I want to start math over... From the beginning.

Originally posted by TheRedneck
reply to post by JackTheTripper

I'm probably going to get a lot of flack for this, but it is my sincere belief that introductory algebra should be taught around the third grade, right after the addition/multiplication tables. Not advanced concepts, of course, but instead of asking over and over, year after year, "what is 2+2?", we should be asking kids "what is x when x=2+2?". It's not that difficult a concept for young minds, and it would introduce them to mathematical equalities on an intuitive level.

Let the flames begin.

So it is done around here. If I remember correctly, the introductory algebra starts indeed at the second or third grade around here. Check out en.wikipedia.org... ..
You might as well want to read www.forbes.com...





... Otherwise this country sucks. I mean by weather and hostile and jealous people who want to other people suffer because the others have something they have not etc. It's kinda sad how things look now compared to 20 years back. Oh well..

If you want to start from scratch and work your way up to the very high level of familiarity with math so you can do/understand sophisticated science you need to get "Engineering Math" and "Advanced Engineering Math" by Stroud. The two books are thick enough to make 8 books of middle thickness out of them.

The books are extremely comprehensive and packed with ridiculous amount of worked out exercises. Also the flow of info is very smooth. For example, in "Quadratic Equations" section you aren't just tossed couple isolated techniques like "completing the square", "decomposing the function", "factoring the quadratic" or resorting to the "quadratic formula" to solve quadratic equations like boatloads of math books do, but shown when each of them are specifically called upon. You will start out with primer: Arithmetic, Intro into Algebra, Trig, Binomial Series, Functions, Differentiation, Integration...The analysis topics in the primer aren't complete, but keep expanding within later topics when you actually need them to understand other topics...so your mind is not cluttered with tons of info you can't use right away.

If you survive through these two books- that is, truly able to solve EACH AND EVERY PROBLEM on your own-you will kick major ass in any science class. Mind though, working through every problem can sometimes feel like getting your head repeatedly smashed with a frying pan by God Of Math . Some problems and topics are very difficult or somewhat confusing so you'll need some assistance from time to time.

Here are the topics in those books.

Engineering Math:

Part 1 Foundation Topics:

Arithmetic
Introduction to Algebra
Expressions and Equations.
Graphs
Linear Equations and Simultaneous Linear Equations
Polynomial Equations
Partial Fractions( This one kicked my butt)
Trigonometry
Binomial Series
Functions
Differentiation
Integration


Part 2:

Complex Numbers1
Complex Numbers2
Hyperbolic Functions
Determinants
Matrices
Vectors
Differentiation
Differentiation Applications 1
Differentiation Applications 2
Partial Differentiation 1
Partial Differentiation 2
Curves and Curve Fitting
Series1
Series2
Integration1
Integration2
Reduction Formulas
Integration Applications 1
Integration Applications 2
Integration Applications 3
Approximate Integration
Polar Coordinates System
First Order Differential Equations
Second Order Differential Equations
Introduction to Laplace Transforms
Statistics
Probability

Advanced Engineering Math:

Numerical Solutions Of Equations and Interpolation
Laplace Transforms 1
Laplace Transforms 2
Laplace Transforms 3
Z Transforms
Fourier Series
Introduction To Fourier Transform
Power Series Solutions Of Ordinary Differential Equations
Numerical Solutions Of Ordinary Differential Equations
Partial Differentiation
Partial Differentiation Equations
Matrix Algebra
Numerical Solutions of Partial Differentiation Equations
Multiple Integration 1
Multiple Integration 2
Integral Functions
Vector Analyses 1
Vector Analyses 2
Vector Analyses 3
Complex Analyses 1
Complex Analyses 2
Complex Analyses 3
Optimization and Linear Programming.

Good Luck!

Originally posted by zigmeister
I've come to realize that I née mathematics. In school, I was one of the sort who would at "I'm never going to use this in life". Ive come to realize how seriously debilitating a lack of mathematical knowledge really is. I did well enough in mathematics up until the sixth grade, where I encountered some sort of mental stumbling block (of which I have no idea what it is or when I encountered it) which has made it difficult for me to understand some of the simplest and fundamental concepts in more advanced mathematics, (algebra, advanced geometry, trig, calc, etc)

Me too. It helps to make math apart of your language. Most of the use of math is for communication. Try to explain things in terms of math.

"If you don't understand something in math, there is a simpler element that you have missed or incorrectly defined"

reply to post by apeofapeland


Wouldn't it be best not to be taught by books but rather to come up with the formulas as you need them...?
As TheRedneck stated: "The hardest math anyone ever takes is 2+2=4... those addition and multiplication tables. They're all memorization. Everything after that is just a few rules and how to make them work. "

Originally posted by JackTheTripper
reply to post by apeofapeland

 

Wouldn't it be best not to be taught by books but rather to come up with the formulas as you need them...?
As TheRedneck stated: "The hardest math anyone ever takes is 2+2=4... those addition and multiplication tables. They're all memorization. Everything after that is just a few rules and how to make them work. "

I think you might be thinking in terms of simple Newtonian Physics where formulas are easily derived one from another. For that you just need to know how to transpose variables. All you need is Elementary Algebra. You won't be able to derive any new formulas, for instance for derivatives if you, at least, aren't familiar with the concepts of derivatives and difference quotient. Arithmetic and Algebra don't contain anything of the sort. Just knowing Derivatives or formulas for different areas of different shapes like triangle or circle won't help you if you need to calculate irregular shaped area- You need to be familiar with Integration. You could, of course, come to realization that integration is the opposite of differentiation by tweaking derivative rules, but it took the world of math almost forever to do just that...And there are a lot of isolated topics complete with their own set of concepts, ideas, rules and procedures to just be able to derive formulas on your own. Unless you happen to be a math genius it's going to be real tough (we are talking millenia of mathematical thought) to be able to learn all math has to offer on your own (without books) just by way of logical deduction.

