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So you want to study mathematics

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Re: So you want to study mathematics

#271

Post by mrjangles »

susanrigetti wrote: post #184
mrjangles wrote: post #178

Earlier quoted context omitted.

Yep, I came here to say this. I think it is important that anyone who wants to study math understand that real math is not at all like what you learn in a physics or engineering department. In these departments you will always hear people say things like >"proofs are not useful, all you have to do is memorize the 'trick' they use. Once you know which trick to use, it is easy" or you will hear them say. >"Math isn't a…

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…

It's just that it is very much a "mathematics for engineers" style course. I think very few of the subjects outlined there give you a flavor for what "real" mathematics is really all about at all (except for algebra, which you do mention).

Apart from the applied stuff you mention, the real core of a mathematics education involves, I think, 4 main areas with significant overlap

Group A: number theory, graph theory, combinatorics

which shares concepts with

Group B: Algebra, Topology, complex analysis, differential geometry, metric spaces...etc

which shares concepts with

Group C: Functional analysis, measure theory

which shares concepts with

Group D: probability and statistics.

As for the applied math that you mention, you should really need to add vector calculus and I'd highly encourage anyone to take a course on fluid mechanics (from a mathematics department instead of an engineering department) to get a real feel for vector calculus in action.

Re: So you want to study mathematics

#272

Post by rg111 »

dunefox wrote: post #179
criddell wrote: post #53

Earlier quoted context omitted.

I looked up the Chartrand Mathematical Proofs book and it's been a while since I had to buy a textbook, but $175 for hardcover and $75 for paperback or ebook? That's nuts. If I were a student today, I'd pirate that and feel absolutely no remorse for doing so.

Thing is that I just can't read PDFs.

Use an iPad, or any tablet, rather than smartphones.

I also read PDFs full-screen on my high-res, high-dpi laptop.

Try these two.

I have read tens of thousands of pages in PDF. (Yes, I checked)

Re: So you want to study mathematics

#273

Post by throwamon »

Buttons840 wrote: post #109
cptaj wrote: post #87

Earlier quoted context omitted.

I just want a place I can go to weekly for 15min to practice math. It keeps track of what I know and gives me exercises of stuff so I can retain the skills. I've forgotten 90% of the math stuff I learned

Khan Academy. Finish a course, retake the course exam once a year afterwards, fill in knowledge gaps as needed. Doing this should keep all undergraduate math fresh in your mind.

I wanted to like Khan Academy, but the pacing of the exercises is so frustrating. They become too easy too fast and then it's an extremely repetitive slog of useless computations.

I wish for a service just like them but with many more difficulty levels and less (non-spaced) repetition.

Re: So you want to study mathematics

#274

Post by novok »

kjasdfj3 wrote: post #239
joatmon-snoo wrote: post #49

Earlier quoted context omitted.

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

> My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. I'm questioning your math pedagogy. Calculus is the single most important math anyone, of any field, can learn as it's the first "practical math" you actually learn. Life behaves like calculus and in order…

Unless you are dealing with subjects that would actually use calculus, people in their day to day lives would do much better to understand probabilities, statistics and experiment design. Most of our lives are dealing with the results of empirical studies, in business, science and policy and humanity could use a big reminder that life is not a binary black or white, but a huge pot of maybes.

Otherwise it just gets absorbed and forgotten like another 'useless information' class. Ask how many CS majors post college use or remember calculus vs understanding stats for the seven millionth badly designed A/B test they ran at work today.

Re: So you want to study mathematics

#275

Post by diffeomorphism »

jll29 wrote: post #62
joatmon-snoo wrote: post #49

Earlier quoted context omitted.

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

Calculus and linear algebra seem to _totally_ dominate the curriculum in most (all?) countrie. What about meta-mathematics? Topology? Logics? History of mathematics? Philosophy of mathematics? Combinatorics? Number theory? Discrete mathematics? Graph theory? In the post, the fieds under "electives" are by far the most interesting ones, IMHO. And I fully agree, in-depth knowledge of probability theory as well as descr…

These come as a second step.

In the first year (non US) you learn linear algebra, some real analysis and how to write proofs as well as important basics. In your second year you can choose all these electives, which then don't have to spend time introducing natural numbers, induction etc.

Re: So you want to study mathematics

#276

Post by adgjlsfhk1 »

bee_rider wrote: post #195
SamReidHughes wrote: post #155

Earlier quoted context omitted.

Well, AP statistics covered the area under a probability distribution function and people seemed to understand that -- you look up the answer in a table (or use the TI-83 function). Presumably they'd do the same for a cumulative distribution function.

Highschool is pretty early to teach people that math is too complicated for them to actually evaluate their expressions.

