As a fellow penn alum, I can totally vouch for Ghrist's approach to calculus. Check out his youtube channel: https://www.youtube.com/c/ProfGhristMath
So you want to study mathematics
111–120 of 371 posts
Re: So you want to study mathematics
#112As a math PhD I have to say the only way you're going to learn mathematics is if you actually have a pressing need to do so. i.e. You have a project at work that needs some math, you have a hobby that needs some math. In this case you just learn what you need. Just learning math for its own sake outside of a University STEM track is just too hard (I wouldn't be able to do it and I've tried).
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Re: So you want to study mathematics
#113The curriculum guides Susan Rigetti provides are an amazing resource for self-study. And the fact that she worked through all of this is truly inspiring. Not to be greedy, but do any of you know of other thorough curriculum guides like this? I know about https://teachyourselfcs.com already -- another amazing guide. Are there others? I would love to find one for statistics especially, but really any subject would be i…
Susskind’s Theoretical Minimum is fantastic for physics self study: https://theoreticalminimum.com/
Re: So you want to study mathematics
#114If you actually want to study math, you probably shouldn't touch calculus until you've take linear algebra and a fair amount of topology, since these are the two structures on sets that (differential) calculus is founded upon.
For other subjects, you can briefly substitute an intuition for the underlying structures with sufficient finesse in the presentation of the material (see the theory of knots and links, for an example), but calculus is not, in my experience, such a subject, and the early emphasis on it is harmful for the study of mathematics, which is supposedly what your list is for.
For some reason this is heresy, but I have honestly no idea how you are supposed to appreciate calculus from a mathematical perspective without being able to define the large stack of terms that constitute it. The situation is potentially different for a physicist, but if you want to study mathematics, the physical world is not the object of study, rather it is precisely the definitions that we have chosen.
Re: So you want to study mathematics
#115As a math PhD I have to say the only way you're going to learn mathematics is if you actually have a pressing need to do so. i.e. You have a project at work that needs some math, you have a hobby that needs some math. In this case you just learn what you need. Just learning math for its own sake outside of a University STEM track is just too hard (I wouldn't be able to do it and I've tried).
I experienced something like this recently. I struggled to grasp linear algebra when I took it in undergrad and as a result was always intimidated by the subject. Now, years later, I'm taking a course in graphics and naturally needing to relearn linear algebra and suddenly everything just clicks.
Re: So you want to study mathematics
#116Earlier quoted context omitted.
It’s amazing how different the subjects of mathematics are. It’s like the difference between a drum and flute. You listed some of my favorite stuff. Weirdly, when I was 11, my math tutor told me I’d probably really like finite mathematics. She turned out to be right.
> It’s amazing how different the subjects of mathematics are. It’s like the difference between a drum and flute. I think it’s amazing how connected the fields are. It’s almost like “pick any two of analysis, algebra, geometry, number theory, topology, turn one into a adjective and you’ve got a new subject area”. Topological algebra? Check ( https://en.wikipedia.org/wiki/Topological_algebra ) Algebraic topology? Check…
You can add 'combinatorics' to the list of primitives.
Algebraic combinatorics (imo) encompasses related structures in all three of combinatorics, algebra, and geometry, though.
Re: So you want to study mathematics
#117I find it hard to believe that the author started to appreciate physics by reading The Feynman Lectures on Physics before any exposure to physics or even algebra, and in less than three years went from barely knowing high school math to enjoying advanced mathematical physics and graduate-level quantum physics. It looks this is one-in-a-million level brilliance as learning the sheer amount of requirement knowledge in…
More like one in 50-100 million brilliance, and such people do exist. It's a statistical certainty they exist. Terrance Tao for example.
Re: So you want to study mathematics
#118I find it hard to believe that the author started to appreciate physics by reading The Feynman Lectures on Physics before any exposure to physics or even algebra, and in less than three years went from barely knowing high school math to enjoying advanced mathematical physics and graduate-level quantum physics. It looks this is one-in-a-million level brilliance as learning the sheer amount of requirement knowledge in…
I agree that this does not on its surface seem possible, but I can think of a few explanations. 1. I recently spent a week on one section of one chapter of a math book. I was able to follow it within an hour on the level of "these are the rules and this is the sequence of their application," but I have stuck with it since then because I wanted to understand it well enough that the proof they chose to use would seem o…
women had an advantage over men in regard to memorization. this helps greatly at learning.
Re: So you want to study mathematics
#119Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…
You don’t need proofs, but you still need an intuition for why things work the way they do.
Otherwise you will be lost as soon as you leave the textbook territory.
Proofs are just one way to build intuition.
The best way to learn applied maths and get intuition is an “Introduction to Maths for Physicists” 101 course.
Re: So you want to study mathematics
#120Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…
> Are there any "math for people who just want to use it" tracks in math pedagogy? Use it for what ? That is the question. If you pursue the what , you will inevitably be exposed to genuine ways that mathematics may be employed by it. The academic standard for "learning math" is like "learning programming" by reading the C++ language/STL spec from front to back. No one productively learns programming that way, and ev…
I agree. If anyone wants to study "math in practice," they should pick a science or engineering track they like. Math will be included.