Page 1.1.1: Advice For Success
We first start off our journey by noting that it is important to be aware of how to succeed in mathematics. Although the following is not a comprehensive list, I hope that it serves as a guideline on how to excel in your math classes. We will try and practice many of these skills here in our boot camp! Whenever we do so, we will highlight it and make a note.
1) In mathematics, we should try to see many examples and non-examples. In doing so, we obtain a clearer idea on the topic that is being discussed.
2) Whenever we have a definition or a theorem, try to translate the definition or theorem in words. Often, students tend to memorize a formula by repeating the symbols, but instead we should be able to explain the formula in words! For instance, instead of saying "The Pythagorean Theorem states that \( a^2 + b^2 = c^2 \) ", a more detailed answer would be "The Pythagorean Theorem states that for any right triangle, the square length of one leg plus the square length of the other leg equals to the square length of the hypotenuse". At first, the second suggestion may seem like it is a lot of work for a little value. However, in your journey in calculus, you will be required to demonstrate a strong grasp on interpreting what a formula may mean.
3) Try to reflect on every rule/theorem. Can you understand why the rule/theorem makes intuitive sense?
4) Form a study group since a good habit to get into is to try discussing the material with someone. Mathematics is a language and if we only write math, then we have never practiced speaking it! There is a rich vocabulary associated with mathematics and the act of forcing yourself to find the right words and explain an idea will give you a better command of the material.
5) Math is not a spectator sport! To learn math, you must practice, practice and practice. It is easy to attend lectures and watch your professor work out all the examples. But just because you watched someone work out, it does not mean that you, yourself, can also work out! Remember, your instructors have an excellent command of the material. Just because they may make a problem look easy, it does not mean you can replicate their process on the day of the exam without practicing first.
6) Although this may sound excessive, perhaps for your math courses we have four separate notebooks. In one notebook, we should copy down the lecture notes. When we go home, we should actively copy these lecture notes into our second notebook. Doing so forces us to go over the lecture and grants us an opportunity to solve the problems done in class. This is important because many students do not realize that it is one thing to read someone's solution and understand it. However, it is a completely different thing to be able to come up with that solution, on your own, from scratch. Students (myself included) often read their notes and think they can imitate the same type of thinking on the test because our instructor makes it look so easy. However, this is often not the case. We really don't know how much we actually know until we are forced to come up with an answer on our own. For some students, the first time they are actually trying a problem on their own is during the exam. If the first time we are actually trying a problem from scratch is on the exam, then it is not going to go well! The third notebook should contain all the homework problems worked out in as much details as possible. And finally, the forth notebook should contain summaries/outlines of the textbook. The textbook can offer a different viewpoint from the instructor and serves as another place where you can actively study.
7) Make use of your professor's office hours, the Learning Commons ( https://www.qc.cuny.edu/academics/qclc/ ) and the Math Lab ( https://www.qc.cuny.edu/academics/math/getting-help/ ).
8) Here is a more comprehensive list of tips: https://mathstat.slu.edu/resources/success-in-mathematics .
Again, all of the above is merely advice. It is important to find which combination of strategies works best for you. The one thing to keep in mind is that simply attending the lecture might not guarantee good grades! There is a lot of work to be done outside of the classroom and hopefully the above list can point you in the right direction.