Teaching of maths back home

[Admin Khan]

Question: is this is what is being taught in mainstream computer science?

Depends on the program, and it's quality. For example, in my school 'Theory of Computation' is very theoretical, along with other foundations of Computer Science courses. So I guess it depends on the program, and the concentration you choose within the program. There are usually many concentrations a CS major can choose from, and enough room for electives to take those core theoretical math courses to complement your studies. Generally, when the program is offered through the Math department, it can be incredibly theoretical. When an Engineering school(which I attended)offers it, it's a lot more practical, so they kind of go over the theory, but focus more on it's apps. Do you get my point?

[RevolutionThroughReason]

Depends on the program, and it's quality. For example, in my school 'Theory of Computation' is very theoretical, along with other foundations of Computer Science courses. So I guess it depends on the program, and the concentration you choose within the program. There are usually many concentrations a CS major can choose from, and enough room for electives to take those core theoretical math courses to complement your studies. Generally, when the program is offered through the Math department, it can be incredibly theoretical. When an Engineering school(which I attended)offers it, it's a lot more practical, so they kind of go over the theory, but focus more on it's apps. Do you get my point?

Sure but I still don't think computer science/cse is really mathematical; there are attempts of course to infuse stronger mathematical rigor into it. But they're doing the same in Physics.

However I think Physics is a better candidate for the Transitional between Theoretical Math and other topics. So I am not sold as of yet.

Bear in mind I was not originally a Mathematician or Physicist at all. I was an environmental scientist who decided on a different career path. Much of this stuff is very new to me as well.

[Admin Khan]

Sure but I still don't think computer science/cse is really mathematical; there are attempts of course to infuse stronger mathematical rigor into it. But they're doing the same in Physics.

However I think Physics is a better candidate for the Transitional between Theoretical Math and other topics. So I am not sold as of yet.

Bear in mind I was not originally a Mathematician or Physicist at all. I was an environmental scientist who decided on a different career path. Much of this stuff is very new to me as well.

RTR, while it's true that the language of Physics is Math, it's just as true for CS as well. In an Algorithms course, or ToC course, or logic, Discrete structures, Graph theory, combinatorics(all core CS classes)or nearly any CS course, you will be applying mathematical concepts and theorems. In fact, as one specializes in a certain field, say AI, it won't take them long to realize how mathematical it is. Any CS program screams applied math. In fact, it's a rude awakening to those who thought CS is merely writing "Hello world" in Python, or C sharp. That's why those "programmers" end up majoring in Information systems, or Computer Information Systems, or something which is more programming oriented. CS, is a whole different animal. It's a mathematical animal, that weeds those who lack a strong foundational background in Math. You can be a great programmer, yet flunk out of a CS program since you can't handle the math that comes with it. Courses like Numerical Analysis, Topology, Linear Algebra, Calc 1,2,3, Combinatorics, Graph theory are the basics before you begin your actual CSE curriculum. Trust me RTR when I say it's a rude awakening, hence the outstanding demand for CSE students, out of all Engineering or Science related disciplines, CS dwarfs them all with respect to demand, and some might go as far as saying toughness(depending on your curriculum, and school -- some schools go very very hard with ground projects). I've seen talented programmers drop out of CSE programs because they couldn't handle the Math that came with it. Most viewed it as "useless".

For example, in an EE program you can cruise through the exams once you learn how to apply the formulas. In a CS program, if you can't crack the algorithm, hand in the exam and ask for the polite zero. There is no room for discussion, it's either you get it, or don't. This comes from someone who has taken a handful of EE courses. The CSE ones, in my school, were brutal.

[RevolutionThroughReason]

well I'm not talking about merely using Mathematics as a tool to describe things, I mean theoretical mathematics as being the provision of acquired information.

C.S. programs and applied mahematics from my understanding is different; I am using C.S. as a tool for advancing mathematical concepts. Not as mathematics itself. When a Mathematician tries to find roots of Nth-order polynomials, we use computer algorithms; or if we want to develop a program for that. I usually just do everything of that sort in MATLAB, and I am no expert in MATLAB.

I've been looking at CSE curriculums online; and asides from certain research oriented projects at MIT and Carnegie Mellon, doesn't seem to be standard curriculum for most CSE. Even the stuff you showed me is rudimentary level Topology/Point-Set Topology, which although surprising, isn't that deep in the subject itself. But I don't believe it's the "beginning" of CSE, I think more advanced C.S.E. people caught wind of the uses of such topics and buttressed it to C.S.E. It is no more a branch of Mathematics than Biology is.

[Admin Khan]

We have rights to distinctive opinions. I however disagree with your analysis. Thanks for your time.

[RevolutionThroughReason]

that's cool :p, I'm not trying to be a jerk, in fact I am actually a bit more interested now on the interface of advanced math with computer science. How they use the concept of Spaces in Comp Sci.

