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Calculus (VI): How To Really Learn The Power Rule?

Published on September 18, 2022 by Hemanth

Calculus (VI): How To Really Learn The Power Rule? - An illustration showing that d(x²)/dx = 2x. Below this equation, the following question is asked: "But How??"
The power rule is arguably the most frequently used calculus rule. This essay presents the mathematical fundamentals behind this useful rule in detail!
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Correlation (II): How To Spot The Surrogate Endpoint Problem?

Published on September 17, 2022 by Hemanth

Correlation (II): How To Spot The Surrogate Endpoint Problem? - A cartoon illustration showing two stick figures. On the left, a happy stick figure says, "To complete the study, we have to wait for you to die!" On the right, a sad stick figure with a green face seems uncomfortable with the conversation.
More than 130 years after the discovery of correlation, the surrogate endpoint problem is still unsolved. It tricks researchers into making false conclusions.
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Calculus (V): How To Differentiate, Actually?

Published on September 14, 2022 by Hemanth

Calculus (V): How To Differentiate, Actually? - y = f(x) = x² → dy/dx = ??
Knowing how to differentiate is one of the fundamental prerequisites of calculus. Learn the math and motivation behind the ‘dy/dx’ computation in this essay!
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Learning Better Using Tacit Knowledge

Published on September 12, 2022 by Hemanth

Learning Better Using Tacit Knowledge? - An illustration stating the following: "Know-How Vs. Know-What"
Tacit knowledge is not only essential for learning better but also for highly personalized expertise. Be an expert whilst being YOU at the same time!
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Calculus (IV): How To Replace Limits With Infinitesimals?

Published on September 11, 2022 by Hemanth

Calculus (IV): How To Replace Limits With Infinitesimals? - An illustration asking for the value of lim x →0, sin(x)/x = ??; The 'lim' limit is struck diagonally. What could this mean?
This essay is all about an alternative version of calculus that aims to replace limits with infinitesimals. The history behind infinitesimal calculus is rough!
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Ant On A Rubber Rope Paradox – How To Solve It?

Published on September 9, 2022 by Hemanth

Ant On A Rubber Rope Paradox - How To Solve It? - An illustration showing a black ant crawling on a pink rope. The ant is crawling at the rate of 1 cm/s, while the rope is stretching at the rate of 1 km/s. Below, the following text is written: "Can the ant make it??"
The Ant on a rubber rope paradox exposes intuition's blind side via mathematical logic. Will a slow-moving ant ever reach the end of a faster stretching rope?
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Can You Really Solve This Tricky Logic Puzzle (III)?

Published on September 8, 2022 by Hemanth

Can You Really Solve This Tricky Logic Puzzle (III)? - An illustration showing four smiling stick figures collectively saying "Every person next to me is a liar!" Below them, the following question is posed: "How many liars?"
Welcome to the third entry in the tricky logic puzzle series. Test your verbal reasoning skills as well as your spatial reasoning skills with this puzzle!
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Correlation: One Of The Most Misunderstood Concepts In Science

Published on September 5, 2022 by Hemanth

Correlation: One Of The Most Misunderstood Concepts In Science - An illustration featuring a comic, where a stick figure standing behind an announcer table is pointing to a presentation of what appears like linear regression data. The stick figure says, "Here, we see correlation between correlation and causation!"
Correlation is at the heart of scientific discovery. Yet, researchers abundantly misread this term. This essay covers the counter-intuitive math behind it.
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Calculus (III): What Is A Derivative? How To Really Integrate Differentials?

Published on September 3, 2022 by Hemanth

Calculus (III): What Is A Derivative? How To Really Integrate It? - An illustration showing a fast moving car driven by a stick figure on the left. On the right, the following question is written ∫dx = ??
When it comes really understanding what a derivative means, many people take things for granted. People seldom ask the fundamental questions. This essay does!
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How To Actually Solve The Bouncing Ball Puzzle?

Published on August 30, 2022 by Hemanth

How To Actually Solve The Bouncing Ball Puzzle? - An illustration showing a ball bouncing multiple times. With each bounce, the height covered by the ball seems to be lower and lower.
The bouncing ball puzzle features a special elastic ball than bounces an infinite number of times. To solve it, you will need a strong grasp of ‘Limits’.
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