
  • session 39: Standard forms
  • session 40: classification of Mobius transformation
  • part 10: Week 10
  • session 41: Commutator
  • session 42: Commutator and fixed points
  • session 43: Commuting Motions
  • session 44: Centralizers
  • part 11: Week 11
  • session 45: Conformality of stereographic projection
  • session 46: Conformal automorphisms
  • session 47: Conformal maps of spheres
  • session 48: Rotations of Riemann sphere
  • session 49: Subgroup of elliptic elements
  • session 50: Subgroup of elliptic elements-II
  • part 12: Week 12
  • session 51: Finite group of rotations
  • session 52: Elements of arc length
  • session 53: hyperbolic upper half model
  • session 54: Geodesics
  • session 55: Hyperbolic isometries
  • session 56: Concluding words

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