Mathematics

[s243a 0]

People don't need to know about derivatives or integrals to get an education. I also hate the standardized tests, such as the OGT (Ohio Graduation Test) which I will have to take next year.

I agree with you on both points but that is not really the point.

[no9t9 0]

I said no engineering work experience. I worked for public works, I?ve worked in factories, I?ve tree planted, blueberries racked, picked strawberries. I have tutored marked assignments and now I am writing some code for mechatronics labs. Anyway to suggest that I won?t need to know any high level math as an engineer is a little ludicrous. If that wasn?t what you were suggesting why bring it up.

<{POST_SNAPBACK}>

So, in all that work experience have you needed more than basic math? Remember, no school related stuff (ie your tutoring and labs, etc.)

 

If you think being an engineer will require "high level" math, you are mistaken. Like i said before, COMPUTERS do all the work. Just so you know, I have a mechanical engineering degree and have worked in engineering jobs. Since my background is in engineering, many of my friends are also engineers in various disciplines. Many of my friends even went on to do an Masters in engineering.. their jobs don't require high level math skills.. Like I said before, there are obviously exceptions.

 

Ok, now that i've got the engineering side covered.. I, unlike my friends, went on to do an MBA. And, I can tell you for a fact that all the people I met there do not use high level math in their jobs. The only part of business that MIGHT use high level math is financial engineering.. and that is a HIGHLY focused job dealing with producing models for predicting/analyzing risk, trends, etc. in the market.

 

Higher level mathematics don't just teach math skills - they are an introduction to more complex modes of thought, as well as an introduction to higler learning in general. Students who like calculus are probably more likely to work towards a math or science degree... and this country certainly needs more mathematicians and scientists!

nobody is arguing this point. I never said that learning math is bad. I just said you will most likely require only basic math in your job.

 

Is this so hard to understand?

[Zenchi 0]

Googlue, please don't delete this topic, delete the spam posts.

Anyway, I had my mother explain this, like I said earlier, I can grasp it, but not fully.

I understand what you mean (except on how to help you), I'm just not used to doing it flat. ([(a* (c*d)])

I'm curious to your first helpful post, but either I do not understand what Sum_{over all elements} means, or I missed something.

For example here,

[2 3] * [4 5] = ac+bd[br]-> ac=(2)(4)   bd=(3)(5)[/br]--> ac=8   bd=15[br]---> ac+bd=23[/br]----> Sum_{over all elements} /=/ ac+bd[br]-----> 2+3+4+5=14=E[/br]------> 14 /=/ 23

[s243a 0]

I mean the sum over all elements after you did element wise multiplication. Recall for matrices/(row vectors) [a b] and [c d] element wise multiplication is done by multiplying corresponding elements to obtain a matrix of the same size.

Thus:

[a b] .* [c d]=[(ab) (cd)]

Gives a two by two matrix with the first element equal to (ab) and the second element equal to (cd). Notice the dot product is:

[a b] dot [c d]=(ab)+(cd)

Thus you can think of the inner product/(the dot product) as element wise multiplication followed by a sum. It is not really necessary to think of the intermediate step. However the programming environment MATLAB allows you to do element wise multiplication by using the sybol .*. Incidentally it also uses semi colon for a new row and space or comma for a new column. Thus I am also teaching a bit of MATLAB without you even knowing it. So the answer you are looking for is 23 and not 14.

Also in linear algebra books they say mathematicians did not define matrix multiplication element wise because they instead formulated a more useful definition. Although true element wise multiplication is very useful for programming and it does make certain mathematical expressions easier to express. I think that linear algebra books shouldnt so easily dismiss it as a useless idea. If I get around to showing you how to write a program that will do a generalized multiplication of arbitrary dimensions you will see how I will use element wise multiplication to define normal matrix multiplication.

[s243a 0]

Matrices are a Great deal of help.. Atleast in Boolean Algebra where this stuff is really used! Getting the order and type of the sets ... Discrete Structure ( the whole subject ) could had been so much complicated! Matrices really ease the job!

