Geometry and its Applications

Course Description

Have you ever wondered that Geometry can give you an insight into many scientific problems?

Do you know that a wide range of problems in Physics & Maths can be easily solved using Geometry?

Have you ever tried to think in terms of geometrical figures just like the great Archimedes did?

While everybody studies Geometry at some point of time, very few of us actually get a chance to understand its application on Sciences and Engineering. And this one-of-its-kind course shows you how to approach scientific problems through geometry.

Geometry and its Applications online course also shows you how the other branches of mathematics combine with geometry. Real-world application of geometry in areas like finance and, technical analysis of equities and derivatives is also touched upon.

Gain a new perspective on how to solve geometrical problems, theoretical or practical, in a more efficient and shorter way!

For whom is this course meant for?

• A foundation course for high school students
• A refresher course for under-graduate and post-graduate students
• Engineering entrance exam aspirants for shorter and faster methods
• For scientists and engineers for introduction to algebraic geometry
• For research students it will provide a new approach to analyze problems

Structured via 50 LIVE interactive online classes, this course covers all major topics on Geometry and its applications. Additional courseware: Audio Files + PPTs + PDFs + Docs are also available for practice and quick revision purposes.

Geometry and its Applications online course package:

• 50 LIVE interactive online classes + Access to class recordings
• Course Timings in IST: Mon - Sat between 9 AM - 9 PM
• Courseware: Audio Files + PPTs + PDFs + Docs

Geometry and its Applications online course outline:

• Euclid’s Elements
• Axiomatic Systems and Incidence Geometry
• Axioms for Plane Geometry
• Neutral Geometry
• Euclidean Geometry
• Hyperbolic Geometry
• Area
• Circles
• Constructions
• Transformations
• Models
• Polygonal Models and the Geometry of Space
• Rational and Polynomial Parameterizations
• Fractional Linear Transformations
• Cubic Curves
• Cubic Surfaces and General Hyper surfaces
• Outline of the Theory of Plane Curves
• Affine Plane and Projective Plane
• Sphere with Handles
• Functions and Differentials on a curve
• Polynomials and Power Series
• Review of Abstract Algebra
• Some Commutative Algebra
• Hensel’s Lemma and Newton’s Theorem
• More about Newton’s Theorem
• Branches and Valuations
• Divisors of Functions and Differentials
• Weierstrass Preparation Theorem
• Intersection Multiplicity
• Resolution of Singularities of Plane Curves
• Infinitely Near Singularities
• Parameterizing a Quartic with Three Double Points
• Characteristic Pairs
• Criterion For One Place and Jacobian Problem
• Inversion Formula and Jacobian Problem
• Surfaces
• Hyper surfaces
• Resolution of Singularities of Algebraic Surfaces
• Birational and Polyrational Transformations
• Valuations and Birational Correspondence
• Rational Cylinders through a Variety
• Resultants
• Spill-over classes; Q&A Sessions; Pictorial Demonstration of Applications

Each class will be of 2 Hours each.