Just a word of advice. I did it my self before I started with pre-calculus. But memorizing mathematics is not the way to go. It will only take you so far. Try to use a little more time and understand it. Read the proofs thoroughly, when you understand them, you can do them on exams if you forget something. At my university we are not allowed any formula sheets on the final exam. So basicly, if you understand them you won't need to memorize, and you can do things without wasting so much time checking your formula sheet if you are allowed to have one. But the most important reason, it's just so much more fun when you know how and why.

Just the usual applied stuff:
calculus/algebra/trigonometry/geometry
real analysis/complex variables
probability theory and statistics
set theory
odes and pdes
numerical methods,finite differences/linear algebra
tensor fields

No nonstandard analysis or topology or number theory. Maybe someday..
Useful? Never thought the point was for it to be useful.

I need more math skills.

Mathematician is something that I am not, but I have decided to get a minor in math to go along with my bachelor's in computer science. That being said, I have looked at discrete mathematics and linear algebra. Something that I don't know well enough yet, because I must have already taken at least one level of calculus, but they seem interesting to me.


Oddly enough, although I am minoring in math, and studying essentially a math related major, I don't have to take the final level of calculus, which involves multi-variable cal. I kinda don't know why my uni. decided that I don't HAVE to have cal. III, as a core requirement. However, I can't add cal. III as part of my minor in math, because it is not considered a high level math course. Oh well.

We seem to be all discussing chicken feed when it comes to mathematics. If you want a real brain buster of a math course, go look into abstract algebra. Now THATS something scary.

There is no real practical use for it, unless you are planning to go into theoretical physics. Other than that, abstract algebra is just plain.....weird. I sat in an abstract algebra class just to see what they talk about. I came out thinking: "Are they doing algebra in a new universe or something?"


Wrap your minds around this if you will.

We all know how to solve this simple algebraic problem:

Well, in the world of abstract algebra, x = 2. How? I wish I could remember the entire explanation I was given. The gist of it, is having to do with what two numbers gives you 5. 2+3=5. However, in the realm of abstract algebra, multiplication isn't really multiplication, but the addition of numbers. Yea... Its really really really WEIRD.

http://en.wikipedia.org/wiki/Abstract_algebra

I've got a real good question, then.
How would you briefly describe calculus to someone who doesn't know anything about it, other than saying "it deals with change"?
How would you briefly sum it up?

Calculus:

Many mathematical problems cannot be solved by simple algebra or trigonometry. This can happen when the formulas are very complex (and perhaps non-linear or discontinuous) and where there are large amounts of data. Before calculus, these problems were solved by a variety of methods, including multi-step processes in which a calculation is repeated for many different values of one or more parameters. Calculus generalizes this process and provides a set of tools which come to the same solution, but much faster.

Depending on the level of layman you are dealing with, you may then get questions like: What is algebra? OR: What is math?

Close. It is more like algebra in all possible universes.

Did you miss the point that what you were being told was just an example, not a general rule?

Abstract algebra tells you the rules for defining any of an infinite number of possible systems (I forget the exact terminology) and tells you various universal principles about such systems.

In Abstract algebra, you mostly don't deal with numbers. Your example is an algebra with ordinary numbers but using addition in place of multiplication. But abstract algebra is more often used with something else in place of numbers as well as something else in place of the basic operations on numbers.

Long ago, when I hadn't yet forgotten nearly as much math as I have now, I saw a Rubik's cube for the first time. I immediately invented an algebra in which the "quantities" used in place of numbers were all possible changes you could perform on a Rubik's cube. I then did a bunch of math with pencil and paper and discovered several aspects of that algebra that then allowed me to look at any state of a Rubik's cube, write down a concise name for that state and quickly compute (with pencil and paper, not touching the Rubik's cube) a sequence of rotations that would solve the cube. Of course that process didn't compute the solution as fast as some of the systems other people invented and taught for solution directly manipulating the cube. It just was (for me at the time) a fun application of abstract algebra.

Re the main topic of this thread: In high school after completing integral calculus with older high school students, I took four math classes with college math majors. The easiest of those was differential equations, then one whose title I forget that included the abstract algebra with some harder stuff, then one I can't remember at all at the moment, then one innocently titled "functions of a complex variable" that included in its initial review of material we were already supposed to know everything that other colleges (including MIT) put in their entire "functions of a complex variable" course, then when on to stuff so abstract that for the first time in my life I was totally lost in a math class (I got a good grade somehow anyway).
Then I went to MIT, where I took no math classes, because I was already far beyond all their undergraduate math and I didn't want to major in math (I was already forgetting math rapidly and knew less than I had a couple years earlier) I was (and still am) focused on computer programming.

So ... like so many other people you don't really put the mathematics you learned to use when programming, I take it?

In all fairness, I may have because I did not, and still do not have the pre-reqs. for such a course. 99.9% of what was being talked about in that class went 100+ feet over my tiny head.


Wrong, without mathematics, programming would be next to impossible. You have to think logically, be organized and you DO in fact at times take a mathematical formula and translate it into code. I'm not talking about FORTRAN (which does exactly that), but also higher level languages such as C/C++ Java. In my first semester of CS in uni. our professor bombarded us with summations, and we had to take that, and write it as a loop. Maybe that sounds like a poor example, but it was just a start.

I don't mean to oversimplify, and correct me if I am wrong, but in 'short', isn't calculus just the study of limits, and integration mostly? (The gist of calculus I mean).

I've read many programming tutorials and books and own "C in a Nutshell" and have read for very long about programming and computers, and have never needed mathematics. I've seen very, very many educated people say that the mathematics they learned isn't often put to use (and seen many sites saying the same thing). It depends on what you're trying to accomplish with your program, they all say.

Well, if it were true, then my degree wouldn't require me to take all these mathematics courses, as well as digital logic, etc. Math may not seem as prevalent in the programming world, but trust me, the concepts are there, and also one can't even get a degree in CS, without passing all the req. which is plenty of mathematics courses.

I know. I attended college for a semester and dropped out. I learned the software development pre-requesites, and some of what you learn in the process. It's very mathematical. But I've read many sites and things posted by very educated people that say much of the mathematics they learned they don't really put to use.

I forgot most of the math that I knew when I was a teenager, but I remember more math than most programmers ever knew and far more than most ordinary people do.

I don't put the math I forgot to use when programming. Some of that math is required for some of the programming I do and I need to ask for help from some coworkers who remember more math.

When programming I do use quite a bit of the math I didn't forget.

Calculus is a toolkit---Integral, differentials, differential equations, Laplace transforms, etc. The concept of limits (e.g. DeltaY/DeltaX as X approaches zero) is simply part of defining and building the toolkit.)

I can (or at least I could 20 years ago....) solve a problem using a compound integral without EVER have studied limits, series, or maybe even trig.