And yes, there tons of rules and tables to memorize after those addition and multiplication tables.

The best advice I was ever given in relation to mathematics is to look at your problems logically, and use logical steps to solve them. I know it may not help, but if you break down an equation (especially the most difficult) and work to solve what you know from your logical understanding of mathematics, you will come closer to solving the problem (or you may solve the problem) than trying to attack the equation or problem with the understanding of maths you have.

You always need logic in math. No matter what. If you aren't familiar with certain Concepts and Algorithms, Logic won't help you and without logical thinking you won't solve jack even you have memorized all the tables and rules in the world.

reply to post by JackTheTripper

No one memorizes formulas. Formulas can be looked up in reference literature, and as another poster pointed out, manipulated to fit the conditions of the problem. Math is not about memorizing formulas, but about using formulas.

A great example: earlier this semester I had a student come to me with questions about the standard form for the equation for a circle. As I looked at his work, I recognized a little of what I was seeing, but not all... 25 years is a long long time. But I also knew the definition of a circle and the Pythagorean theorem, and was able to, within a few minutes, re-educate myself on circle formulas.

I think that's what you are talking about, using mathematical thought to develop formulas from more basic relationships. That's what math is.

I also did not remember the Quadratic Formula, but I simply hopped on line, typed it into Google, and had it within seconds. Now, I can pretty much rattle it off the top of my head again, having used it so much in class, but I made no real attempt to memorize it. At home, if I had need for that particular formula, even without the Internet, it is in several of my books; I simply look it up.

Electronics professionals can rattle off E=IR.... Mechanical engineers can recall F=ma.... Physical theorists know E=mc². Structural engineers can spew out any one of several equations for bending stress. It all depends on what formulas you need on a regular basis as to which ones you know... not rote memorization.

TheRedneck

reply to post by zigmeister


You don't need math dude! math sucks. Dam you have no idea how much I don't like math, sometimes its to the point of even hating it....And I really suck at it to, my mind wanders every time anything involving any sort of math comes into play...In school it was the only subject that basically for whatever reason my brain switched off and my mind regressed and wandered, I could never concentrate on math at all.

But then again maybe its for the best, because there are days when everything is just a number, a statistic, a probability, literally even people are walking talking compositions of patterns and numbers...And if i was better at math I would probably be even more machine like when in that mind-frame...

Anyways stay away from math dude, its evil...In fact once it becomes of no more use, it needs to be gotten rid of. Oh yes it's on the list of things to destroy. I will be damned if I sit down and be bored out of my mind again, much less going out of your way to sit in a classroom and do a bunch of mind numbing boring and pointless number crunching problems.

But I suppose it could be worse believe it or not there are even more boring, meticulous and always predictable if a bit faulty languages and mind-frame constructs out there, the grayness of math is not the only one that makes me want to, zzzzzzzzzzzzz.

It's just the most easily deconstructed and constructed. It's like taking the same thing, and applying the same thing to it, to come to the same conclusion by a portion of it. Really you end up at the same place you started to begin with.

reply to post by zigmeister


In the US, we have a lot of math being taught as "watch me do this, then you do it" vs. this is the mathematical concept, and this is its application (so that you can understand it)/here are some examples of its use in the real world (to further help understanding). Understand something, and why anyone would give a damn about it, and you are bound to remember it much longer.

An example: a lot of geometry/other math exists in video game/graphics/physics programming. Would have been a lot more interesting for me to work with/understand some of that stuff in high school than to just copy and attempt to memorize the steps the teacher was doing...

I've learned what I need to learn for my job. The rest is really just bull# which I've never used or will be using ever in my life. I wish they would give you the math that you really need for the job you're going to get, when I realized what I needed I learned it super fast because I could see the meaning. but when I didn't see the meaning at all it got more difficult.

|.|SLO7H|.|

Originally posted by SLO7H
I've learned what I need to learn for my job. The rest is really just bull# which I've never used or will be using ever in my life. I wish they would give you the math that you really need for the job you're going to get, when I realized what I needed I learned it super fast because I could see the meaning. but when I didn't see the meaning at all it got more difficult.

|.|SLO7H|.|

Not too sure about that. Jobs in industry do not require a high degree of technical competency. For example most programmers will just glue libraries together written by other people. But if you want to understand the computer better you'll need math and mathematical maturity. For example do you know why hex numbers of the form 0xYYY0 are dividable by 16, where the Ys are arbitrary? Or can you prove why 2's complement works? If you understand the theory you will have the tools needed to be a great programmer but it is also possible to be and average one without much understanding.

Originally posted by thisguyrighthere
Math rules. School ruined it for me. Even in college too much time was spent going over the same crap over and over and over in a fruitless effort to bring the dullards up to speed. At the beginning of every semester when it was apparent 90%+ of the class had no business being there the teacher always went on a rant about how it wasnt his job to teach the last class over and he spent half the semester doing just that. So it never went anywhere.

I loved it, then school made me hate it, now that all that structured catering to the lowest common denominator is done with I love it again.

I've been on an engineering and mechanics kick that is spilling over into organic chemistry. Stuff I always thought I loved until I took them as classes. Nothing quite ruins the excitement of education like being dragged down along with the bell curve.

The real shame if it is that as much as I may learn on my own it's all basically useless since it doesnt mean anything without that fancy and expensive piece of parchment to verify it.

www.math.com...
www.openculture.com...
www.openculture.com...

edit on 8-12-2011 by thisguyrighthere because: (no reason given)

those are some good links.
I will enjoy checking them out.