2019 undergrad from IIT Guwahati. Have qualified NTSE, KVPY, multiple Olympiads... Wrote CSE mains 2020.

Utkarsh Ujjwal

This course deals with fascinating results/ theorems/instances of the past etc. that shaped the world of Mathematics. This course is meant to help the learners develop inherent interest in Maths and numbers.

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This is the overview lesson of this must watch course on Mathematics. This course deals with many fascinating mathematical results, theorems, instances etc that shaped the world of mathematics. Presented in a very interactive manner, this course will help everyone who fears mathematics and numbers. Also, this course is beneficial for any student preparing for Mathematical Olympiads (RMO, INMO, IMO etc)

Overview of the Course

Here, Utkarsh has discussed a problem posed in 1644 which remained unsolved for 90 years. He has shown, with the help of sufficient illustrations how the answer, which seems so strange does exist. He has also discussed how different Mathematicians approached the problem to get the precise sum.

Basel Problem - An Infinite Series of Surprises: Part 1

In this lesson, Utkarsh has explained in a detailed manner, the method used by Euler in 1735 to solve the Basel Problem. He has also discussed how Euler thought of the method and how he developed on the idea.

Basel Problem - An Infinite Series of Surprises: Part 2

In this lesson, Utkarsh has discussed a real life incident where Ramanujan solved a Diophantine Equation within seconds using the method of Continued Fractions. Utkarsh has also explained the concept of Continued Fractions so that the method proposed by Ramanujan is easily understandable.

Ramanujan and Continued Fractions: A Beautiful Love Story: Part 1

Here, Utkarsh has explained the Continued Fraction that solves the problem given to Ramanujan by P. C. Mahalanobis. The solution to the Pell's Equation is also explained in a very lucid manner.

Ramanujan and Continued Fractions: A Beautiful Love Story: Part 2

In this lesson , Utkarsh has discussed and fully solved an Elementary Geometry Problem posed in 1922 by Edward Mann Langley that became very popular for being notoriously difficult to solve in spite of the problem statement looking extremely easy. Utkarsh has shown how the problem can be solved only by using elementary Geometry if  constructions are done intelligently.

World's Hardest - Easy Geometry Problem (Langley's Adventitious Angles Problem)

In this lesson, Utkarsh has discussed the Golden ratio and Fibonacci sequences in detail. The lesson also covers the fascinating properties and widespread use of these two Mathematical topics. Utkarsh has given examples of how these things are present everywhere in nature and how they are closely related with each other.

Fibonacci Sequence - Where Mathematics Turns Golden

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Lessons

7 lessons • 1h 20m