"If you want to create a different kind of tomorrow, you have to take time today for personal growth and development." There are many ways in which we can do this. One way is by reading books that enrich and educate the mind. You can start by reading Les Miserables from Victor Hugo or The Alchemist from Paulo Coelho.
Another way is through taking online courses with Coursera or edX. There are over 2200 free online courses offered by top universities like Harvard, Stanford, MIT, University of Tokyo and more. You could take courses on algebra, macroeconomics, machine learning, algebraic topology and more.
There are many other ways as well. You can learn new things by trying out new activities, volunteering in an organization that is dedicated to social causes or starting a business idea that you have been thinking about for long.
Once you start doing these things regularly, it will become a habit and you won't need to make so much of an effort to keep doing them. And eventually, you will see positive results in the form of increased confidence levels and better personal growth. [ARTICLE END]
Updated on 16 February 2016: I revised some grammar mistakes that I had made in this article earlier.
Updated on 21 August 2016: I added a new paragraph about online courses with Coursera and edX for the reader's benefit.
Updated on 29 January 2017: I have removed the reference to The Alchemist in the article's introduction because the book has been given away for free by its publisher downloadfreeebooks.net. It is against copyright laws to give away a copyrighted book for free, and so this has not been done by any other publisher or website.
Updated on 27 May 2017: I have added a new paragraph that discusses ways in which one could explore personal growth through reading books and taking online courses. Any suggestions for improvements in this article are welcome.
Updated on 3 December 2017: I have added a new paragraph on how you can learn new things by trying out new activities, volunteering in an organization or starting a business idea that you have been thinking about for long. This article has also been translated into Persian by Parvaneh Nasiri on her blog click here .
Updated on 24 June 2018: I have updated the links.
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1. What is the role of creativity?
2. What is the difference between science and mathematics?
3. When was mathematical thinking discovered and who was the first to do it?
4. What are the two ways in which numbers can be written?
5. How is mathematics useful in solving problems in everyday life? (If you haven't read this chapter yet, please do! There is a lot of interesting stuff here. I'll show you why we haven't figured out how to make a perpetual motion machine!)
6. What is the difference between the numbers 2 and 2?
7. How is mathematics similar to music?
8. What is the difference between length and distance?
9. Can you give an example of a problem where you have to measure length, weight, and time when doing a job? (These are all 'measurement problems'.)
10. In what way does mathematics help us communicate with others, both verbally and non-verbally? (If you haven't read this chapter yet, please do! There is a lot of interesting stuff here.)
11. How are measurement and estimation related to each other?
12. How can you estimate the height of a building using a barometer?
13. How can you find out the distance between two places without using a measuring tape?
14. Why are estimation problems not measurable?
15. How does the language of mathematics make it easier for us to solve problems in everyday life?
16. What do we mean by the language of mathematics?
17. What is the connection between geometry and music? (I am discussing this in an upcoming blog post.) 18. What is the difference between the set of numbers and the counting numbers?
19. How is a group of geometric shapes similar to a group of apples?
20. How is mathematics similar to art and music?
21. Are there any problems that cannot be solved using simple mathematics?
22. Why do you think mathematics isn't taught in elementary schools the way science is? (This question is asked in this chapter.) 23. What should be taught and what shouldn't be taught in schools? (This question is asked in this chapter.) 24. How would you define science, maths and engineering ? 25. Is mathematics an art or a science ? (Read both my answers .) 26. Why do you think that more girls are interested in maths than boys? 27. Why do you think that more girls are interested in art and music than boys? 28. What is the connection between the five senses and small groups of numbers ?
29. What is the difference between a mathematical idea and a mathematical proof? 30. Can you define maths , math , geometry and arithmetic as opposites or as synonyms? 31. Is it impossible to solve problems using only pure mathematics? 32. How can we benefit from using pure mathematics without any application of it ? 33. In what way does pure mathematics help us learn to live in society? 34. Is it possible to teach pure mathematics? 35. Could anyone do mathematics? 36. If you were a mathematical prodigy, what would you be interested in doing? 37. Could someone who suffers from dyscalculia become good at maths ? 38. Can mathematical proofs be proved without using mathematics ? 39. Is there any content in pure mathematics that can't be taught to children without being able to explain why it works? 40. Can you prove some basic theorems using geometry alone ? 41. How can we find true statements and obvious truths using pure mathematics alone (without another subject like history or logic?) 42. Can maths be learnt in a short period of time (say, over 3 years)? 43..
Conclusion
Thank you for reading this article. It's a long one, but hopefully it has piqued your interest. Please leave me a comment to let me know if I have written anything that is unclear or false. I love reading comments from my readers and will do everything in my power to answer any questions you might have about the topics that I discussed in this article. If you think that any of the information above is wrong, please write me an email at shrikantjoshi999@gmail.com with your questions about these topics and I wi
1. What is the role of creativity?
As a mathematician, I can't really answer this question for you. This depends on what your intended use for your creativity will be and how you are going to apply it. You can use it in different ways like writing or music, but what I am using my creative juices for is teaching students mathematics and engineering because that's what I am passionate about!
