Mathematicians like to talk about the beauty of mathematics. This beauty is seen in the harmony, patterns, and structures of numbers and forms – classical ideals of balance and symmetry. While experienced mathematicians can envision tangible representations of notations made on a page, mathematical beauty is not so well accessed by the non-mathematician.
Mathematics is a means of discovering and participating in new and important ways of thinking. One is reminded of an important component of an evolved, civilised human behaviour: the cardinal principle that if you can know, then it is criminal not to know!
We have greatly failed in furnishing or creating a beautiful mathematical environment in schools and universities. That is because, instead of some accomplishments and high-level research in the subject, we have produced such students who are scared at seeing a mathematics book, because they fail in getting to the various formal techniques which are used for evaluating various mathematical problems.
A teacher can build confidence and motivate a student at doing mathematics, and introduce it as a useful and interesting tool for a student. Later a student can improve basic skills, which will lead to a logical mind that aims to solve various problems and to design mathematical models.
What is Mathematics to you?
Have you ever read a book, watched a movie, or played a video game that you got really into? Just everything about it is extremely engaging and you lose yourself in that world. Then you reach that one part, where there’s some incredible scene, some unexpected twist, or some ingenious plot development that blows your mind, and you get really excited. You run into the other room where you find a friend, and you excitedly tell them all about what just happened. And they sort of shrug and say, “Oh, that’s cool I guess.” And you’re a bit disappointed that your friend isn’t as excited as you are, but you know deep down that you’ve gotten so deeply involved with this story that you’re seeing it from a much different perspective than everyone else.
That is how you should be involved in Mathematics.
Apart from tutor’s role, the main game changer is the student himself/herself. Most students don’t know how to learn Mathematics. In this article let’s see how to learn Mathematics.
As poetry calls for a different set of strategies than fiction, and fiction a different set than non-fiction, Mathematics has a reading protocol all its own. Just as we learn to read literature, we should learn to read mathematics. Students need to learn how to read mathematics in the same way they learn how to read a novel or a poem, listen to music, or view a painting.
Mathematical ideas are by nature veracious and well defined, so that a veracious description is possible in a very short space. Don’t assume that understanding each phrase will enable you to understand the whole idea.
Students of Mathematics must know that “a three-line proof of a subtle theorem is the distillation of years of activity”.
A Mathematics article usually tells only a small piece of a much larger and longer story. The author usually spends months discovering things. At the end, he organizes it all into a story that covers up all the mistakes and presents the completed idea in a clean neat flow.
Mathematics says a lot with a little. The student must participate, though. At every stage, he/she must decide whether or not the idea being presented is clear. Ask yourself these questions:
• Why is this idea true?
• Do I really believe it?
• Could I convince someone else that it is true?
• Why didn’t the author use a different argument?
• Do I have a better argument or method of explaining the idea?
• Why didn’t the author explain it the way that I understand it?
• Is my way wrong?
• Do I really get the idea?
• Am I missing something?
• Did this author miss a particular argument?
• If I can’t understand the point, perhaps I can understand a similar but simpler idea?
• Which simpler idea?
• Is it really necessary to understand this idea?
• Can I accept this point without understanding the details of why it is true?
• Will my understanding of the whole story suffer from not understanding why the point is true?
There is no substitute for work and time. Reading mathematics too quickly results in frustration. A half hour of concentration in a novel might net the average reader 20-60 pages with full comprehension, depending on the novel and the experience of the reader. The same half hour in a math article buys you 0-10 lines depending on the article and how experienced you are at reading mathematics. You can speed up your math reading skill by practicing, but be careful. Like any skill, trying too much too fast can set you back and kill your motivation.
Mathematicians often say that to understand something you must first read it, then write it down in your own words, then teach it to someone else.
In a nutshell, besides the book, you need paper and a pen. Second, you must do the exercises of the book. Third, you must do the exercises of the book. Fourth, you must do the exercises of the book…
The writer is studying for a Masters at JK Institute of Mathematical Sciences, Srinagar