This summer, my schedule is:
Mondays: Topology (Willard)
Tuesdays: Linear Algebra (Axler) and "Baby Rudin"
Wednesdays: Topology (Willard) and Algebra (Fraleigh)
Thursdays: Topology (Willard) and Linear Algebra (Axler)
Fridays: "Baby Rudin" and Algebra (Fraleigh)
My goal?
- Become entirely proficient with, at the very least, undergrad linear algebra and algebra. I took these courses almost in their entirety as an undergrad and mostly need to become more familiar with the theory (the courses were not as proof-heavy as I would have liked).
- Work through as much of Rudin and Willard as possible. These texts are heavier and take a lot longer to work through. My goal at the start of the summer was to complete them, but I'd probably have to devote my entire summer to working only on these texts, and that's not worth it. I'm not even doing all of the exercises--just around half!
This blog is planned, mostly, to be a record of my progress and a way to motivate myself to typeset some proper proofs. I'll be posting my favorite proof of the day, or perhaps two!
If you stumble across this in your studies feel free to use this to help you, but don't copy! You don't learn by copying. You don't even get better grades.
Image source: Abstruse Goose
Don't just read it; fight it! Ask your own questions,
look for your own examples, discover your own proofs.
Is the hypothesis necessary? Is the converse true?
What happens in the classical special case? What
about the degenerate cases? Where does the proof
use the hypothesis?
--- Paul R. Halmos
Also, keep in mind I'm learning so my proofs may be incorrect anyway ;)
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