Poll: High Level Math in the Escapist

[kurokotetsu]

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I'm at end of university level, so I can solve theorems of a basic nature, but really out of date with modern theories.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.

 

[Pimppeter2]

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[Pimppeter2]

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[Elfgore]

Voted I hate math, because I'm terrible at it. I can't keep track of all the formulas and whatnot. I never reached proofs and I am so happy about that. I'm one of those people that see advanced math as being useless, unless you are going into a career involving it. I may be slightly biased though.

The furthest you had to go was Algebra 1 to graduate from my Highschool. I'm not sure what it is to get into university, but I got in with no problems only reaching Algebra 2. And the only math class I'm required to take is the most basic math, which I think is basic algebra and a little geometry. Most students start at Algebra though at college level.

 

[kurokotetsu]

In America it depends more on the students level what courses he or she takes. I knew some people in High school who were taking Advanced levels of Calculus and others who never made it past Algebra. And of course in University now there are those who never get past basic Statistics while others are taking levels of Maths and Physics that are way above anything I could ever imagine. Its all relative, basically.

8 out of the top 10 Universities in the World are American so its safe to say that it's the individual case rather than a universal rule.

There are probably many people in your university that don't take higher level math courses. You seem to be in the field of mathematics, did it ever occur to you that you and your peers may be the exception rather than the rule?

Well, yes. Of course it may be an individual case. (Also how those statistics are made and be iffy, as there are no standarized metric for ranking universiteis). The American Universities are indeed very good, but a lot of them are better in the post-grad levels than in their basic levels. Hell, seeing the description of an introductory Harvard Calculus class, while it mentions the fundamental theorem, it also talks about applications of optimization and graphing problems, things that should be proven in that level, not done into basic problems.

I have a good dela of friends that aren't into math nor study math. They don't have any math courses at all. But they still did Calculus and had to pass Algerba to get out of high school.

What I find troubling is that if you take a Math course in college, well, that it isn't really Math. I get that those are lower level, but in the colleges here, lower level is basic theorm proofs, sets, basic algebra theorems, etc. No numerical problems in a pure Math class.

 

[geK0]

I'm in accounting so I've had to deal with some (fairly simple) math in my finance, economics and statistics courses. I've always had a bit of aptitude to mathematics but the most complex courses I've taken are highschool calculus and physics. I feel like I could have done well in an engineering course if I had taken one.

 

[Pimppeter2]

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[dyre]

In the US, public schooling ranges from very good to spectacularly awful, so the people entering college have a varying degree of math background.

I would say that a decent student probably has taken up to Calculus I before entering college, so trigonometry is something he would have covered maybe in his junior year in high school. However, I've met people who were taking Algebra II as college freshmen.

For reference, the math curriculum goes something like this: random bullshit -> Algebra I -> Geometry -> Algebra II -> Precalculus (including Trigonometry) -> Calculus I, II, III, etc

Personally, I stopped at Calculus I, as I'm pursuing a Finance/History double major and Calculus I (and some basic statistics) are sufficient for the courses I have to take. As for what mathematicians do, I really have no idea.

 

[seventy two]

Well, so many options yet none fit particularly well. At my university, CS majors need to take Discrete Mathematics which is closer to math majors, yet at the same time there is no need to go as deeply into it, I also need less traditional math classes than engineering majors(Only through Calc II, nothing further is needed along those lines).

On a personal level I completed through Calc II in HS, other that that I am taking Discrete Mathematics, and Probability & Statistics this semester. After that I have one math elective before I am done with formal math classes.

Since you mentioned differentials a few times, I will say that here every actual engineering major has to take Differential Equations, but other than them and math majors there is only minor introduction to differentials during Calc.

 

[BathorysGraveland2]

I don't even know what trigonometry is...

I'm absolutely fucking hopeless at maths. Always have been. Maths and science, they always confused the hell out of me and I found them hard as fuck, so in high school I very rarely ever payed attention in their respective classes. On the flip side, it just made me more involved with English, which in turn kick started an interest in writing. So I'm not a 100% deadshit, just a 75% deadshit

 

[kurokotetsu]

Yeah, the rankings aren't pure but obviously America leads the world in top universities both Undergraduate and graduate. We wouldn't be stealing so many foreign students if we didn't. No matter what lists you look at American Universities dominate the top 50s everywhere.

