What to Study in Technical Calculus

Algebra is very important component of Technical Calculus. You will find that when working calculus problems, you will do a lot of algebra. For this reason, among others, students need a good background in algebra to be successful in their study of technical calculus. This section should help identify areas of misunderstanding and give students a refresher of their algebra skills.

The Language of Mathematics

In order to understand mathematics you must be able to use the language. Students who have difficulty with mathematics fail to realize how important knowing its language is. The language of mathematics has two parts: the words it uses for concepts and ideas and the notation it uses for conveying these concepts and ideas. As a start to learning mathematics successfully a student must grasp the importance of learning definitions of mathematical words. The instructor uses these words in his/her classroom explanation of the material. If your understanding of these words is fuzzy, then the explanations will likewise appear to be fuzzy. Imagine how frustrating it is trying to watch a television show when the reception is fuzzy. To fine tune your reception of classroom presentations, put greater emphasis on knowing definitions of mathematical terms.

Notation and its proper use are also important to understanding mathematics as well as doing correct mathematics. Notation has a grammar just like good spoken and written English has a grammar. People who use English grammar incorrectly always risk being misunderstood. So it is with the mathematical grammar of notation. Two simple examples are given to illustrate the importance of correct use of notation.

Many students take great liberties with their use of “equals” symbol “=.” For example, take the problem to solve the following equation for x: . Work looking like this is unfortunately quite common:

What does the student mean here? Could the student have meant the following correct way to lay out this problem?

Which of the two do you understand better?

Another example which illustrates the value of good use of notation, particularly the use of parentheses, is the following. Solve for x:

A student’s solution can look like this:

The correct solution with the appropriate use of parentheses is:

As a final reminder: learn the definitions of mathematical words and terms with precision and make it your practice to use the notation of mathematics correctly. Doing these two simple things will go a long way towards increasing your success in learning mathematics.