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So you want to study mathematics

susanrigetti.com

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Re: So you want to study mathematics

#331

Post by bick_nyers »

helpfulclippy wrote: post #47
brimble wrote: post #31

Are 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.…

I did a degree in applied math. You’d think this would be “math you’ll use,” but the fact is that despite my program having a CS concentration, most of the stuff I did was not really applicable in practice. However, one thing that has been VERY applicable is proofwriting. Although math proofs are far more rigorous than most real world stuff, the discipline I learned in writing proofs has carried over into pretty much…

Applied-focused courses (like modeling, optimization, etc.) are very broad, and I think that's where some application gets lost. For me, learning proofs within an applied-subject-domain (like partial differential equations) helped me a lot, because it was a different "flavor" of proofs, where you could understand that applied domain much much deeper.

Re: So you want to study mathematics

#332

Post by susanrigetti »

adastra22 wrote: post #293
susanrigetti wrote: post #184

Earlier quoted context omitted.

For what it’s worth, the curriculum in this guide is modeled after the math major maps of many universities, including the one I attended (Penn). I would be curious to know what part of an undergraduate math curriculum will lead people very far astray…

Except for the course ordering, it lines up almost identically with the math major at my university. I'm not sure what the other posters are going on about. Most of their preferred topics that they feel you missed are either upper division electives or graduate level.

I suspect that people forget that undergraduate programs don’t really cover very much. This true not just for math, but for pretty much every other major. I mean, think about how little of physics you learn if you only take undergraduate courses!

Re: So you want to study mathematics

#333

Post by wbsss4412 »

kjasdfj3 wrote: post #240
wbsss4412 wrote: post #169

Earlier quoted context omitted.

You can certainly make significant headway with some basic combinatorics and basic tables for things like the normal distribution, no calculus needed. This is in fact how most people currently learn statistics.

What happens when you dont have tables? In the land of the blind the guy with one eye walks everyone off a cliff.

That’s question is akin to someone saying what happens when you don’t have a calculator. Everyone has one in their pocket at all times.

How would the typical person go about calculating the normal distribution by hand? Are we going to call everyone blind because they haven’t memorized e to arbitrary precision?

Re: So you want to study mathematics

#334

Post by susanrigetti »

bgroat wrote: post #242
philomathdan wrote: post #104

The 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…

I posted recently asking for exactly this... but for medicine. I have a body, everyone I know has a body. The operate pretty much the same everywhere in the world. I would like to know how it works.

I want this too. Let me know if you find anything!!

Re: So you want to study mathematics

#335

Post by susanrigetti »

ouid wrote: post #114

If 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…

That’s what the real analysis course is usually for, and why it comes after linear algebra and algebra.

Re: So you want to study mathematics

#336

Post by susanrigetti »

dmitrybrant wrote: post #256

The author doesn't seem to take her own brilliance into account when composing these self-study guides. For the other 99.99% of us, it would take many lifetimes worth of free time to make a substantial dent in these materials. To me, guides like these are too intimidating to even begin. Maybe what's needed is a meta-guide on structuring one's time and developing the necessary focus to be able to do this within one hu…

I will tell you the secret: just jump in.

Grab a pen and paper, open up the first book in any of the guides, and start reading. Read for 15 minutes, or 20 minutes, or whatever time you have on your lunch break or before you go to bed or while you’re using the bathroom. Do it again the next day. And the next. And the next.

That’s how I did it. There’s no brilliance involved. It’s just jumping in. The more you do, the easier it gets.

Re: So you want to study mathematics

#337

Post by susanrigetti »

frostblade wrote: post #225

Setting aside the question of motivation, how would a working adult find the time to work through all these books? The author of this clearly leads a busy life outside of reading math textbooks. Reading a math textbook is time consuming endeavor, regardless of underlying ability. The author herself mentions this in the introduction. I can think of a few factors that might make it possible for a busy person to go thro…

For me, it’s all about consistency. It’s spending a few minutes to a few hours every day, forever, til the day I die.

I usually can squeeze in 30 minutes to an hour every day to study something (whether it’s math or something else — right now I’m studying cinematography). Sometimes that’s in 15-minute chunks if it’s a busy day. Usually it’s before bed or while I’m eating lunch or if I have extra time on the weekends while my kids are napping.

It’s all about just doing a little bit every day. That’s been successful for me.

Re: So you want to study mathematics

#338

Post by ChrisLomont »

wizzwizz4 wrote: post #324
ChrisLomont wrote: post #305

Earlier quoted context omitted.

