Random photos from around campus

This gallery contains 28 photos.

Just a few shots from around where I live, and on my way to campus.

Sorry about the recent note-lag (if you’ve been following my 1125 notes, you probably noticed that there’s a lot of diagrams I haven’t yet included and so on). I have a big algorithms assignment due next Wednesday, which I’m sure will involve tons of lovely stuff like proving things from the definition of big notation, but anyways… I’ll try to bring things up to date this weekend. Also hoping to do a new video soon.

Final recap of tensor products. Ironically, I may have a bit more to say about tensor products (heh…) but I promise we’ll do some other exciting stuff before having to go back there.

A random comment from the internet: “In the extensive amount of mathematical knowledge I acquired for my degree in finance, I have never heard of an ‘Abelian Group’. Undoubtedly it is another part of ‘Pure Mathematics’, That useless branch of study that many academics turn to when they find they are ill-prepared to survive in real world subjects, and must pick something which allows them to spend their time poring over obscure symbols that have no bearing on reality whatsoever. Too weak to deal with the uncertainty that is real life, they must study a field with clearly defined axioms so that they can feel ‘secure’ in their ‘knowledge’. Such pursuits are vain and self-masturbatory, and I find it repulsive that you would consider any of it’s practitioners to be a ‘heavy-hitter’ in mathematics.”

Pretty accurate.

Effective immediately, I’m self-studying out of Spivak’s Calculus on Manifolds (it’s about time). Here’s a tentative outline of which sections I’ll be covering when. If time permits, I’m thinking of creating a full lecture series based off the book (such a thing doesn’t really seem to exist at the time), although it’s unlikely I could finish by the end of the term.

May 1 — May 7: p. 1-15. Finish first chapter, Functions on Euclidean Space.
May 8 — May 14: p. 15-30. Basic definitions, basic theorems, partial derivatives.
May 15 — May 21: p. 30-43. Derivatives, inverse functions, implicit functions.
May 22 — May 28: p. 44-56. Notation, basic definitions, measure zero, integrable functions.
May 29 — June 4: p. 56-67. Fubini’s theorem, partitions of unity.
June 5 — June 11: p. 67-80. Change of variable, algebraic preliminaries.
June 12 — June 18: p. 80-97. Algebraic preliminaries, fields and forms.
June 19 — June 25: p. 97-109. Geometric preliminaries, fundamental theorem of calculus.
June 26 — July 2: p. 109-115. Manifolds.
July 3 — July 9: p. 115-122. Fields and forms on manifolds.
July 10 — July 16: p. 122-126. Stokes’ theorem on manifolds.
July 17 — July 23: p. 126-134. The volume element.
July 24 — July 30: p. 134-137. The classical theorems.

Extra references:

1. C.H. Edwards Jr., Advanced Calculus of Several Variables.
2. W. Rudin, Principles of Mathematical Analysis.
3. V. Runde, Math 217 Lecture Notes.

Music of the primes

So, this Spring term, I’ll be finding the zeros of in PMATH 740 (analytic number theory), alongside CO 342 (graph theory 1) and CS 341 (algorithms 1). 3 courses seems a bit light, but I think it’ll be nice since 740 will probably be demanding, and I’ll also be working on a few other things on the side as well. One of those things is a self-study of differential geometry, to prepare for PMATH 763 (Lie groups), since I will have to override the PMATH 365 prerequisite. I’ll also be typesetting Stephen New’s PMATH 352 this term (I couldn’t resist — as an excuse, I’ll blame it on the fact that my own complex analysis notes are subpar and I need to review the material, due to 740). Aside from that I’m contemplating some simple musical endeavours, time permitting. Learning math is a pleasure, but you know, I’d rather not consume it as fast food.

I hope Winter went great for everyone, and I’ll see you soon! Cheers.