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Mathematics

How To Really Solve This Tricky Algebra Problem (VIII)

Published on September 27, 2022 by Hemanth

How To Really Solve This Tricky Algebra Problem (VIII) - On the left-hand side, two equations are hand-written: xy + z = 1000; x + yz = 1001; Given these equations, on the right-hand side, the following questions are written down: x = ??; y = ??; z = ?? Below these questions, the author writes that x, y, and z belong to the set of all integers.
The Tricky Algebra Problem Series celebrates the joy of algebra! Problems range from beginner to advanced levels. This one has an easy difficulty level!
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Calculus (VII): How To Differentiate Constants?

Published on September 26, 2022 by Hemanth

Calculus (VII): How To Differentiate Constants? - An illustration showing that d(ax²)/dx = 2ax. Below this equation, the following question is asked: "But How??"
The seventh entry in the calculus series — an account on how to differentiate constants. This essay uses the product rule to formally differentiate constants.
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Modern Math Is Full Of Symbols. Is This Really Necessary?

Published on September 24, 2022 by Hemanth

Modern Math Is Full Of Symbols. Is This Really Necessary? - On the left is seen, a snippet from Johannes Wildmann's book for merchants. The language is old German. And the snippet seems to suggest 'plus' and 'minus' symbols for the usage of merchants. On the right, the author poses the following question: "How much is too much?"
It is no secret that modern math is full of symbols. Not only does this drive young students away, but even experts face problems. Just how much is too much?!
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Correlation (III): How To Avoid Berkson’s paradox

Published on September 21, 2022 by Hemanth

Correlation (III): How To Avoid Berkson's Paradox - An illustration showing a stick-figure with a chef's hat stirring dough in a pan while holding an engaged look on its face. It is quoted saying "I'm skilled and ethical."
Berkson’s paradox traps researchers into thinking that there is correlation between two variables when there is not. This essay shows how to avoid this trap!
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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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