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Why Study Mathematics

By Keith Campbell,2014-04-08 08:55
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Math is learned by doing problems. Homeworks and assignments are the first and the most important means of learning fundamental ideas and processes in

    Why Study Mathematics?

    Mathematics reveals hidden patterns that help us understand the world around us. In

    addition to theroems and theories, mathematics offers distinctive modes of thought

    including modeling, abstraction, optimization, logical analysis, inference from data, and

    usage of symbols. Hence, the study of mathematics can lead to a variety of exciting

    professional careers such as:

    ? Academic research ? Business(portfolio analysis, design

    ? Engineering studies, statistical analysis, software

    ? Finance(actuarial fields, design and testing, computer

    economic forecasting,etc.) simulation and other areas of

    ? Government service operations research, etc.)

Mathematics, as a major intellectual tradition, is a subject appreciated as much for its

    beauty as its power. It is a universal part of human culture like language, art and music.

    A career in mathematics can be very attractive.

    University Math is Different from High School Math

     In University you are expected to absorb new material much more quickly than high

    School.

     You definitely need to spend more time studying per week - you do more of the

    learning outside of class than in High School.

    I- How to Study Mathematics in University?

    Classwork

    In the classroom, have all necessary equipments (book, pencils, notebook,...) with you.

    Concentrate on the classwork and ask questions when necessary. Also, listen to the

    questions asked by others, and the answers given to those questions. Take part in class

    discussions.

Active Study vs Passive Study: Attend class every day and take complete notes

    Ask questions in class!

     Go to office hours and ask questions. Don’t be afraid to ask questions.

    Any question is better than no question at all. But a good question will allow your helper

    to quickly identify exactly what you don’t understand.

How to use the textbook : Read the related part of the textbook before, and again,

    after class. You cannot read a math textbook as a novel. If you can’t do an exercise,

    reread the explanatory material in the book and/or go over your class notes. After

    reading an example and working it out for yourself, try to think of other examples that

    would fit the idea being discussed. Think of other relevant problems and try to solve

    them. Use more than one math book.

Problem Solving : The most important step in solving a problem is to understand the

    problem. Firstly, you read the whole problem very carefully. Next, you need identify

    which skills and techniques you have learned can be applied to solve the problem at hand.

    Then, you carry out the plan. Finally, you review the problem and the method of solution so that you will be able to more easily recognize and solve a similar problem.

    Some problem-solving strategies: use one or more variables, complete a table, consider a special case, look for a pattern, guess and test, draw a picture or diagram,

    make a list, solve a simpler related problem, use reasoning, work backward, solve an

    equation, look for a formula, use coordinates.

Homework : Math is learned by doing problems. Homeworks and assignments are the

    first and the most important means of learning fundamental ideas and processes in

    mathematics. Do the homework when it is assigned. Take responsibility for keeping up

    with the homework. Make sure you find how to do it. The problems help you learn the

    formulas and techniques you do need to know, as well as improve your problem-solving

    prowess. As you do homework, make lists of formulas and techniques to use later when you study for exams. Homework problems may seem harder because they cover

    more material. Ask your instructor questions as they arise; do not wait until the day or two before an exam. Take as much time as you need to do all the homework and to

    get complete understanding of the material. When doing homework, getting prepared

    and lining up the ideas are important. Also, trying to teach a topic is very helpful in learning it.

    Learning From Your Errors: When you realize that you made a mistake in your

    homework or in the exam, analyze the error and find out what you did wrong. In your notebook, keep a page entitled: “Warning: Errors to Avoid.”

    II - Studying for a Math Exam

     Everyday study is a big part of test preparation !

    Start by over each section, reviewing your notes and checking that you can still do the

    homework problems ( actually work the problems again). Use the worked problems in

    the text and notes- cover up the solutions and work the problems yourself. Check your

    work against the solutions given. Do the homeworks when it is assigned. Ask your instructor questions as they arise; do not wait until the day or two before an exam. Put yourself in an exam-like position: work problems from review sections at the end of

    chapters and work past exams if you can find some. Start studying exam early. Get lots of sleep the night before the exam.

How to review for test :Start reviewing far enough in advance so you have time to do

    a careful unhurried job, and still are able to go to bed early the night before exam. Use the review materials at the end of each chapter. If you are having trouble on a problem,

    go back to that section in the book and rework some problems there.

Taking a Math Exam : First look over the entire questions. You will get a sense of its

    length. Try to identify those problems you know to do and those you have to think about.

    Start with the problems that you know for sure you can do. Work as quickly and

    continuously as you can while writing legibly and showing all your work. Work by the

    clock. Show all your work. In a multiple-step problem outline the steps before actually working the problem. Make sure you read the questions carefully, and do all parts of

    each problem. If you finish early, check every problem.

Control your exam paper after grading : Notice the errors in your exam paper. In

    your solution, check the points where you get high grades and loose grades.

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