One, I'm talking mainly about the introductory levels of college education, especially if you are "showing" the discipline, not about how many people graduate. Second, the students moving to America to go to college isn't a very good metric either. There are more colleges in America than in most parts of the world, which means it is easier to go to college there than anywhere else, increasing the flow of foreign students. Also, the reputation it holds (which may be not all that true) increases the amount of students going to American universities, not necesarilly based on the quality. Third, all those top 50s have no empiricial base, no real ranking. I know for a fact that some of those rankings are made by simply asking researches which is best (a terrible metric, as it is completely based on subjective parameters, as for example, a very good that I know of doesn't usually show while having really brilliant researchers and an escelent academic level). So no matter how many lists you could talk about, they are not very convincing proof.

Again, it all depends on the school and level you go to. I had to do Algebra and Calculus to graduate highschool. But then again I didn't go to a low income city public school where those expectations would be unreasonable.

Which actually is the matter and the solution to why I found it so jarring. As dyre said, there is a huge disparity between schools in the US, and I think no unifed school curriculum meaning that remedial courses may have to be given to fresh students in college because there is no assurance that students know what it is needed for a class of the actual level that they should have. All countries have disparites, but the programs are unifed, so there is an assumed level of knowledge by the time you start college.

Bottom line is America is more job-focused and therefore students that take majors and career directions that don't require high levels of math simply don't take them. After intermediate levels of every subject, you specialize in your own field.

You do that here too. I think you that that everywhere. For one, here you start directly into your major, as the intermidate levels are supposedly given at high school. No great need more common classes.

Your friends are still at university. You can't compare your peers to your average person, because they aren't the average person. My average friend has read Plato, Aristotle, Kant, Moore, Machiavelli, ect ect because I am in University and a Philosophy Major. They don't represent the average american.[...]

Yes they are. But my mother has been a high school Math teacher and I know that Calculus and ALgebra are requisites of every high school graduate here. The assumed level of a high school graduate here is in that respect higher than that of an American student and when starting college you are assumed to be at a better place than what is assumed in American colleges (not that it is reality, but that is what it is).

What I'm saying is that the Average American University is ranked very high on a global scale. So if we assume you go to an average university in England, you should compare it to an average university here. Not to just the general global population. And trust me, I don't know where you go to school but you can't walk down the street here at Michigan State without running into someone who hasn't taken very high levels of Math. I know multiple Astrophysicists that I didn't even meet in class but just hanging out. And MSU isn't Ivy League.

Global scale? I'm not sure, maybe. Considering that 14% of colleges(according to a quick statistic I've searhced now, not now how realiable, but is sound about right http://www.webometrics.info/es/node/54) are American, the average American university might be around the average, considering the high number of schools that there are. Between China, Japan, Brazil, Rusia, India and America there are 45% meaning they have a high relevance in the average. So not sure about that claim (and that is considering we had a metric to rank them accuretly, which we don't). And of course you can't walk in a University of a certain size without finding other people in other areas. If a University has a department of a certain area, walking around will almost garantee that you will find a member of that departmen, if you walk for long enough/meet enough people. Cosnidering you are in a place where there are almost 50,000 sutednts in 21^2 km it is wuite easy to find people like that (as do I). That is not impressive.

Well, so many options yet none fit particularly well. At my university, CS majors need to take Discrete Mathematics which is closer to math majors, yet at the same time there is no need to go as deeply into it, I also need less traditional math classes than engineering majors(Only through Calc II, nothing further is needed along those lines).

On a personal level I completed through Calc II in HS, other that that I am taking Discrete Mathematics, and Probability & Statistics this semester. After that I have one math elective before I am done with formal math classes.

Since you mentioned differentials a few times, I will say that here every actual engineering major has to take Differential Equations, but other than them and math majors there is only minor introduction to differentials during Calc.

I would calssify it as Applied Math, considering that Discrete math has probably several theormes that you may need to proof (or at least several affrimatiosn, if Knuth's Concrete Math is anything to go by) so theorme proofing is in ti. And unless you go more to the programming aspect almost exclusively and stay in purerer CS it is indeed something kin to a ver large and importan baranch of Applied Math.

ANd yes, I talk about differential equiations a lot. But that is because I think they are very important (and dear to me, I quite like the little buggers) and not just for engineering and physics and math, but to other areas. Understanding a little about them can help a lot to the understanding of our world (even very basic things like Newton's Second Law, which can be seen everywhere) are differential equiations. In chemistry there are diffrential equitions involved. In biology (a thing I love, Bio Math) a great deal of systems can be modeled with differential equitions. Everything with a continuos change cna be modeled with diffrerential equations, so there are a huge amoutn of things around us that are governed by them. (I may even be tempted to say that there are more everday problems involving DE that standard second degree algebraic eqations). Just knowing that diffrential of a fucntion is the immidate chage of the function is a very revealing thing, and why this is so important.

