Poll: High Level Math in the Escapist

[smithy_2045]

I'm a stats major who's just getting started along the PhD path. Where does that put me on your poll?

 

[f1r2a3n4k5]

For example, OP, do you have any background in art history? My college offers intro-level art history courses. Presumably, there may be people who went to artistic schools and know this stuff already. I did not. So, I enrolled into an introductory art class. Same basic premise; different field of study.

No formal background, but I've been visitng museums and been very bathed in art history since quite young (family loves art, unlce is an artists, aunt stuided art hisotry). Also, while no being disrepectful, Math is a very central subject in our modern world (we are after all, talking throgh computing machines) and not knowing its real roots seems to me as a huge downfall (in all the world actually), as Math rules the physical world. Alos, those courses are given here in an extra-curricular manner, and they can be at a similar leel to those of the specialized students.

I would be inclined to agree that math is more useful than art to an extent, although that is certainly open to subjectivity. Whole trains of thought exist that art is the ultimate expression of humanity. And when you compare the ability to talk cogently on art to the ability to talk about advanced theoretical maths, I'd argue that artistic knowledge may better serve you in the social sphere.

But more importantly, it was to illustrate a point. What about your background in genetics? We are all formed of our genes, surely that's important to be taught at the high school level. Maybe oceanography? We live on a planet that's 70% water, after all.

What I'm saying is that different people come from different backgrounds. Offering introductory lessons in math is no more a sign of failure of the educational system than offering an introduction to Latin or an introduction to chemistry.

Would it be great if everyone left high school marginally versed in every conceivable topic? Definitely. But, that's not the case, unfortunately.

I, for one, LOVE that introductory courses are offered in virtually every field in colleges. I can go around and scoop up education I may not have gotten in high school. Not because my high school was bad, but because it had a certain set of goals (STEM) and some things didn't fit the budget (art).

 

[the doom cannon]

I did calculus bc in high school and managed a 5 on the ap exam. But really you only needed to take up to algebra 2. In college, they start you with calc 1, unless you did extremely poorly during high school. It then goes up to differential equations for engineering majors, which is what i am. In my upper level engineering courses, there is a whole lot of differential equations and complicated calculus on the more theory oriented side. Courses like structural dynamics and advanced steel design are chock full of differential equations. Granted we dont have to solve them, just know the solution forms.

What do i think mathematicians do?
Solve complicated differential equations so us engineers can more easily do complicated design and optimization work. Thanks mathematicians

 

[kurokotetsu]

I'm a stats major who's just getting started along the PhD path. Where does that put me on your poll?

Do you proof theorems? Or are applied staticians more interested in applying the principles to real world problems? An acclarations is now in the first post about the options.

I would be inclined to agree that math is more useful than art to an extent, although that is certainly open to subjectivity. Whole trains of thought exist that art is the ultimate expression of humanity. And when you compare the ability to talk cogently on art to the ability to talk about advanced theoretical maths, I'd argue that artistic knowledge may better serve you in the social sphere.

But more importantly, it was to illustrate a point. What about your background in genetics? We are all formed of our genes, surely that's important to be taught at the high school level. Maybe oceanography? We live on a planet that's 70% water, after all.

What I'm saying is that different people come from different backgrounds. Offering introductory lessons in math is no more a sign of failure of the educational system than offering an introduction to Latin or an introduction to chemistry.

Would it be great if everyone left high school marginally versed in every conceivable topic? Definitely. But, that's not the case, unfortunately.

I, for one, LOVE that introductory courses are offered in virtually every field in colleges. I can go around and scoop up education I may not have gotten in high school. Not because my high school was bad, but because it had a certain set of goals (STEM) and some things didn't fit the budget (art).

Well yes it would be nive to have it in everything. But the truth is that almost every single school in the world and educational system has math as a madatory course for a large amount of time and nearly till the end of mandatory education pupuils are thought some form of Math. While it is impossible to cover all subjects, if a subject is part of the stadard curriculum for most part of your previous academic life, not covering it accuretly (and harming the intetion of showing true introductory mathematics to new students) is indeed a failure. No all schools teach Latin, but all teach Math, so arriving wihtout the basics covered seems a shortcoming of the system. Of course there are different backgrounds and all, but if a good portion (I would say majority) of your population has a supposed matehmatical background, it should be in a decent level.

