# What you should be learning in your math course.

When taking a math course there are four things that a student should learn.

The Fundamentals

The fundamentals include the definitions, the rules of operations, and the tactics of manipulation. It is essential that you understand the definitions and can visualize them. The rules of operations need to be practiced until they are second nature but they should never be divorced from a simple illustration that explains the rules. The tactics of manipulation are the sequences of steps needed to solve the types of problems that will be encountered.

“As strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations”. (Ernst Mach Paul)

The Applications to Problem Solving

Math is the language of science. Math was developed to solve problems. You are in this course because you have other courses that will require the problem solving tools you will learn here. Math includes the translation of words into symbols and the symbols into words. If you can’t solve problems, what good is your math?

“What is mathematics for? To delight the mind and help us understand the world.” (E.T. Bell)

The Background

The background of the subject explains when, how and why it came about. It humanizes the subject and gives perspective on why we need to know it and what it was like before we had these nifty mathematical tools.

“Biographical history as taught in our public schools, is still largely a history of boneheads, ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals— the flotsam and jetsam of historical currents. The men who radically altered history, the great creative scientists and mathematicians, are seldom mentioned if at all.” (Martin Gardner)

The Beauty of Logic

Another reason we study math is that it helps cultivate our abstract thinking. Math is the pinnacle of human thought. It is pure and lasting. Its logic is ordered, economical and irrefutable. Math is an art as well as a science.

“The science of Pure Mathematics…may claim to be the most original creation of the human spirit”. (A. N. Whitehead)

“Mathematics has a light and wisdom of its own, above any possible application to science, and it will richly reward any intelligent human being to catch a glimpse of what mathematics means to itself”. (E. T. Bell)

Most of all, I hope you have fun with your math course and learn something that will enhance your ability to reason.

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Paul K.

Experienced, Understandable and Memorable Math Tutor

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