Misconceptions in Mathematics | Mathematics concepts | How to overcome misconception in mathematics

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How to overcome misconception in mathematics? What causes those misconceptions? In this video, you will be learning the root case for the misconceptions in mathematics. You will also learn that how translating or drawing analogies with daily objects always does not make sense. This video, will teach you to identify the common misconceptions about mathematics and physics as well how you can overcome these misconceptions. I have also demonstrated using simple examples what are the common misconceptions, their reason and the way you can overcome them, By doing this, you will do mathematics much better and you will also fell motivated and happy, feeling that yes, you can also do mathematics.

00:00 - 02:14 - What is the problem in mathematics
02:15 - 06:30 - Analogies are not always perfect
06:31 - 11:43 - Misconception about Vectors
11:44 - 13:42 - Misconception about negative
13:43 - 15:59 - What is an equation
16:00 - 17:39 - Flipping of the coin
17:40 - 20:29 - Misconception about derivative
20:30 - 23:37 - How to unlearn mathematical concepts
23:38 - 27:13 - How to overcome misconceptions in mathematics
27:14 - 30:02 - Summary

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My name is Shounak. I teach in a college. My subject of specialization is the general theory of relativity, tensor calculus, and topology. I also teach communicative English.

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[jullyanolino]

Insightful.

Thank you so much for your lectures.

You are serving the human civilization in a promising way!

[rknowling]

Just an observation about "negative" meaning an opposite operation: As a notational convenience, it is sometimes useful to write the nth derivative of function f(x) as f^(n)(x). In this notation, f^(-n)(x) would be the nth repeated integral of f(x). Then we can extend n to be any sort of number we like, not just integers, and enter the realm of fractional calculus operators.
Or how I independently imagined tensors/ "hypermatrices" into existence by thinking "what if matrices were 3 or more dimensional arrays of numbers?" Then discovered they already existed and were called tensors haha. (Of course now I know that tensors have additional special properties, but that is another story).
Thus *sometimes* we can use an analogy (or notation) to extend an existing idea, leading us to create mathematical objects/ operations that we had not considered.
But I agree, sometimes analogies can also be dangerously limiting. To quote William Blake, "mind-forged manacles".

[nilimananda]

Thanks sir for the video
It is very helpful sir 🙏

[HisHigherness]

To me a vector is a direction of a well cone... Which emanates from a quantum field.. How close, or far off am I, in this idea? ..
I wonder 🤔

[YouMeverse]

In pure mathematics, abstract concepts cannot be visualized or represented physically in every equation we solve. If this is true, then without any tangible reference or physical embodiment, how do pure mathematicians solve problems? In other words, if there is nothing to reference or relate to, how do mathematicians approach problem-solving?