Nanda Ram Aryal
Often students ask questions: why mathematics? Can the study of mathematics be interesting? Do imagination and creativity have any place in mathematics? These are some of the issues that the article tries the address. Long ago, at the dawn of the western civilization, the scientist-philosopher Pythagoras proclaimed that the universe is structured in the form of mathematics. The numbers in the pages reflect the world outside. Mathematics reveals the hidden patterns that underwrite the world around us. The process of “doing” mathematics is for more than just calculation or deduction; it involves observation of patterns, testing of conjectures, and estimation of the results. As a practical matter, mathematics is a science of pattern and order. Its domain is not molecules or cells; but numbers, chance, form, algorithms and change. As a science of abstract objects, mathematics relies on logic rather than on observation as its standard of truth. Yet it employs observation, simulation, and even experimentation as means of discovering truth. Thus, imaginative leaps have abundant place in this science of numbers.
Mathematics is a subject appreciated as much for its beauty as for its power. The enduring qualities of such abstract concepts as symmetry, proof and change have been developed through 3,000 years of intellectual effort. Like language, religion and music, mathematics is a universal part of human culture. Studying mathematics is different from studying other subjects. Every one studies differently and there is no single right way to study mathematics. We cannot learn mathematics by just going to class and listening to the instructor’s lecture and working on the problems. In order to learn mathematics we must be actively involved in the learning process. We have to attend class with total attention to the lecture. At the same time a good set of notes taken in the class can be helpful while practicing at home later. Even if your instructor does not assign any homework, please! Don’t miss practicing at home everyday because the maxim “practice makes a person perfect” exactly fits to mathematics. We have to study on a regular schedule, not for the sake of exams only. In other words, we need to be involved in the learning process quite intensively.
If we are not willing to be actively involved in the process of learning mathematics, both inside and outside of the classroom, then we will have trouble with mathematics. While there is certainly a fair amount of memorization of formulas in mathematics one needs to do more. We need to understand how to use the formulas and that is often for different from just memorizing them. If one doesn’t understand how the formula works and the principle behind it, it can often be very difficult to use the formula. Mathematics is learned by solving the problems. The problems help us learn the formulas and techniques we need to know as well as improve our problem solving prowess. One needs to be actively involved in managing the learning process. Some helpful suggestions could be:
•Take responsibility for studying, recognizing what one does and does not know, and knowing how to get one’s instructor to help one with what one doesn’t know.
•Attend class everyday and take complete notes. Instructors formulate test questions based on material and examples covered in class as well as on those in the text
•Be an active participant in the classroom. Get ahead in the book; try to work on some of the problems before they are covered in class; anticipate what the instructor’s next step will be.
•Ask questions in class. There are usually other students wanting to know the answer to the same questions one has.
•Visit the instructor during the office hour and ask questions. Instructor will be pleased to see that his/her student is interested.
•Develop good study habits throughout the study period to make it easier to study for exam.
We can apply the following steps on solving the problems:
1.The first and most important step is to understand the problem, that is, to identify exactly which quantity the problem is asking one to find or solve for (make sure you read the whole problem).
2.Next, one needs to devise a plan, that is, identify which skills and techniques one has learned can be applied to solve the problem at hand.
3.Carry out the plan.
4.Look back: — Does the answers you have found seem reasonable? Also, review the problem and method of solution so that one will be able to more easily recognize and solve a similar problem.
Courses on mathematics are preparation for business calculations as well as for other major applications in science, engineering and technology. At the same time practicing mathematics is deeply associated to one’s inner mental disposition and sensibility. Mastering mathematics suggests acquiring an especial eye to see the world in a different light. One should view mathematics as an opportunity to strengthen one’s thinking skills and imaginative creativity.
When in the domain of mathematics, one should not only meet calculations to do but also the chain and thread of reason and persuasion which justifies them and links them together. Understanding and following the rules and patterns of mathematics nurtures an ability to think and reason well. Mathematics provides a neutral territory for the practice of rule and pattern-based reason and logic. The opinions and views one meets in daily life say and care little about what mathematics conclusions should be. Thus master it and be the different person knowing the inner workings of the cosmos as it knows only the language of the numbers.