Shoutout to http://www.rethinkstudying.com/video-game/ for giving me a methodology to study, not only for actuary exams, but mathematics as a whole!
The Beginning of My Journey into the Wonderful World of Mathematics
As an avid gamer, I’ve came upon the aforementioned site and my mind was blown by the beautiful, simplicity of trying problems out; before tackling the actual concepts. I’ve struggled to make the transition from a strong science background to the beautiful and often vexing, yet enrapturing world of mathematics.
I began my journey back in 2015. I took a break from work for a semester, to become an actuary (which is still in progress, with exams to be passed and technical skills that need to be rectified). The first class I took really challenged me to start thinking out-of-the-box: more so than I did already. Multi-variable calculus with Linear Algebra was meant for undergraduate math majors. I didn’t pass the class, possibly due to the fact you can’t get anything lower than a C with the graduate grading scheme.
Anyway, that is a whole other story altogether. The real reason for me writing this short blog, is to detail my journey, as both an introspective journal and a possible inspiration for young friends, looking to either transition into mathematics or are looking to become actuaries. I feel it is my responsibility to impart my knowledge and experience in 7+ years as a sleep technologist and the rigor/difficulties of transitioning into a very tough, analytical field to get into.
With this digression, I come to the actual Multivariable/Lin algebra class that inspired me to begin this journey. The professor was excellent and the graduate TA was excellent at explaining things. But, where I really got the most benefit, was my tutor at the academic tutoring center at Stony Brook university. This young man had an absolutely thorough understanding of the material and also explained things to a layman, like myself. Our talks led me to become more and in love with the subject of multivariable calculus. I know now that what I learned in that class is quite applicable to higher levels of topology, including manifolds and application of Green’s/Stokes’ theorems. I have found what is equivalent to the abstract concept of a mistress, for a mind yearning for knowledge!
Mathematical Maturity
This topic is clearly something that I’m just beginning to touch upon. I have just had my first day in an Abstract Algebra, second-semester classroom and a Complex Analysis classroom. What I found so fascinating, was that the topics in Complex Analysis correlated very closely to the study of bilinear forms and transformations to the complex plane in Abstract Algebra! Clearly, I was lost in the Algebra class. However, seeing it on the board a second-time helped to somewhat plant an idea in my mind: an Inception-like phenomena, for those Inception movie fans out there.
The professors were both truly passionate about the topics were teaching, which I find absolutely fantastic! Though I may not have had a semester of group theory, field theory, tensor products etc., I was able to follow the idea of mapping, which was found in both Abstract Algebra and Complex Analysis. With rudimentary knowledge in linear algebra, I am still trying to process all that was learned, in this block of about 3 hours of lecture.
One thing I found on mathematical forums, was an opinion, where proofs should be taught with the class. Analysis is a very rudimentary part of mathematics and I believe it can be learned via practice. Still, I ended up getting a proof book that showed some analytical techniques for group theory, so I have an idea on how to proceed for proofs of this nature. At this point, I love reading and understanding proofs. I have a lot of work to developing the skillset of writing proofs, though I have some exposure to proof by induction (due to studying Marcel Finan’s exam P manual, which has beautiful proofs for probability theory).
I believe that mathematical maturity can be obtained, by taking these difficult classes. For a lover of mathematics, I am taking Abstract Algebra and Complex Analysis for fun. I believe a student of from any major can benefit from taking on rigorous class on mathematics or applied mathematics. Mathematical maturity helps to think more abstractly and logically; very important in this chaotic, yet beautiful thing we call life.
Thank you and I hope this blog helps career-changers and younger folks out there!
Update: Self-studying Abstract Algebra and Complex Analysis at my leisure, so I can study for actuary exam P!