1.2: Suggestions to Students

All mathematics courses are difficult. It takes hard work and patience to learn mathematics. Rote memorization does not work. Here are some suggestions that you may find helpful:

1. Do not skip classes.
2. Read the text, including the examples, before the lecture; review what you have learned after each lecture.
3. Do the exercises.
   1. First, study the examples in the book.
   2. Make an effort to understand how and why a solution works, and remember how certain types of problems should be solved.
   3. When you do a problem, ask yourself if you have seen something similar before; if you have, follow the steps in its solution.
   4. After solving a problem, look for alternate solutions, analyze and compare their differences.
4. Get help from the instructor, your friends, and whatever facility your college provides.
5. Develop good study habits.
   1. Keep working every day: study the book, your own lecture notes, and, most important of all, do the exercises at the end of each section.
   2. Form a study group of two to three students, and meet on a regular basis to study together.
   3. Check the solutions for any nonsense or discrepancies.
   4. Learn how to solve the problems systematically.
6. Perseverance. Do not give up easily.
7. Be willing to help your classmates. Trying to explain something to others is the best way to learn anything new.

Attitude is the real difference between success and failure. Nothing comes easy. To succeed, you have to work hard. But you also need to learn how to learn mathematics the right way.

• Do not rely on memorizing formulas or procedures by rote. Instead, try to understand the concepts and ideas behind them. It is important to learn when and how to use them.

• Of course, it does not mean that you need not memorize anything at all. On the contrary, many basic results and definitions need to be memorized. You may find it helpful to use a highlighter to mark the definitions and keywords that you have trouble recalling, and I urge you to review them frequently.

• Do not compartmentalize the material; all sections are connected in one way or another. Consequently, as you move along from chapter to chapter and from section to section, try to observe the connections between the concepts you have learned. Without saying, it is understood that you need to remember what you had learned earlier.

• Write down all intermediate and partial results clearly. For instance, if the value of \(x\) is 7, do not just jot down the number 7; instead, write \(x=7\). Otherwise, you may forget what 7 is after just a few minutes. In brief, present your results in such a way that they can be read and understood by everyone in the class.

• While we are on the subject, let us comment briefly how to write up a solution. Take your homework assignments seriously. Keep in mind: to study for a test, you may want to review your homework, so you need to be able to read your own work. Write everything clearly and neatly. The process of writing out everything correctly helps you think about what you write. Very often, incoherent and incomprehensible writing is an indication of lack of understanding of the subject matter.

• When doing your homework assignments, start with a draft, then look over it carefully, check the spelling and grammar, and revise the solution. Make sure you write in complete sentences and use correct notations. If necessary, you may have to polish it further. Before turning in the final version, be sure to check again for any mistakes that you may have overlooked.

How should a student use this workbook?

1. Read the workbook before class, and study the workbook again after each class.
2. Read and study the examples in the workbook.
3. Do the hands-on exercises.
4. Do the section exercises.