I began studying mathematics when I began attending a community college. I took Trigonometry, Calculus I, II, and III, and Differential Equations. These subjects involved memorization of formulas, plugging in given values, and using algebraic skills to clean up the answer. Since I did very well in these subjects, I decided to major in mathematics when I began attending a university. Mathematics then suddenly changed.
The very first advanced math class I took was entitled Introduction to Advanced Mathematics. I was completely lost from the very first lecture. I was no longer finding limits, taking derivatives, and performing integration. I was now required to prove using rigorous proof techniques all of the equations, formulas, and theorems that I had learned, memorized, and used in previous math classes.
I was getting ready to just give up on my major in math, when an instructor informed me of the real problem. I was missing a very important prerequisite. My academic advisor never told me about this prerequisite. My academic advisor did not have a math degree. Her degree was not even related to math. Thus, she probably did know that I needed this course. Therefore, it’s really important for students who want to major or minor in math that they research the prerequisites on their own. Then, if they have any questions, they need to ask a math instructor.
The prerequisite that I needed was Discrete Mathematics. Discrete math covers topics such as logic, proof techniques, and set theory. An understanding of all of these topics is needed in order to study and succeed in advanced math. Advanced math classes involve doing a lot of proofs. Some of these proofs are very rigorous proofs. Rigorous proofs are done using definitions only.
Once I studied and understood discrete math, I obtained a strong foundation for understanding advanced math. In addition, I began to love math even more than I had before. I was no longer just doing repetive problem solving. I was now having to make decisions and come up with ideas of my own. Proofs also involve a lot of ingenuity. Advanced math is also very abstract. I learned that I was better in theory than I was in applied math.
I eventually received my Bachelor of Science in General Mathematics. But, I could not have done that had I not studied discrete math. Many of the advanced math classes don’t start with discrete math topics before plunging into the rigorous proofs. They simply don’t have time. Therefore, it is beneficial to take a discrete math course before starting advanced math.