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By: Vijay GarG

by Vijay Garg
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Mathematics is the language of nature. There’s no better tool out there to study and learn about the world and the universe in general other than mathematics. We use it in our everyday lives from buying things to calculating our calorie intakes to stay fit. Hence, it isn’t just important for mathematicians or physicists but everyone. Mathematics, for most people- specially students-is considered to be a difficult subject. The thing that makes math difficult for many students is that it takes patience and persistence. For many students, math is not something that comes intuitively or automatically — it takes plenty of effort. It is a subject that sometimes requires students to devote lots and lots of time and energy. German-American mathematician, Richard Courant once famously said,
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality, and individuality.
If you are here to get tips about how to cover the syllabus a week before your finals then this article might not be for you (you can still have some great takeaways though). Mathematics isn’t something that you can do well in just by sitting in all-semester classes and then cramming one week or few days before the finals. The reason is that many of the concepts in mathematics are built on other concepts, for instance, to learn concept A, you need to understand concept B, which requires you to already understand concept C. So here are certain techniques explained that are very effective when it comes to learning and understanding mathematics.
Create a distraction-free study environment
Shut down all distractions such as watching TV, chatting with friends, playing video games, smartphone notifications, and so on. Mathematics is a subject that requires more focus than any other discipline. Typically, the best place to study is somewhere at home, where you can sit in a comfortable, but upright position, where you can set up your computer, books, and other study materials and know that they will be exactly where you left them. When you can concentrate on something, you usually can learn the information more quickly and effectively. Hence, it is very crucial that you have set up and distraction-free study zone for yourself.
Master the key concepts and teach them
The main goal of studying math is to understand, not memorize, the material. You need to stop yourself and ask if you understand a concept before moving on. Constantly ask questions. “If I change this parameter, what would happen?” Try using different resources (like a new book, web article, or video lecture) if you encounter a concept you can’t make sense of. You can memorize formulas and rules to solve math problems. But don’t memorize every step in the solution. You should understand the underlying concepts behind what you are doing. If the concepts are not clear in your mind, it is not easy to solve problems successfully. Try to teach those concepts to someone else who is unfamiliar with it. Teaching is considered to be one of the best ways to master something. This is especially true in Math, since communicating your solutions and process is a huge component. If you stumble a little in your explanation of some particular concept, that is a great way to diagnose and pick out areas you can work on. I have written an article on the Feynman Technique of learning:
Use good resources and create a mathematical dictionary if possible
Try to get your hands on as many good resources as possible- textbooks, notes, video lectures, pdf, etc. Mathematics has tons of vocabs and terminologies. Dictionaries play an important role in the development of vocabulary and connecting words with their true or multiple meanings. Mathematics has a vocabulary that consists of words and symbols that allow people to have a common base of understanding of mathematics. Creating a mathematical dictionary helps you understand the concepts and make better connections.
Practice, practice, and more practice!
Let’s be honest here unless you’re relatively gifted at mathematics then you might not feel like this applies because you will have breezed through your high school mathematics while barely lifting a finger. But otherwise, mathematics requires practice, lots of practice- every single day. This really adds up to your mathematics problem-solving skills. 
Review your errors
Now, this is a very important factor when it comes to learning mathematics. While you are practicing mathematics, it is very obvious that you shall come across several instances where your solutions don’t right and you will have to approach a different method to solve the problem. Understanding where you went wrong, analyzing those mistakes, and working on them are crucial for stronger mathematical understanding.
You understand something when it is so obvious to you that you start to think that you should have discovered it.
Here are some extra tips that will help you understand the stuff much better:
> If you don’t understand something, focus on mastering that topic before moving on to the next topic
> Work example problems and check your answers to gain practice with every lesson
> When beginning to work on a Mathematics problem, do not map out a path from problem to answer in your head before writing anything down
> Two hours of extra sleep is almost always a more efficient use of your time than two hours of tired studying.
> Sometimes the best way to make progress on a problem is to take a break, work on something different, or sleep on it.

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