The Art Of Mathematical Problem Solving

10 useful tips that can make math easy for you

Photo by Dan-Cristian Pădureț on Unsplash

1. Math is everywhere. Irrespective of what academic background you come from, you use mathematics in your everyday life. From buying groceries at the grocery store, or managing spreadsheet of your bills. Understand the importance of mathematics.
2. It is the best tool that helps us understand nature. Mathematical thinking is required in every discipline from diagnosing a medical disease or putting a rocket into space. The applications of mathematics are widespread.
3. If you find math boring or difficult even if you want to pursue it, change your teacher. It really matters a lot what kind of connections you have in terms of mathematical expertise. Not everyone, and I tell you this, not every person gets excited about mathematics and mathematical problem solving. Get in touch with the ones who do.
4. Get good resources. The resources and references you choose play a crucial role in your understanding of mathematical topics. Choose your books, notes, PDFs, videos, lectures, audiobooks, journals, and articles very wisely.
5. Learn how to make connections. In mathematics, several concepts are interconnected. Trigonometry, for instance, is widely used in co-ordinate geometry. The concepts of matrices and vector analysis are greatly interconnected.
6. Solve problems. You cannot expect to master the skill of mathematical problem solving unless you solve problems. And by problems I mean, many problems. Practice is the key. It’s like learning music, the more you play with the instrument, the more fluent and expert you become at it. The more you solve problems, the more skilled you become at problem solving.
7. Stay with the problems a little longer. We usually give up or get frustrated when we cannot find the solution. Sticking with the problem, and trying out new methods can eventually lead you to solve it. There’s a famous line that Albert Einstein once said, and I quote”

“It’s not that I’m so smart, it’s just that I stay with the problems longer.”

8. Have the concepts clear before jumping into the problems. The theorems, formulae, and fundamental principles of each topic have to clear and distinct in your head before starting to solve the problems. You cannot solve the problems of mathematical analysis if you don’t know what real numbers are, or what boundedness of a set or a function is.

9. Use multiple methods. The same problem in math can be solved by multiple approaches. There isn’t always a single method that leads to the solution. Sometimes trying out several methods can help you widen your thinking skills. It’s important.

Image from ‘A beautiful Mind’, movie based on prolific mathematician John Nash Jr.

10. Apply the problems to real life scenarios. It becomes much easier to solve problems if you can visualize them differently. Many areas of mathematics like probability, statistics, geometry, number theory, game theory, and so on can be better understood and the problems become much easier to solve if you can connect those to practical world. Also, learn how to create your own problems, and solve them.

You can’t learn mathematics and be skilled at problem solving in a day, and likewise you cannot expect to excel your mathematics exam by studying for the last few days before the exam. It takes time, and with small but important efforts with important methods every single day you become pro at it. Mathematics is one of the most fascinating disciplines to pursue if you really understand it. You look at the world and the physical processes with a different lens once you grasp the concepts clearly. That perspective provides you a great sense of pleasure and satisfaction in being able to truly understand the world around you.

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