>I'm half-convinced that the “rank of a matrix” is just an artefact ... The rank of a matrix is fundamental to understanding linear transformations, since it given you knowledge about the dimensions of the "output space". It becomes more fundamental if the person goes on to study deeper math. It tells you how to compute the size of a basis for the target space. The uses go on and on. >And distributions aren't everyth…

> The rank of a matrix is fundamental to understanding linear transformations, since it given you knowledge about the dimensions of the "output space". That's more to do with the space of the coefficients, I think. > Saying one can look fundamental stuff up elsewhere means the book is lacking. A list of distributions is not fundamental to statistics. Discovering a new distribution doesn't meaningfully expand the fund…

>That's more to do with the space of the coefficients, I think.

I don't think that phrase is a thing in linear algebra.

I've gotten a PhD in mathematics - I know both these fields quite well. I stand by my assessment of linear algebra - I've been using pieces form it nearly daily for decades.

>Anyone familiar with those basic principles can pick up a new distribution quite easily – and can probably derive new distributions when they're needed.

And a student trying to learn where and why stats is useful should be taught a wide set of distributions so they see the nuances while they're learning. Sure, you can provide only a Gaussian, but when the student leaves completely ignorant of all the places a gaussian fails and what are some choices relevant to different situations, you can failed to teach them the fundamentals, which includes enough nuance to see when and where to apply what distribution.

>A list of distributions is not fundamental to statistics.

You may as well claim all of stats is not fundamental - just learn math principles. You can look up anything in stats and derive it yourself once given the concept if you're good at math fundamentals. Surely with enough math skills, and zero stats, you can derive all the stats knowledge needed without needing to ever see any stats in a book.

But that's a bad way to go about teaching people useful skills.

A student learning about distributions needs some examples. This book has none. You can argue all you want, but this book is crap for learning the topics the OP claimed it covers.

Find a textbook for beginning students that does not cover a multitude of distributions. Either every single author, usually writing from decades of experience, is wrong, or you are.

I think the authors have the right approach.

Re: So you want to study mathematics

#339

Post by wizzwizz4 »

ChrisLomont wrote: post #338
wizzwizz4 wrote: post #324

Earlier quoted context omitted.

> The rank of a matrix is fundamental to understanding linear transformations, since it given you knowledge about the dimensions of the "output space". That's more to do with the space of the coefficients, I think. > Saying one can look fundamental stuff up elsewhere means the book is lacking. A list of distributions is not fundamental to statistics. Discovering a new distribution doesn't meaningfully expand the fund…

>That's more to do with the space of the coefficients, I think. I don't think that phrase is a thing in linear algebra. I've gotten a PhD in mathematics - I know both these fields quite well. I stand by my assessment of linear algebra - I've been using pieces form it nearly daily for decades. >Anyone familiar with those basic principles can pick up a new distribution quite easily – and can probably derive new distrib…

> I don't think that phrase is a thing in linear algebra.

You're right; sorry for the typo. I meant the span of the coefficients (which is a space).

I'm not saying the concept of “rank” is useless, or anything. I'm saying a lot of linear algebra is based on high-level techniques and algorithms, but I don't think they're not truly fundamental concepts that you need to learn to understand linear algebra, if you learn / intuit a different high-level formulation instead.

> And a student trying to learn where and why stats is useful

That's not what I mean by “fundamentals”: I mean what stats is and how it works. A solid grounding in applied statistics is just as much about human psychology as it is about mathematics, and you never need know where your distributions come from so long as you memorise the rules.

> Sure, you can provide only a Gaussian,

Is that what the book does? If so, then I completely agree. But I don't see why you can't teach statistics using a Gaussian, a Poisson, a beta (three arbitrary distributions) and a general “some distribution”. I'm more of a pure mathematician, though, so if the answer's just “that doesn't prepare statisticians well for the kind of distributions that come up in the real world” then I can well believe it.

> Find a textbook for beginning students that does not cover a multitude of distributions.

… Aren't we discussing one?

Re: So you want to study mathematics

#340

Post by boppo1 »

ghufran_syed wrote: post #16

I went from only having done high school math 10 years ago to completing an MS in math and statistics at my local state university while working in an unrelated field. I would recommend NOT starting with calculus if you haven’t done it, instead, just learn how to do proofs - I used Chartrand “Mathematical proofs” - You don’t need to know any math beyond algebra in order to do that most of this book. If you need to re…

How old were you when you started into maths past the highschool level, and how many hours a week were you working in the unrelated field? I’m 29 and have a sincere interest in math, but I’m relegated to self-learning because I earned on.y a 2.3 GPA in undergrad. I’ve been working threough Hammond’s proof book as well as some vector calculus, and while I seem to completely understand the material as I read about it, the exercises leave me pretty bruised up.

I don’t know anyone who knows or values math much past algebra. “I don’t need it for my career, so why would I spend tome on it?” I don’t plan to switch to engineering, so I often find myself distracted & wondering what value math will add to my life other than making my interests more obscure and distant from the everyday people I meet. All I have to go on is “I’m interested & I trust that I’ll find it helpful once I know it. Also some people who are good at math make pretty good money.” But when I get 60% on a set of exercises, it’s challenging to keep faith.

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