My math journey

 

Transitioning from high school math without any kind of proof background is probably the biggest mental shock one can experience. Personally, I went from being at the top of my class, to always feeling like I must catch up. Therefore, every mathematics student must learn that one quality that mathematicians possess is a propensity to persevere.

The first surprise that I encounter as an undergraduate math student, is that in mathematics you must write a lot. My high-school-self thought that I would be working with equations, images and symbols all day long. However, most of my proofs are filled with words like therefore, thus, implies, therefore, by contradiction, counterexample, by the (famous mathematician name) theorem. These words are the ones I use the most when trying to describe and explain my “thought process” (Learning that “thought process” is an entirely different story). Secondly, math problems became extensive. The longest proof I have written was 3 pages long, one page of calculations, and 2 pages of justifications. Additionally, teachers do not actually care about the result, all they care about is that you show you understand the theorems, concepts, and definitions, and that you know how to use them.

The first roadblock I hit in my young mathematical career was my advanced calculus class. This was the first time I really struggled with a subject, and I was not used to the amount of work I needed to do to pass the class. While I understood the concepts well enough, I did not have enough tools to prove the results. And I will often do not know how to get from one step to the next one. I had to retake the class the next semester, but I did all the “leg work” (algebraic concepts, real numbers, functions and set theory) I could during the summer before retaking the class. I passed the class. However, the most important thing I learned was not calculus, but rather how to approach a mathematical challenge. I learned that I needed to read various interpretations of the same concept to enrich my understanding. I also learned that I needed to practice proof writing constantly because it is the only way to develop the intuition that is necessary when you are stuck with a problem. Finally, I learned that I am not alone. I can always ask my teachers and my classmates for help, and I should not be ashamed of not being able to understand something.

In conclusion, learning mathematics is a very demanding and complex task. However, one must be resilient, perseverant, and one has to come to terms with the fact that our efforts will always yield results.