Reading Mathematics Tip 5

Tip 5 from Dr. Del

Learn the vocabulary.
How do you learn the vocabulary?

As you read the textbook:
As you read the textbook, insure that you know the meaning of every word.  In mathematics textbooks, the definition is usually provided when a new word is introduced.

If the textbook does not provide the definition or it is difficult to extract a formal definition, turn to the index to determine if this is the first occurrence of the word.  Turn to the first occurrence of the word in the book and try to find the definition.  If that fails turn to another source such as the chapter summary at the DrDelMath website or the Mathematics Glossary listed on the homepage of DrDelMath.

As you take lecture notes:
As you take lecture notes make sure you write all presented definitions precisely as they are presented in the lecture. Note that it is incumbent on the lecturer to present definitions clearly, completely, and precisely.  They must be presented so the listener can easily recognize the precise wording of the definition.

As part of your daily study plan:
As part of your daily study plan you should memorize all definitions.  This memorization step is required because the definitions used in mathematics are stipulative definitions and will not be learned through common usage. To memorize a definition it is wise to start by writing it ten or more times.  Think about what you are writing.  After writing a definition ten times you should be able to recite or write it without reference to notes.  On a daily basis review the definitions by carefully reading (studying) them.  After committing a definition to memory continue, and extend, your study of that definition.  Think about the necessary and sufficient conditions given in the definition.  Think about how the necessary and sufficient conditions determine whether a mathematical creature satisfies the definition.

As you prepare for a test:
As you prepare for a test review all definitions — think about how they help you to answer questions.

If you must still memorize definitions when you begin your review for a test, you have not been studying sufficiently, or correctly, or neither.

As you use the DrDelMath website:
Insure that all the definitions provided in the chapter summary are committed to memory and that you understand every word in them.  Think about the necessary and sufficient conditions given in the definitions.  Think about how the necessary and sufficient conditions determine whether a mathematical creature satisfies the definition.

Insure that each of the definitions are included in the list that you review on a daily basis.

A deck of flash cards may be the most convenient and efficient way to study definitions in mathematics.  A deck of flash cards makes it easy to review on a regular daily basis.

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