When you set out on a long journey, there may come a time when you have to step back, take a rest and reconsider your initial plan. The routes might not work out the way you had them laid out. Or you might not be able to walk them in as short a time as you had estimated. Nevertheless, you are much closer to your destination now than to the point where your journey started. The thought of turning back, or of abandoning your travels and taking a carriage home, does not once occur to you. There is no doubt that you will make those final steps and walk through the gate of the place that you have set out to reach. Just not so soon.
It has been something short of two years since I took up mathematics again. Since then, the mill has been grinding incessantly, save for a week of vacation here and there. I have not died of sleep deprivation, and it has been an experience that has brought me deep inner joy. Joy of the same kind that will keep me stepping onwards. But now the time has come to make a short halt for revitalization, and then to walk the remainder of the path at a more unhurried pace.
What do we have all wrapped up? There's the classic ‘starter pack’ of analysis and linear algebra, without which there is nowhere to be gone. Add in a morsel of probability theory and ordinary differential equations. I have passed the two oral exams required for the bachelor's―of which one has allowed me a glimpse into the beauty of functions in the complex plane, and the other into the elliptic curves and finite fields of cryptography. I have had an encounter with graph theory, and encounters with a number of people from the teaching staff at the University of Hagen.
Life happens, and as it does, some things simply take priority over others. With my move to the Pacific now imminent, some shifting and arranging of the target curriculum was in order. And this is where the term distance in distance education really comes into play. The University of Hagen allows for its students to take written exams in any location on the planet where an office of the Goethe‑Institut is present. As for me, this means that I will be going to Sydney to write those exams. For the bachelor's, the only time left that I need to be present in Germany will be the presentation of my thesis.
Perhaps this would be the time to address the question that I have been asked multiple times by myself and others―to what end? Or rather, is there anything I have in mind that I would like to do with my degree, once the progress bar reaches the 180 ECTS mark? Or should studying mathematics remain an end in itself, true to the adage of the journey being the reward? Truth to be told, I do not know if I will ever apply any of the things I am learning in any 'professional' or whatsoever way. I do not know if my degree will ever mean anything on a job application. And I am as of yet not fully decided whether or not to pursue a MSc in mathematics after this project reaches completion.
What I know, though, is that I want to keep studying. I am fairly confident that what I started in 2017 will turn out to be a rich, elaborate birthday present to my soon‑to‑be 40‑year‑old brain. It comes at a cost of roughly 1800 EUR. If you add in all the expenses―travel, lodging etc.― perhaps 3000 EUR. Surely below five‑thousand, and at that, significantly less costly than what someone would pay for tuition at a university outside the Germanía, which through the centuries has provided its children a fine education at some of the continent's most venerable universities for the cost of chitterlings.
If I don't pursue a master's with the University of Hagen, I might go on to study something else, and at a different school. Without a doubt, a solid education in mathematics is a good foundation to build upon. There are times when I think I might gravitate towards science. And even if I do not continue my university studies at all, it will have been a worthwhile project to have completed. For molding one's brain into one that has a better understanding of mathematics means acquiring styles of thinking that can be universally useful. An experience that changes the mind and is conducive to personal growth.
But the meat is not only in the subject itself, it is in the entire cultivation of it―getting up early in the morning to study, doing it every business day for a prolonged time, studying in silence and maintaining a focus―these are things that, with time, build a stronghold. Regardless of the subject matter, such a practice helps keeping the mind clear and giving the life direction. And inasmuch as it does, it bears a likeness to physical exercise or meditation.
Another aspect that plays into this is that of solitude. I have had a short flirtation with studying mathematics at an intramural university in 2008/9―hence I know what it feels like to sit in a lecture hall and have mathematics presented to you in the traditional way of oral relay and chalkboard writing, or in the math students' lounge where people are discussing their assignments, among other things. Obviously, all this is part of a culture that one does not have much opportunity to experience when studying distance‑only. But, pertaining to my own learning style at least, the bulk of the actual learning of mathematics would have taken place at home and in solitude anyway.
With all of this said, I am looking forward to the remainder of my bachelor's. Writing the thesis especially will be a stimulating challenge. As of yet, I do not have the slightest idea what the topic will be. Perhaps something that will expand on next semester's 01106 Praktikum zur Algebra. Whatever it will be, it shall be written under the Australian sun―a pathway into tropical geometry, perhaps. Or into realizing the necessity of air conditioning.
Articles on studying mathematics to date:
- Beginning Ascent(14 August 2017)
- Start of First Term(1 October 2017)
- First Exams Getting Closer(5 January 2018)
- On It Goes(24 April 2018)
- My Path to Complex Analysis(29 August 2018)
- A Trip to Hagen and Back(24 October 2018)
- On Chordal Bipartite Graphs(3 February 2019)
- Rearrangements―a Quaint Bucolic(23 August 2019)