My problem is that since most backgorunds include Math, the courses given at coleges are inadecate introduction, as university level should be where you pick your future and an "obsucre" subject like Math (which as I said it is uncluded in most backgrounds) where most poeple are unaware of what a matehmatician does, it is not an introductory class, it is remedial class because of the failure to unite the curriculum and set a decent bacline.

 

[Unknotted]

If you're wondering what mathematicians do, we solve puzzles. That's the easiest way to describe upper-level math. There's generally some teaching involved as well, unless you're working in industry somewhere.

While I certainly do wish that more people got to see the puzzle-solving side of mathematics before they got to college, it doesn't particularly bother me that colleges offer low-level math courses for students who need it. Math just isn't everyone's cup of tea. If someone says they hate math and they don't want to take anything past basic algebra, it makes me sad but I don't see it as some kind of failing of the educational system. I personally don't have much patience for literature or art, and not having to write essays was one of the highlights of my college experience. To each his own.

 

[smithy_2045]

I'm a stats major who's just getting started along the PhD path. Where does that put me on your poll?

Do you proof theorems? Or are applied staticians more interested in applying the principles to real world problems? An acclarations is now in the first post about the options.

Doing proofs was necessary in my undergrad and honours, but my research is more application.

 

[Blood Brain Barrier]

I'm in my third & final year of studying it at a university in Ireland. I've mostly picked modules that specialize in Pure Maths as opposed to Applied or Stats. I'm essentially at the heart of pure knowledge itself.

Maybe you should have done philosophy instead. If you had you'd have learned there's no such thing as "pure knowledge". Well, unless you believe Hegel.

 

[kurokotetsu]

If you're wondering what mathematicians do, we solve puzzles. That's the easiest way to describe upper-level math. There's generally some teaching involved as well, unless you're working in industry somewhere.

While I certainly do wish that more people got to see the puzzle-solving side of mathematics before they got to college, it doesn't particularly bother me that colleges offer low-level math courses for students who need it. Math just isn't everyone's cup of tea. If someone says they hate math and they don't want to take anything past basic algebra, it makes me sad but I don't see it as some kind of failing of the educational system. I personally don't have much patience for literature or art, and not having to write essays was one of the highlights of my college experience. To each his own.

I'm finishing my degree in Math now, and looking into going Mathematical Biology for my disertation (some researches have told me there might be an article there even). But I sometimes wonder how we are percieved beyond our world.

ANd I do. Especially beacuse my problem is that those basic courses do not teach what Math s like. You know that writing essays and disertations is part of Philosophy and English degrees, looking itno the structeres of texts in the latter. But my question and the few answers ehre show me that most people really have no idea what a mathematician does. And that is why I'm sad at this thing. A college student being shown, after years of simple problem solving, that high level maths is that same thing, well it is a misrepresentation and quite sad. Those basic calculations should eb done by high school, because they are quite basic (most of the are even easily programmable), and not showing the real deal with math, well it saddens me.

Doing proofs was necessary in my undergrad and honours, but my research is more application.

The Applied Math would probably be the best option, as you are versed both in theorems and applications of a branch of Mathematics. Knowing both the theory (but not ging that much into it) and application puts you square into applied option.

 

[Exterminas]

I have a doctorate in theoretical philosophy and spend my average work day doing math without numbers.
... Should I just pick the "I hate math"-Option then?

What math without numbers does a PdD in philosphy does do if I may ask?


Also, I will edit the OP with a little more explanation on the options, as there seem to be a few complaints about that.

I would love also that the person that chose Phd doing research, would share what resaerch he is doing.

Basically we apply certain mathematical tools to language in order to analyse the logic of arguments in ordinary language. For example, we can analyse a false inference like:

All cats are mammals.
Peter is a mammal.
to Peter is a cat.

We can express this stuff in formal languages that make the structure of the argument clearer than ordinary language does. This this case it would be something like:

Ax ((x)is-a-cat -> (x)is-a-mammal)
(Peter)is-a-mammal
So: (Peter)is-a-cat

Obviously this is a silly and very simple example, usually we work with more complex texts. But in order to perform an analysis like that we need to have access to a calculus, for example the predicate calculus, which somebody has to build. In order to build a calculus like that you need at least a decent understanding of logic, proof-theory and of course theory of definition. As you see it's not quite math but it also isn't not math.