 

[Blow_Pop]

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.

Yeah.....you've pretty much lost me there. Trig isn't a simple high school thing out here in So Cal...or at least where I went to school. Granted we did have people who did take it but on average, it wasn't simple or required.

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.

Like it's been said, it depends on where you went to school. It depends a lot on teachers too. I had a bunch of math teachers who were godawful terrible at their jobs in that I had one teacher twice during high school who quite literally told us "this chapter is what you're working on in class today and your homework. Don't bother me I have my university homework to finish and am too busy to help you" but due to the tenure thing out here there was nothing the school could do about it(if they had even bothered to take the complaint seriously)

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 have never been good at math. Our high school required 4 years of math to graduate(or courses they deemed equivalent to a math class). I took pre-algebra (which I did decently in due to actually having a teacher that cared), algebra 1a & 1b (again had a teacher who gave a shit so did decently), geometry a & b (which I did god awful in due to teachers and really not fully grasping what they tried to teach me), and algebra 2a & 2b. Or was suppose to for the last. I did 2a and kind of failed it and they let me transfer into a basic computer programming course for math credits and that's how I finally passed my math requirements to graduate. But those courses I listed were the generalised curriculum for math for my high school and the high schools in my city.(we have 4 of them) I can kind of do algebra but I'm really rusty with it, I can do some geometry (but not much and I'd need a refresher in it to be able to do it now as I haven't studied it in 10 years) but mostly I'm good at basics. Addition, subtraction, multiplication, and division(though sometimes long division trips me up). I understand the math that is involved in working on older models of cars(Early 2000s at the latest like 2003 and prior) and I understand math as it relates to cooking. Outside of that, it makes my head hurt and confuses the hell out of me. I am luckily not in a position in which I need to know math outside of basic addition and subtraction so that works for me.

Some people I've found, are just really not good at math and don't have the type of brain to be able to be good at math. Others, like you, do have the ability to be good at it. It's just a matter how your brain is wired so to speak.

Oh and to get to the higher level of math classes, you have to take summer school starting before your freshman year out here.

 

[DanielBrown]

Math has never been anything for me. I can do the very basics, but when slightly-harder-than-the-easiest-algebra gets in the picture I start losing my shit. Eventhough I do everything properly it most often won't come out right. Haven't done any math in over six years, so I don't really remember anything of it.

I assume it has a lot to do with my extremely short attention span... or piss poor teachers. The math teachers I had from when I was 12-16 years old were great and I did fine. After that it went to hell.
Got no clue what mathematicians do. Make stuff up, then solve it for shits and giggles? Become math teachers because they couldn't get another job?

 

[Edryad]

I really dislike math but I'm taking Calculus I at the moment. It all depends where you go to school here in the U.S. In Los Angeles most kids won't get any further than Algebra II and I know a good amount of seniors who haven't even passed Algebra I. In the end it comes down to the student's motivations and the teacher's abilities. I have brilliant math teachers at my school who have close to 100% pass rates on their student's AP tests for Calculus BC. Not sure if they have the equivalent overseas but an AP (Advanced Placement) class prepares you to take a national aptitude test for that subject which are reported to colleges for a better idea of what the students know when applying. Calc BC would be the equivalent of Calc II or III.

The opportunities for high school students to take advanced math courses are definitely available for anybody who wants to try for it but not many do. I don't really have a clue why our high school standards are much lower than overseas though. There's probably some study on that somewhere on the internet

As of now I just hit finding the volume of an object via the area of its cross section (or something like that) and deriving inverse trigonometric functions. My grip on this stuff is shaky at best. I've never really excelled at math before but I've done decently enough to make it into the advanced classes.

As for requirements entering college it really depends on where you're applying and what your major is. Obviously majors with heavy math knowledge required the admission board wants to see good scored in advanced classes and on national tests. Anyone going for a major outside of Mathematics, Engineering, or Physics isn't quite expected to get into the meatier math topics. As a future Biotechnology major my undergrad requirement for math is just one credit. And that credit can be from a Statistics class. My Biology and Chemistry requirements can fill a novel on the other hand

As for what Mathemeticians do I imagine it involves writing down runes and performing sacrificial rites to please the math gods of olde

 

[Edryad]

I also did not just double post. Nope. Not me

 

[Fsyco]

There's a looooot of popular misconceptions about math. There's a general societal stigma against it since most people think its some kind of evil number voodoo that they'll never, ever use. It's not just that it's taught poorly, there's a constant cultural message that Math is hard and for dorks. Most people also confuse 'advanced' math (like, say, trig or calculus) with 'tedious' math (multiplication with lots of decimals).

