Mathematics 101

Mathematics is a field that uses two languages: that of words, and that of numbers. In advanced mathematics, the words largely drop away, because the numbers are a more effective way of communicating mathematical ideas. However, at the level of this course, words are still an essential part of mathematical explanation.

You may find the language of this course difficult, but please note that you must be prepared to read the material presented to you at least three times.

1. When you begin a section of the Study Guide or textbook, we suggest that you read through the whole section once for general comprehension, and to identify unfamiliar terms.
2. Then, reread the section, breaking it up into smaller parts using the examples as points of termination; that is,
   1. read the discussion of each concept and any associated examples, examining any figures carefully.
   2. make notes on the significant points and on the definitions of unfamiliar terms, and copy any formulas into your notebook.
   3. work through the examples with pencil and paper, making certain that you understand the computations involved.
3. Finally, close your textbook or Study Guide, and your notebook, and in your own words, summarize the important points of the section you just studied on a piece of scrap paper. Compare your rough notes to the Study Guide or textbook presentation, or to the notes you made in your notebook, and review any points that you missed.

   Proceed when you are confident that you grasp the material presented. If there is a point that you cannot understand, make a note of it to discuss with your tutor or instructor as soon as possible. Then, continue with the next section.

   Note that we strongly recommend that you “review as you go.” Do not wait until just before an examination to study earlier material: keep the concepts and principles fresh in your mind by reviewing on a daily basis.

   Note: Some students find it helpful to use quad-ruled notebooks (4 × 4 or 5 × 5) for their mathematical studies. This strategy allows students to sketch any necessary graphs or diagrams with comparative ease, and to keep their calculations well organized and clear.