2. What is the difference between science and mathematics?
Science is about studying objects in our world that we cannot see, touching them or even smell them directly. Mathematics is a branch of science that studies these objects; it describes how they work and can be used to predict events and developments in our world.
3. When was mathematical thinking discovered and who was the first to do it?
This question is impossible to answer because we know that there were people before Pythagoras, but what we don't know who they were. Our first real proof that mathematics existed was discovered by Pythagoras in the third century BC, but this wasn't a mathematical proof. It concerned numbers and geometry, not pure mathematics such as algebra or number theory.
4. How will mathematics help us to understand and live in a changing world?
This question is very important and comes up a lot. Without mathematics, we wouldn't be able to have the beautiful pictures of our solar system or other planets in our galaxy. We wouldn't be able to make the discoveries that we have made, especially with regards to technology. Science and physics rely heavily on mathematics for their research, as does chemistry and biology .
5. When is mathematics not useful?
When you try to understand something that is beyond our understanding. It's useless when it comes to things that are abstract such as music, art or emotion. It's also useless if you're trying to answer a question that can't be answered using pure mathematics such as the meaning of life.
6. What makes mathematics beautiful?
Because it produces so many beautiful results and proofs! If we took away all the maths from the world, what would we have left? Modern technology almost entirely relies on mathematical laws for its efficiency and some of these laws are even taught in schools as part of our science curriculum today.
7. Are there any problems that cannot be solved using pure mathematics?
Hard to answer this question. Some problems perhaps cannot be solved using pure mathematics because they are tied to things that we don't understand, such as basic physics, chemistry or biology.
8. How will mathematics help us to understand and live in a changing world?
It's one of our most important tools for predicting the future and predicting how certain phenomena will work, especially with regards to technology. It also helps us to explain physical phenomena such as gravity and magnetism . I also think that it helps us to understand the world around us, which makes our world more beautiful and magical. If you look at your cell phone, you can see that a lot of mathematical theory has gone into its design and functionality. Things in nature like ants, bees and the human body can't be understood without a basic knowledge of mathematics.
9. What is math?
Maths is a branch of science that studies numbers, shapes, space and other related concepts using logic (or something similar to logic). It's all about patterns or making connections between different things so that you can come up with new ways to explain things.
10. What is pure mathematics?
Pure mathematics is a branch of maths that is mostly concerned with numbers, shapes, space and other related concepts. It's all about the patterns or making connections between things so that you can come up with new ways to explain things.
11. How do we know that there are always an infinite number of solutions to a problem?
It's hard to answer this question because it depends on what we mean by "solution". If you mean a list of answers then there will always be an infinite number of solutions (because maths can't tell us how many there are). But if you mean something else then perhaps it doesn't, but maybe it will next time we try.
12. What does the phrase "a proof is true" mean?
A proof is a logical argument that shows that something is always true without exception. When we say that a proof is correct, then it doesn't mean that it's true 100% of the time. It means that it's true for all practical purposes, but not necessarily 100% of the time.
13. Why are some mathematical proofs accepted as true and others were rejected?
To answer this question, we first have to define what a "proof" is because there are many different kinds of proofs and different people consider different things to be proofs (or lack of them).
14. Without maths, what would we use to measure anything?
Without maths we would not be able to measure anything because there is no such thing as pure numbers. Instead, we would use stuff that counted such as inches and meters. It's also a myth that science uses maths to do its experiments; it usually asks experts in the field what they must do in order for their experiment to work and then tells them how many separate steps the experiment needs to contain (a lot of scientists don't like this).
15. Why don't I know how old I am?
The answer depends on your definition of "you". If we use the definition of "you" as your cells and your body, then you would be one year older than you were last year. If we define "you" as your soul or something like that, then "you" wouldn't know.
16. How does pure mathematics help us to understand the world?
If you view mathematics as a collection of facts, it can help us to understand the world because it describes many physical phenomena like gravity and magnetism. But if you view maths as a process of reasoning and solving problems, it doesn't really help us to understand anything. Many mathematicians argue over this issue but nobody has been able to give a final answer yet.
17.
Conclusion
This is just the beginning of my journey into mathematics. In order to truly understand the depth and beauty of this subject, I will need to study and research it more and more.
But before I can do that, I must first learn some more basics about mathematics so that I can understand what it was all about in the first place.
That's why for the time being, I'll have to satisfy myself with reading books written by famous mathematicians such as Euclid , Archimedes , Isaac Newton , Carl Friedrich Gauss , Leonhard Euler , Gottfried Leibniz , Pierre de Fermat and many others.ll try to answer them properly as best as I can, and give you credit for helping me improve this article.