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Calculus (IX): How To Really Understand The Product Rule

Published on October 10, 2022 by Hemanth

Calculus (IX): How To Really Understand The Product Rule - An illustration with whiteboard graphics showing the following information: u(x) = 3x² + 2; v(x) = 2x + 8; y(x) = [u(x)]*[v(x)]; dy/dx = ??
In this 9th calculus series essay, we cover the product rule of differentiation. Learn how to actually use the first principles behind the product rule!
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The Sleeping Beauty Problem: How To Really Solve It?

Published on October 7, 2022 by Hemanth

The Sleeping Beauty Problem: How To Really Solve It? - An illustration that shows the sleeping beauty (stick figure)fast asleep on the right. On her left is a decision flowchart. First, a coin is tossed on Sunday. If the coin lands heads, the flowchart concludes on Monday. If the coin lands tails on Sunday, the experiment is repeated on Monday, and then concluded on Tuesday. What could the sleeping beauty problem be about?
The sleeping beauty problem is a highly controversial decision theory puzzle. It divides experts until this day. Check out what the controversy is all about!
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Fallacy: How To Really Understand It?

Published on October 6, 2022 by Hemanth

How To Really Understand The Notion Of Fallacy? - An illustration showing two stick figures representing two speakers over speaking tables arguing. The stick figure on the left says, "Your logic is weak!" The stick figure on the right asks in return, "How weak is it exactly?"
Fallacy is a term that is often misused in the name of science. This essay explains the formal usage of fallacy and helps you avoid pseudoscientific arguments.
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To Infinity And Beyond? – What Is The Final Destination?

Published on October 5, 2022 by Hemanth

To Infinity And Beyond? - What Is The Final Destination? - An illustration showing white board graphics: limit (t tends to infinity) [Humanity as a function of t = What??]
The phrase “to infinity and beyond” might turn Buzz Lightyear on, but is it the final destination for us? Let us ponder the distant future of humanity and tech!
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Calculus (VIII): How To Learn The Sum Rule And The Difference Rule

Published on October 4, 2022 by Hemanth

Calculus (VIII): How To Learn Sum Rule And Difference Rule - An illustration showing the following information using white board graphics: u = f(x); v = f(x); y = f(x) = (u + v); → dy/dx = ??
In this 8th calculus essay, you learn the basic math behind the sum rule and the difference rule. Get to know WHY the rules of differentiation actually work!
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Tricky Logic Puzzle (IV): How To Really Solve It?

Published on September 30, 2022 by Hemanth

Tricky Logic Puzzle (IV): How To Really Solve It? - An illustration showing a row five turned-on light bulbs. Beside this row, a robot named "Cheat" appears to be in a puzzled state.
Welcome to the fourth entry in the tricky logic puzzle series. Test your logical reasoning skills with this light bulb puzzle! This time, Cheat is backl!
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Polls Mislead Most Of The Time. Here’s Why.

Published on September 29, 2022 by Hemanth

Polls Mislead Most Of The Time. Here's Why. - A stick figure with an emotionless face holding options A and B on either hand. Above its head floats option C. Two question marks (??) are presented in bubbles as being the thoughts inside the head of the stick figure.
As counterintuitive as it might sound, polls mislead most of the time. This essay explains the math and logic behind this fallacy and how you may avoid it!
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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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