School update and upcoming plans

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     As of the end of the Fall semester, my degree is complete save for one easy class I'll take this spring. All of my upper level math classes are complete. Whilst this feels like some relief, I do feel a bit sad because I know that unless I further my studies in math, I have essentially peaked academically. I worked quite hard this last semester, and now that it's over I know that the definitions and theorems which constructed the world I have been studying will begin to slip from my mind.

    The most engaging course I took this fall (and in my degree) was Math 493: Topics in Pure Mathematics. The subject we focused on was commutative algebra. The course was roughly followed on text from Aaliyah-MacDonald, which was written to provide an introduction to commutative algebra for undergraduate/beginning graduates. This textbook is available free online for some light reading if one wishes to find it. In this course we studied what are called commutative rings (basically sets with some kind of addition, and a multiplication which commutes, that is, ab=ba, and a few other rules in there about the existence of "0" and "1", them being different, and additive inverses). Anyways, the subject is incredibly rich and really forms the basis for some of the most central fields in math such as algebraic number theory and algebraic topology, and field theory. We used concepts from the previous abstract algebra, linear algebra, and topology classes I took over the course of my degree. We had 3 homework questions every week which added up to a total of 10 homework assignments and a final exam. We had about 15-20 students in the class by the end of the course, which was the perfect class size to have plenty of discussion and collaboration with the homework problems. I particularly enjoyed the section on the Cayley Hamilton Theorem, Zariski Topology on the Prime Spectrum of a ring, and Localizations and Discrete Valuation rings. Overall the class was very challenging but incredibly rewarding, and I hope to return to the material possibly on my own time at some point in the future. Aaliyah MacDonald's text is full of useful exercises if I ever wish to return to it assuming I sum up the motivation one day.

    My parents have now returned from Ireland, so Christmas felt like old times with Shelby back from Toronto and the grandparents at the house. I even got a few days of skiing in. Now I'm on my way to Victoria to route set at the big lead wall in Victoria. Shortly after that I'm off to Mexico for a month! I'll do my best this time to get loads of photos and a blog post up about the trip shortly afterwards! I'm not really sure how my fitness is heading into the trip though. I'm climbing moderately well on the Board but my endurance might be shot. All the Christmas baking probably hasn't helped. Nonetheless forerunning the big gym should be a good tuneup and I'll have a month in el salto to get back in shape.

I've not yet decided what the summer holds, but it's looking like it will be either climbing in Squamish or at Horne lake. Horne has loads of routes I really want to do, and there's a couple projects and other hard routes around the comox valley which I'm quite interested in. That said, it's not Squamihs. I'll likely see how work turns out and decide from there what I'll do. One thing for sure is that I'll be climbing loads!!

Lots of good stuff to look forward to, so I'll try to get my ppm (posts per month) up. Thanks for reading and until next time!

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