You can check out Wikipedia for more info on philosophical logic: http://en.wikipedia.org/wiki/Predicate_calculus

 

[Spade Lead]

Well, reading the tpoic "When Math Suddenly Makes Sense" I found a thing that confounded me. A poster there said that trigonometry and functions where University level mathemtaics. I'm doumb founded by that. Trigonometry is simple high school stuff and functions unless you are going to the strong definition (and even then, it is not that hard to understand that it is a subset of relations with certain carachteristics) are things that are seen here in high school. In the same topic I found a that "pre-Calculus" seems to be a course in some colleges, which makes me speechless, considering that the mechanics of Calculus (and Pre-calculus, Analytic Geometry, Trigonometry, etc) are all things of the two last years of Math course here.

I'm sure that the British curriculum has stronger Math than that, as I did the Advance Math A level, and it went into Vector Caluclus and more advanced Mechanics (we did a little on the principles of momentum and stuff, not Hamiltonian Mechanics or anything). With the A level being about basic calculus and analytic geometry, if I recall correctly.

So, are really American students un such a basic level when arriving to college? And do these introductory classes only teach the mechanics of Math? Because at college level you should be past just solving simple derivatives and integrations. You should start to go into the real meat of Math. Theorem solving, logic, the different branches of Math (Analysis, Algebra, Applied, etc.). Solving differential equiations and that kind of stuff. Are thos things really not seen except for the really advanced courses to Math majors? Or when do you start with real math? Because Calculus theorems are day one thing in my univiersity.

As an addition to have a poll, what level of math do you have? High school problem and equiation solving? Trig and functions? Able to solve basic differential equiations? Theorem prooving? Are you a reseearcher? And if you are not into Math, what do you think a mathematician does?

I'm at end of university level, so I can solve theorems of a basic nature, but really out of date with modern theories. I can't read Navier-Stokes' "proof", but a good amount of introductory knowledge about different areas I do have, although some has to be polished.

Edit: A little explanation on the poll. The catehgories shouldn't be read too luiteraly, but as gross divisions fo the posible level of knowledge. Here is is what I see the levels more or less to be.

Option 1 (PhD): Not necessary a PhD as it mught be a Masters or similar, but somone that is working in resaerch. Very high knowledge of Math, and has publsihed or is in that world.

Option 2 (Math major): One of the more exact cathegories. You are speciallized in Pure Maths and have a good knowledge of Thoerem proving and the different areas of math. FOr those that do Pure Maths (if you are proving theorems for CS you rpobably belong here)

Option 3 (Enigineering): More interesitng option. While higher level math is taken, it wasn't with a real methematical focus, as in the results where not proven theorems or studying the underlaying parts of the theory. Able to solve ODEs, maybe PDEs, knows vector calulculs, and other subjects not seen in high school, but has not taken a lot about rpvign the results and uses them as tools. NOt necessary to be an engineers, just have the this focus on higher level math on solving real problems rather than the underlying math (solving math problems but not caring that much about theory).

Option 4 (Applied Math): Another interesting one. Has a middle ground between options tow and three. He has done pure maths and proven a fair share of theorems, but at the same time has more of the problem solving and modeling of real phenomena. Most CS and IT would be around here (especially if you know Automathon theory, Discrete Math, P problems and the such, which are still purely matehmatical stuff), but only opt if you have some knowledge of theorems and such.

Option 5 (High-school): Option for those that never pursed higher level math. No problem solving and at most basic Calculus is known. Never proven a theorem nor seen a Differential Equation. It is not about the average of the country, it is more about seeing really higher math in any form after finishing the basic requirements.

Option 6(Statistics): Not limited to Science and medical degrees. For those that have taken a decen high level Statistics and Probability course. So you know your standard deviations, your sampling, your regressions and correlation tests. PolSci, Economics and such that use this branch of methematics extensively should vore here too, if they have a good level in Statistics.

Option 7 (Self-thought): FOr those that have little to no formal training in higher Math. If you took a class or two, never delveing too deep into Math this is the option too. Whether it is because you studied by yourself or because you had a disjointed classes, it is a broad option for those that have no formal math training but have sutdied high level math in some form but not as extensively as the otehr more specialized cathegories (for example if you've read about topology wihtout taking a course, or only took an Advanced Algebra class in college).

Option 8 (Hate): If you hate Math. Because it will be a popular option in a Math realted topic.

The catherogires defined this way I believe cover a wide enough spectrum while being deistinct enough that it should cover most cases. Of course there should be an "other" option, but it would give little infomration on sight (what the poll is for) and would be dependant of the eprson giving a written answer. Also, there are no more options aviable for me, as 8 is the maximum number.

