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So you want to study mathematics

susanrigetti.com

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Re: So you want to study mathematics

#201

Post by secabeen »

davidmr wrote: post #133
mbustamanter wrote: post #13

> My goal here is to provide a roadmap for anyone interested in understanding mathematics at an advanced level. Anyone that follows and completes this curriculum will walk away with the knowledge equivalent to an undergraduate degree in mathematics. NO, NO, NO. There is no real way to go up to the real deal without having understood elementary Functional Analysis, which the article doesn't even mention. FA is roughly…

This is certainly not universally the case, even in very well-regarded departments. The University of Chicago, for example, does not require it: http://collegecatalog.uchicago.edu/thecollege/mathematics/ .

For those of you interested in the Chicago approach, a bibliography of textbooks used in Chicago UGrad math is maintained here:

https://github.com/ystael/chicago-ug-math-bib

Re: So you want to study mathematics

#202

Post by screye »

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.…

This is more of a university perspective, but......

> Are there any "math for people who just want to use it" tracks in math pedagogy

It's called Industrial Engineering /s (but only kind of)

It is tame as compared to a pure math or physics B.S. But, you pretty much cover the gamut of every math tool that is useful in the real world. From stats, supply chain, search, calculus to combinatorics and so on. Each concept is squarely grounded in a field where it is used.

I was surprised at how well my mechE (usually the closest undergrad degree to Industrial) degree prepared me for applied math and ML coursework for my CS masters. In comparison, a lot of CS undergrad peers struggled in those courses.

Re: So you want to study mathematics

#203

Post by bigger_cheese »

ghaff wrote: post #161
jll29 wrote: post #62

Earlier quoted context omitted.

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…

Interestingly the ascent of linear algebra is a relatively recent thing. I have an engineering degree but while I was certainly exposed to basic matrix stuff, never took a linear algebra class. When I was an undergrad, you took differential equations in addition to basic calculus for engineering. (You needed for system dynamics among other things but it was very cookbook.) Linear algebra became a lot more interesting…

When did you do your Engineering degree? When I did my BE Degree (2004 to 2008) Linear Algebra was included. We were introduced to the basics of linear Algebra in year 12 of high school (simple matrix manipulation, intro to vectors, dot and cross products that sort of thing). I'm Australian if that makes a difference.

The Math in my 4 year engineering degree was structured something like this:

First Semester Year 1 two math courses: Calculus 1, Linear Algebra

Second Semester Year 1 two math courses: Calculus 2, Sequences and Series (this one was probably least useful all I remember from this 15+ years later is Taylor Series and Binomial Theorem)

First Semester year 2 two math courses: Differential Equations, Statistics for Engineers.

From second semester year 2 onwards there were no more discrete math classes this was where the degree really specialized into various engineering streams, Mech Eng, Chem Eng, Civil etc. Had their own courses. I studied Materials Engineering some courses were shared with other eng students (For example I shared Thermodynamics with Mechanical Engineering students) but others such as Non-ferrous metallurgy were pretty deeply specialized.

A lot of subject used built on earlier math (Fluid Dynamics was backed up by lots of differential equations for example, stuff like Gamma Function would come up in a lot of places. Solid Mechanics had a lot of integrals second moment of area etc.), Linear Algebra I can remember from Fracture mechanics and crack propagation (Stress and Strain tensors etc.)

Re: So you want to study mathematics

#204

Post by paulpauper »

ChrisLomont wrote: post #131
paulpauper wrote: post #121

You don't need so many books. many of the old texts will cover many important college-level concepts in a single source. https://www.gwern.net/docs/statistics/1957-feller-anintroduc... this is linear algebra + combinatorics + probability + stats If you understand the material in this one book it's reasonable to say that you are pretty good at math

At a first glance that book completely fails for an undergrad lin alg course, and looks weak in other areas too. Examples: the words nullity and kernel don't appear, rank of a matrix is not in it, and, well, every topic I can think of for undergrad linear algebra is simply not in the book. It's equally bad for stats: no mention of many common distributions a student would learn for example.

I give a book recommendation and ppl complain, yet no one complains when ppl recommend Khan Academy. Do people think Khan Academy is more rigorous than a textbook?

Re: So you want to study mathematics

#205

Post by brimble »

Jach wrote: post #144
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.…

Yes, all tracks of math involve people using math. Proof writing is a part of use for a lot of it. There are also very many tools within the use of proof writing where a lot of education is around learning a bunch of tools so that you can better "recognize which tool to apply, then apply tool", in a future real-world use where you want or need to prove something. I'm a little snarky, but you have a broken idea of wha…

> I'm a little snarky, but you have a broken idea of what math is.