Yeah.....you've pretty much lost me there. Trig isn't a simple high school thing out here in So Cal...or at least where I went to school. Granted we did have people who did take it but on average, it wasn't simple or required.

I went to High School in southern California, and basic trigonometry was 9th grade material. The unit circle and trig identities were 10th and 11th grade material that everyone had to take. Everyone also hated it.

Got no clue what mathematicians do. Make stuff up, then solve it for shits and giggles? Become math teachers because they couldn't get another job?

They go work for the NSA as code analysts. No, really. The NSA loves mathematicians. Or they get research positions. Or they become like that one guy on Numb3rs that uses math to predict how things work and then apply those models.

I'm a Physics major, which is a fairly math-intensive field, but I like math. The major problem with how it's taught though is that you're taught math in a vacuum so to speak. They just tell you how the thing works, not why it's useful or what you'd do with it. It's like if they taught English by having students just study individual letters and words. Math is really boring unless you're given some kind of context for it (like Physics applications). They'll teach you how to do algebra and trig but they never explain what practical things you can do with those skills.

 

[Blow_Pop]

Yeah.....you've pretty much lost me there. Trig isn't a simple high school thing out here in So Cal...or at least where I went to school. Granted we did have people who did take it but on average, it wasn't simple or required.

I went to High School in southern California, and basic trigonometry was 9th grade material. The unit circle and trig identities were 10th and 11th grade material that everyone had to take. Everyone also hated it.

Yes but which part of so cal as different areas of so cal have different requirements. It should also be noted that my school taught almost strictly to the standardised testing tests and required us to do portfolios and senior projects and with all the homework those alone gave us, we had next to no time to get a decent amount of sleep AND do regular homework. Because those were all English homework and essays up the ass. And considering we couldn't teach some basic history stuff we should have been taught (such as the battle of the alamo everyone refers to isn't part of the mexican american war and actually happened well before and what the mexican american war actually was and not just the battle for the alamo) it's of no surprise that we severely lacked in what we probably should have been for math.

 

[Shymer]

I have a Masters Degree in Engineering and Computer Science from Oxford. About 1/3 of the course was pure mathematics and much of the rest applied mathematics. I did single maths at A level, but also S level maths. By the time I reached university I was grounded in trig, calculus, mechanics and statistics. At university we studied predicate calculus and logic, proofs and theorems and further advanced applied mathematics like transforms.

Now I am 42 and I have lost a lot of that knowledge. I am a communications network designer and seldom use my previous skills. I can still bring numerical analysis to business challenges more easily than others who work with me.

 

[FPLOON]

Well... Despite graduating high school kinda passing Calculus II (even though I could have stopped after Algebra II during my sophomore year... and choose to COMPLETELY skipped Calculus I because I could during that time), I can safely say... that I choose to not go any further than that mathematically...

I still remember those times of my backpack being called an elephant by my Trig teacher while he complemented my "triforce" tetrahedron model, matching wits with both my Algebra II and Pre-Calculus teacher (since they were the same teacher), and making A LOT of gaming references during my Calculus II "extra credit" reports... But honestly, given the class requirements needed to graduate the high school I went to, I basically took them all prior my junior year... and since those grades were just a little above average at best (Out of a 4.0 GPA, I was a 3.2), that's not saying much... I mean, you actually had to TRY to fail in some cases... But, I'm getting slightly off topic...

Anyway, I'm more of an English major at this point, so I'm basically just above the average of my high school's basic math... (Then again, I have not used Calculus since high school, so... Yeah...)

 

[skywolfblue]

I was made to re-take Algebra 2 in university even though I'd already finished Pre-Calc in high school, because I scored low on my SAT. Luckily the university had a provision where you were only required to pass the tests of Algebra 2 to pass the class (so I only needed to show up to the class a grand total of like 5 times).

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.

Things aren't quite as fixed here in the US. Not everyone gets to take Pre-Calc or Calculus in High School. So the university courses are there to provide backup.

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?

The highest "Pure" math classes I took were "Differential Equations" and "Linear Algebra". In truth I don't remember which was exactly "higher"?

Because Differential Equations sure look complicated at first, but then you realize there's only a few ways you can solve them (or at least the problems that I deal with in engineering), so it gets kinda easy when you can recognize what "type" each problem is.

Linear Algebra begins as "oh, matrices, boring" and then as time goes on I realize that these simple matrices are describing really interesting N dimensional spaces, then I was like "Cool!".

Electrical Engineering does require a lot of math. Not too much of the theoretical stuff, just that which pertains to the physics of electrical fields.