Teaching people that there are lots of problems where solving them numerically is the best way of solving them is often just the truth. Also, you then get to discuss some of the really cool numerical techniques which tend to get short-changed in traditional math classes.

Re: So you want to study mathematics

#277

Post by [deleted] »

Koshkin wrote: post #189
criddell wrote: post #53

Earlier quoted context omitted.

I looked up the Chartrand Mathematical Proofs book and it's been a while since I had to buy a textbook, but $175 for hardcover and $75 for paperback or ebook? That's nuts. If I were a student today, I'd pirate that and feel absolutely no remorse for doing so.

Maybe, but this is not so bad, if you realize that the time and the effort you would spend on learning the material from such textbook is in some ways incomparable with the price of a couple of dinners at a restaurant.

[deleted]

Re: So you want to study mathematics

#278

Post by eternityforest »

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 am literally working on exactly that, as an project I'm calling Math: ELI5, all open source on GitHub: https://github.com/EternityForest/AnyoneCanDoIt/blob/master/...

The catch is that I myself don't actually understand this well. It's just "What I learned googling stuff while working as a programmer. I've had help reviewing it but there could be errors.

I'm trying to cover all areas of math that a nontechnical person, or typical non math focused programmer would need to know, but I treat actually doing any of it by hand on paper as an arcane thing for the really dedicated, so there's not really any excercises.

Instead of actually teaching a real understanding of math, which I can't do, because I don't know it well, I just explain what people who do understand it use it for and why you might want to go actually learn it.

I also have any historical math related stuff that I find interesting.

I can't tell you how to derive or prove Euler's equation , but you don't need to know math to understand the emotional impact from a humanities perspective, and be amazed that all those constants fit together like that, and that someone could discover it.

Ultimately, I think traditional math education has it totally right. My life would be so much better if I knew it, because there's jobs that seem to require exactly what they tech in math class.

It's not directly useful for non STEM types, but the idea seems to be give everyone a head start since so many do want STEM jobs.

I think you really do have to get to the being able to do proofs level to make use of it in the real innovative applications.

The common everyday applications math people like to cite can usually have a dedicated software package. It's not like we still need to add two numbers on paper. If you want to build something, we have RealThunder's FreeCAD.

Excel's Goal Seek and CAS systems do the stuff people say we will use algebra for.

But if your in tech eventually you run into the wall and need to do something like a Kalman filter or calculate stresses in a bridge and you're screwed.

Re: So you want to study mathematics

#279

Post by eternityforest »

joatmon-snoo wrote: post #197
geebee wrote: post #151

Earlier quoted context omitted.

I'm really wary of this. House wiring would be more useful than Shakespeare. That's not to knock house wiring, or statistics. I'd love to know more about both. But don't deny yourself an understanding of the meaning of limits. Almost all mathematics before calculus leaves you with a misimpression that neat formulas exist to solve problems. In reality, you've learned to draw straight lines with a ruler, and maybe a fe…

Education is a Hard Problem TM because the knowledge of those links isn't useful without sufficient existing knowledge, and you need to introduce things in a way such that the things you hand-wave away are tolerable knowledge gaps. Knowing that a CDF is an integrated PDF isn't useful for someone who doesn't even have a notion of what a PDF is. Describing a state machine that satisfies conditions X Y Z as an Abelian g…

What would someone other than a scientist use regressions for?

I've used one once. I wanted to make a volume control that I thought sounded subjectively even across the range and gave the right amount of control. So I used a polynomial regression calc on a random website and gave it some data points I wanted it to go through.

But that's not actually doing a regression, just knowing it exists and computers can do them.

Is there any math that has any use whatsoever unless you know a whole lot of it and plan to do some technical projects? I thought the whole point of learning any math(Even arithmetic, since phones exist now) is just so you can learn other more advanced math, and maybe someday be a solid state chemist or something.

Statistics lets you read a scientific paper, but you don't actually need to understand it, unless you're actually going to be reviewing their raw data. Most everyday people just trust the p values and move on to wondering about confounders they forgot.

Seems like you could cover all the statistics people will actually use it about 4 hours.

Re: So you want to study mathematics

#280

Post by ALittleLight »

geebee wrote: post #151
joatmon-snoo wrote: post #49

Earlier quoted context omitted.

My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…

I'm really wary of this. House wiring would be more useful than Shakespeare. That's not to knock house wiring, or statistics. I'd love to know more about both. But don't deny yourself an understanding of the meaning of limits. Almost all mathematics before calculus leaves you with a misimpression that neat formulas exist to solve problems. In reality, you've learned to draw straight lines with a ruler, and maybe a fe…

But Shakespeare is incredibly useless. People don't even talk or write like that anymore. Any imagined benefit of Shakespeare is just fanciful wishful thinking.
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