What to do when you and your degree are going through a rough patch

I have heard it said multiple times in movies and on the internet that Mathematics is beautiful-that it helps you make sense of things. As a final year student of Mathematics, I have, at times, struggled to make sense of my coursework. I am, therefore, writing this, especially for students entering their second year and, all the fresher batches that might go through the trouble of actually looking at this publication. The pedagogy of mathematics is mostly routine and mechanical at the high-school level, however, once we take up Mathematics in college, we must always strive to be independent thinkers. It is always up to the students of this subject to get out of their comfort zones and try to think differently. If you are someone like me, you probably spend more of your time on the \mathematics subreddit or on StackExchange than you do with your course material.

I am not an ideal student of Mathematics but I enjoy it and that is what I want from each one of you reading this article. Curiosity does not always kill the cat. At the very heart of it, this subject explores and studies patterns around us. Whether it is music, nature, architecture, or art- all the things are precise to the grain and employ the use of mathematics in one way or another. I, for one, find that studying sequences and series is almost meditative and those of you who just survived your second semester might get offended by this statement. But it gets better once you start connecting two and two together when you advance in your degree and suddenly, the pieces start falling into place. Every person reading this article is likely to have a paper in the CBCS system that they don’t completely understand and it’s fine. I struggle with abstract algebra at times. The important thing is that you try to think of this problem paper as not simply mathematics. Try to visualize what the equations say. As kids, we are taught languages with the aid of visual imagery. A 3-year-old child knows that ‘A’ is for ‘Apple’ and as soon as she recites the alphabet ‘A’, an image of a big red apple pops into her brain. This is how you remember and make sense of a language that isn’t your own at just 3 years of age. As college students, similar associations must be formed in your brain when you study any topic if you want to be able to fully understand it. As I am not someone who can grasp things extremely quickly, I have found a few tricks that worked for me and it is pertinent that I reveal them to you. Differential Equations and Calculus will be an easier challenge in your degree, not because they are easy but because they are familiar. Analysis is every student’s nightmare but all it takes to understand this subject is graphically visualizing each equation/theorem that is thrown at you. Also, if you think that you understand the difference between ‘if’, ‘only if’, ‘if and only if’, and other conditional statements, I would strongly suggest that you reconsider. Understanding logical statements is of utmost importance if you want a smooth-sailing academic experience. With Abstract Algebra, things become tricky. You can’t really visualize groups and rings because they are, as the name suggests, abstract concepts. A good trick is to consider this subject like a game of chess. Memory and strategy are of great value when trying to understand this paper. If you are at point A and want to reach point B, the background information about point A must completely be written down with a strategy to arrive at point B. In simpler words, remember every step involved in arriving at a particular result and at the same time, think two steps ahead as well. A good exercise is to approach your teachers and ask them about alternative solutions to a question that you struggled with. Go on the internet and look up the answers on StackExchange and read as many of them as you can. When you feel lost and frustrated with the subject, look at math memes.

Do whatever it takes and put in that extra effort. Scoring good marks in the university exams is extremely easy but what is difficult at times is realizing that mathematics can be beautiful, calming, and more accessible than you imagine. Don’t break up with maths because of temporary struggles. It might get awkward when two of you try to get back together again.