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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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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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Calculus (II): What Is A Limit? How To Really Grasp It?

Published on August 29, 2022 by Hemanth

Calculus (II): What Is A Limit? How To Really Grasp It?- An illustration showing a limit of x tending to 'L' that applies to a function f of 'x'. The limit part is highlighted and arrows point towards two question marks. This illustration seems to ask the reader what this limit is supposed to mean.
Seldom does any calculus user learn the core fundamentals behind what is a limit. For instance, did you know that a derivative is actually a limit?
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Regression To The Mean: Why Success Fades With Time

Published on August 27, 2022 by Hemanth

Regression To The Mean: Why Success Fades With Time - An illustration showing a breakfast table with a stern looking father (wearing glasses) sitting with folded hands on the right, and a happy and cheerful little girl seated on the left. The girl seems to be saying the following, "My grades are not falling. They are regressing to the mean!"
Regression to the mean is an extremely deceptive statistics concept. It makes sure that any amount of success fades with time. It deceives even the ‘experts’!
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Calculus: How To Really Understand A Function

Published on August 23, 2022 by Hemanth

Calculus: How To Really Understand A Function - An illustration showing a 2-dimensional cartesian x-y plane. There is a circle in the upper-right quadrant. The text above it says "NOT A FUNCTION". There is another curve that is convex in upper-left quadrant and concave in the lower-right quadrant. It looks like a wave. The text above it says "FUNCTION".
In calculus, the function is arguably one of the most basic concepts. In this essay, experience a deep dive into this concept and its related technical terms.
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Can You Really Solve This Tricky Math Puzzle?

Published on August 21, 2022 by Hemanth

Can You Really Solve This Tricky Math Puzzle? - An illustration showing a weighing scale that has a 40 Kilogram object on the right-hand side pan. On the left-hand side pan, there is an unknown box that is marked 'x'. The right-hand side is lower than the left-hand side. Below the weighing scale, the following text is written: "How Many Weights?"
This tricky math puzzle requires you to solve for the minimum number of weights you could use to balance 40 Kilograms. It stumped me. Can you fare better?
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