I happen to fit into none of those categories. I have some lower level college Math (Physics and Algebra) but not a degree in any of that stuff. I have found the mass of planets and the Space Station, which is far above High School level.

 

[Synthetica]

I have a high school level, but here we have multiple "difficulties" of highschool, and multiple difficulties of math for each difficulty of high school. So, "High school level" might vary a lot from person to person

 

[xshadowscreamx]

Maths? Get it away from me.

I like any class where I can be creative, so I prefer English.

But maths is all about creativity. Solving for x in x + 8 = 14 isn't creative, but inventing new ways to optimise construction or travel is.

The number is already predetermined. It will always be 6.

Creating a story or art from imagination is creativity.

It occurs to me I've always seen this from the bias of an engineer, even when I was a kid. To me creativity came from taking things apart, figuring out how they worked, and then putting them back together in new and exciting ways (AKA, I was nuts about LEGOs ).

So I see "creativity" in literature and art the same way, great writers take elements from great stories they've read, and combine them and use them in new and interesting ways. (Even the imagination has to have some grounding in what-we-know or it just comes across as alien and nonsensical)

Higher leveled maths works much the same way, combining elements of this logical process, with elements of that logical process, to produce new equations, new proofs, new derivations. There's a vast structure(playground) of mathematical logic out there, we've barely scratched the surface.



In short, I think there is a lot of creativity in many fields, the stylings and tools may change but they're all creativity nonetheless.

Yes and A good example would be minecraft, you are constructing but it's from your own imagination.

 

[SonofaJohannes]

I have but one thing to say in this thread: Math is for nerds.

That is all.

 

[MeChaNiZ3D]

Well I'm doing Engineering and I hate maths. I think my lecturer this semester for Signal Theory put it best: "This subject has a lot of theory. A lot of maths. But that's alright. Because we love maths. If we didn't, we'd be over there - in the faculty of Law." Excuse me sir, I'd like to be with the people who do not love maths, can I just...walk over, please? I would like that very much.

 

[Auron225]

I'm in my third & final year of studying it at a university in Ireland. I've mostly picked modules that specialize in Pure Maths as opposed to Applied or Stats. I'm essentially at the heart of pure knowledge itself.

Maybe you should have done philosophy instead. If you had you'd have learned there's no such thing as "pure knowledge". Well, unless you believe Hegel.

You're right - then I would have had so many career opportunities.

 

[Zio_IV]

I only learned math up to basic Algebra and some Geometry, and decades later I still have never needed to use those skills once in my life. Aside from the most basic of basics (we're talking elementary school levels of basic here) I've never had need of math as a whole.

I wasn't bad at it in school, and I certainly don't hate it or anything, so I'm not sure where I stand in the poll, especially considering that many people here seem to be saying that high school math includes Trig and Calculus (certainly wasn't the case where I was).

It just has no presence in my life, is all.

 

[omega 616]

I hate math and I suck at it, not sure if one relates to the other but my brain freezes around numbers ... I should be good at it, it's logical and clean but my brain treats math like socially awkward male teens treat super models, it just melts.

The reason I am posting: In high school all you should be learning is the basic stuff, addition, subtraction, times, division, decimals, fractions etc. For all the other stuff, trigonometry, algebra, calculus etc it should be part of your college course.

I have been out of high school longer than I was in it, still have never used algebra! EVER! I think it would be better to have a society of people very able to use basic math, than a society of people who are all over the board 'cos the curriculum forced them to learn algebra.

Of course don't hold the able back from learning the never used stuff but I am god awful at math but I had to learn a useless skill set like algebra? That's like taking the swimming thing in the first Deus ex!

 

[Weaver]

Oh, I picked before reading the thread.
I belong in the "Math major" section despite majoring in CS. Oh well.

 

[Cloned31]

Oh, I picked before reading the thread.
I belong in the "Math major" section despite majoring in CS. Oh well.

I know I was looking for CS and got really disappointed :/.

When it comes to discrete mathematics, I'm your man. However, proofs have always been a thorn at my side. Especially Mathematical Induction. But I use discrete to help with things like numerical analysis and fun stuff like that.

So I'm kinda more like a math major

 

[Scarim Coral]

High School level which within that level I was in the middle. Granted there was one year that I was above average but then I got put down a lever which I blame it on my mate (I end up chatting to him in Math lesson). It was a shame since that Math teacher was awesome to talked to and teaching unlike the one I got stuck with (he was total bore at teaching as he pretty much end up teaching it as if it was a lecture)!