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I'm at end of university level, so I can solve theorems of a basic nature, but really out of date with modern theories.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