[Toramana]

You know Admin Khan mathematicians call only that model/system a math which has mathematical beauty i.e., which is more exact/precise and where every thing falls in line beautifully (where things can be measured exactly). They would not call even statistics a proper math because of the stochastic ism and interpolation/approximation involved in it. Computer Science drifts rather more remotely from maths because it cannot be formulated that beautifully and precisely as math---and is not that general.

[RevolutionThroughReason]

well stochastics are mathematics, approximations do not necessarily make something not mathematical , sequences and series and generating functions are also approximations, you can argue most things in mathematics are just approximations with various degrees of rigor. What makes math as math isn't precision as much as RIGOR, whether or not something can be described as generally or abstractly as possible.

Dealing with a topic of point-set topology, how many dedekind cuts can you make between the numbers 0 and 1, well by definition 0 and 1 are the greatest/lowest upper/lower bounds, but really, we're approximating between 0.000.....000.....000....001 to 0.999....999.....999...999

[RevolutionThroughReason]

why I don't fully embrace computer science as mathematics but an offshoot is because really you're dealing more with performing a task and how you can make a machine operate a function, teaching the machine HOW to do Math, rather than the machine or programming/machine proving a mathematical theorem. It's tool OF mathematics, it is no different than really a calculator. You're teaching a machine to be a Mathemaatician, but a Mathematician is NOT Mathematics.

[Admin Khan]

No.

Toramana, I politely disagree with your statement. Its inaccurate to say the least.

[Admin Khan]

why I don't fully embrace computer science as mathematics but an offshoot is because really you're dealing more with performing a task and how you can make a machine operate a function, teaching the machine HOW to do Math, rather than the machine or programming/machine proving a mathematical theorem. It's tool OF mathematics, it is no different than really a calculator. You're teaching a machine to be a Mathemaatician, but a Mathematician is NOT Mathematics.

Your confusing CS with something else. IT is not the same as CS.

Again, there is a reason why CS is traditionally offered through the Math department. I, along with millions of mathematicians view CS as a field/branch of Math.There is more to CS than calculating, or programming.

Its similar to how an EE is an applied physicist.

[Toramana]

well stochastics are mathematics, approximations do not necessarily make something not mathematical , sequences and series and generating functions are also approximations, you can argue most things in mathematics are just approximations with various degrees of rigor. What makes math as math isn't precision as much as RIGOR, whether or not something can be described as generally or abstractly as possible.

Dealing with a topic of point-set topology, how many dedekind cuts can you make between the numbers 0 and 1, well by definition 0 and 1 are the greatest/lowest upper/lower bounds, but really, we're approximating between 0.000.....000.....000....001 to 0.999....999.....999...999

You are right. And I meant, mathematics is more objective with its principals (and theory and models) applicable to the most general situations. Statistics (as well as applied math as we use in Physics & Engineering) is subjective (empirical data is important there) and concerned with specific forms of the general problems/situations. Therefore, it is considered kind of lesser maths.

[Toramana]

Your confusing CS with something else. IT is not the same as CS.

Again, there is a reason why CS is traditionally offered through the Math department. I, along with millions of mathematicians view CS as a field/branch of Math.There is more to CS than calculating, or programming.

Its similar to how an EE is an applied physicist.

I think a few CS areas like Theory of Computation, theory of program correctness, etc. have solid axiomatic (and so mathematical) foundations. One can also cite Digital Logic(Boolean algebra), micro programming (BA), Cryptography (computer security), etc. that have strong mathematics. Overall it is closer to logic than maths (if I am correct in that categorization). Still it is heavily linked with maths.

[Admin Khan]

I think a few CS areas like Theory of Computation, theory of program correctness, etc. have solid axiomatic (and so mathematical) foundations. One can also cite Digital Logic(Boolean algebra), micro programming (BA), Cryptography (computer security), etc. that have strong mathematics. Overall it is closer to logic than maths (if I am correct in that categorization). Still it is heavily linked with maths.

Logic is Math Toramana. I don't know how things work in Canada, China, Pakistan, or India. But in the USA, Computer Science is offered at times directly from the math department. It's a field developed by Mathematicians, where writing code is like writing proofs. Obviously, if all one has written is 'Hello world' they won't see the connections, but when you are writing 10,000-20,000 lines of code, the correlation is visible.

Digital logic, Semiconductors, is more applied physics. Where as, Graph theory, Applied combinatorics, Logic, are all courses that a CSE major has to take, and they are cross-listed directly with the Math department. There is more to math then integrating, or cracking tough derivatives, CS is a form of Math where only the logical ones can remain in the major. Nearly every friend of mine, who taught it was all about "fixing computers" dropped out to choose EE, or Civil, cause they couldn't keep up with the rigorous coursework.

I think the problem generally arises when people confuse Computer Science with IT, or CIS, or CpE or another sub-field. Remember, it's like apple and oranges.


RTR,
I respectfully disagree, and still think you are totally confused on this subject.