I do not, which is why I explicitly acknowledged that what I want is not "real math". I don't care about math for math's sake, even a little. Not my thing, never will be.

Basically I want to learn to apply useful results from hundreds-of-years-old "advanced" math the same way I learned math in grade school: memorization, pattern recognition, heuristics, intuition, and drilling, all with a focus on application. Keep the proofs far, far away unless there's some excellent reason I have to know them (and perhaps there's actually no way around that, but I suspect the current situation has more to do with the interests and world-view of people who design math curricula, i.e. mathematicians, than strict need, if you're mainly focused on application). Ideally, almost every single problem set would consist mostly of so-called word problems, drawn from realistic circumstances.

Re: So you want to study mathematics

#206

Post by ghaff »

bigger_cheese wrote: post #203
ghaff wrote: post #161

Earlier quoted context omitted.

Interestingly the ascent of linear algebra is a relatively recent thing. I have an engineering degree but while I was certainly exposed to basic matrix stuff, never took a linear algebra class. When I was an undergrad, you took differential equations in addition to basic calculus for engineering. (You needed for system dynamics among other things but it was very cookbook.) Linear algebra became a lot more interesting…

When did you do your Engineering degree? When I did my BE Degree (2004 to 2008) Linear Algebra was included. We were introduced to the basics of linear Algebra in year 12 of high school (simple matrix manipulation, intro to vectors, dot and cross products that sort of thing). I'm Australian if that makes a difference. The Math in my 4 year engineering degree was structured something like this: First Semester Year 1 t…

Late 70s in Mech E. Fluid dynamics has a lot of IMO nasty math. (Navier-Stokes specifically.)

Have a Master's in Material Science and still don't remember a lot of Linear Algebra specifically.

Re: So you want to study mathematics

#208

Post by mmmpop »

ghaff wrote: post #172
mmmpop wrote: post #167

Earlier quoted context omitted.

In my high school experience, this was avoided if you had the desire and aptitude to just take Honors Physics instead. To work around the fact that many of us were still in precalc, our teacher just taught us the power rule, the relationship between slopes of tangent lines, etc., without diving into the "why" of why those things worked. That said, yeah maybe for the most basic of university of physics the whole "deri…

For tests and the like, when I was an undergrad, it was fairly common to be able to bring in a one-page "cheat sheet." The idea was that you probably could derive a lot of the stuff given time and maybe references, but you almost certainly couldn't in a 1 hour exam in addition to solving the actual problems on the test.

>> 1 hour exam

I'm trying to remember when I had one of those last!

I actually don't love the idea of cheat-sheets but maaaybe if it's a cumulative final I could see it being helpful? If you're taking chapter exams on some material, I think you ought to have worked enough problems so that formulas/constants are drilled into your head. But I guess too, where do you draw the line at engineering appendices? I sure don't have the MoI of every common body memorized.

Re: So you want to study mathematics

#209

Post by brimble »

pnin wrote: post #176
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 have some sympathy for this sentiment, and there is no doubt that the producers of mathematics could and probably should spend more time making life easier for the users and consumers of mathematics. This is true even /within/ the discipline, for very theoretical stuff. In the end this takes vastly more work than people expect. That's not an excuse, but it's true. However, I also have a fundamental objection. I don…

I do not have the right background to be an authority on this, but from going through school myself and paying a fair amount of attention to math reformers over the years, it seems like they usually believe:

1) The problem with math in school is that there's not enough "real math".

2) Relatedly, insufficient exposure to "real math" in compulsory schooling is also (a major part of) why people think they don't like math.

My suspicion (again, without the actual background to make this claim with any authority) is that they are dead wrong on point 2—the "real math" parts probably contribute strongly to most folks' dislike of the subject, and the parts the mathematicians didn't like are probably relatively popular among people who don't go on to become mathematicians. This puts point 1 on some shaky ground (though it could still be true and well-justified, for other reasons).

Re: So you want to study mathematics

#210

Post by technosamay20 »

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…

On the other hand I sometimes wonder why Calculus is made a big deal out of. It was probably the easiest among all the parts of maths. You just have to imagine an small unit and how to extrapolate for integration and imagine how to break it down to small parts for differentiation. When I originally learnt Calculus in high school it was couple of days of learning the concepts and the a week of deriving everything from that and move on!
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