I never used matrices for boolean algebra or discrete structures but it sounds interesting. I havnt taken a discrete structures course but I have taken a discrete math course (close enough). I agree that expressing things in matrices can greatly simplify some expressions. For instance simpler is simpler
y=Ax

or

y1=a11 x1 + a12 x2
y2=a21 x1 + a22 x2

As for Tensors, I have studied matrices but I havent hit this word. I know the following concepts related to Matrices,

I have seen it mentioned in a first year linear algebra course,( I think in the context of linear transformations) but it is more something for a second or third course in linear algebra. I my self have only taken one course in linear algebra but I have seen bits and peaces of matrix algebra in other courses. I learned about tensors because I was interested in relativity. Maybe I picked it up on a news group or something. Unfortunately I never was able to fit relativity into my schedule. I forget which courses I chose instead even if I could fit it in. When I was at Mount Allison University doing physics it was taught by Dr Hawks. He was a really good teacher and the course would have been exceptional. Oh well hopefully some day I will learn it on my own. On book I read mentioned that many material properties can be expressed in terms as a tensor. For instance strain and modules of elasticity.

1> Multiplication ( which is row to column one )2> Adjacent Matrix
3> normal Matrix
4> transpose
5> complement
6> conjugate
7> skew matrix
8> Hermatian skew matrix
9> Inverse of a matrix
10> General Matrix properties & types also the properties related to Matrix Determinants! ( this thing is assumed though  )

I am surprised you have leaned about Hermatian matrices. The only place I have used those is in quantum mechanics courses. Maybe they might also be used in electromagnetism somewhere.

Being a Computer Engineering Student, I havent gone deep into this topic. But I gues tensors are really advance topics of matrices.
There are many other things about matrix, but they aint clicking me at the moment.. but if you get an idea regarding my knowledge from the above points, feel free to continue this post ahead!  May be my knowledge about Matrix is still in the beginner level.

I think one good course in linear algebra can get you quite far. I suspect it gets pretty abstract once you get to the third course. I have only taken one course on linear algebra anyway. Some interesting matrix concepts you might be interested in are:

Positive definite matrices
Positive semi definite matrices
Singular value decomposition
Pseudo inverse
Orthonormal matrices

[googlue 0]

OK. The reason I wrote that I would move this to spam was that the initial few posts did not make absolutely any sense.When you start posting about something, you must give a clear introduction and then start.There was none and I did not see any points being told or asked. It looked like blablabla...Mathematics does not go over my head... I used to be very good in it before I changed my professional direction...Now the posts do seem to be making some sense but those who are into mathematics, please tell me whether it is useful.

[s243a 0]

Since the interest in matrices has seemed to dry up for the moment I will shift the topic to what is mathematics and why does it exist? I have studied math both in the context of engineering and for it own sake. It is rewarding studding the applications because you can see the utility of mathematics but can lead a person to miss what mathematics is in it's most pure and abstract form.

In the most pure and abstract form mathematics becomes language and philosophy. Complex ideas are created out of a minimalist set of principles. Since much of our conception of existence depends on our ability to describe things, much of the universe can be described by mathematics, then our concept of existence in inherently related to our understanding of mathematics. I will now quote from an article I recently read which discusses mathematics in a philosophical context I have not yet explored and thus am not well equipped to defend or attack such arguments.

There is no Darwinian explanation for the presence of mathematical abilities within the mind. The ability to understand physics could not have arisen by evolution. Although our bodies may well be the product of random mutation and selection al the way from amoeba to man, our minds have some 'unevolved' dimension.  To quote Hamming:
"But it is hard for me to see how simple Darwinian survival of the fittest would select for the ability to do the long chains that mathematics and science seem to require".

Consider also that the universe began as a quantum event which remained in a superposed state of all possibilities until acted upon by the mind of an observer (Copenhagen interpretation of quantum mechanics).
Now an observer existing in the absence of any objects or forms will have no knowledge of any material things. She will, however, have knowledge of mathematics, as mathematics arises from mind comtemplating emptiness, and needs no material objects or things to count.

from: http://forums.xisto.com/no_longer_exists/

The mind observes the empty set. The mind's act of observation causes the appearance another set - the set of empty sets. The set of empty sets is not empty, because it contains one non-thing - the empty set. The mind has thus generated the number 1 by producing the set containing the empty set.
Now the mind perceives the empty set and the set containing the empty set, so there are two non-things. The mind has generated the number 2 out of emptiness. And so it goes on all the way up.

http://forums.xisto.com/no_longer_exists/

[osknockout 0]

Yeah, I'm like 15 now and I'm barely getting the tensors idea....and yes googlue, this is pretty useful! I just dropped my attemptto evolutionarily correlate mathematics and growth of the cerrebrum.Sin and cos I got some time ago.Why does mathematics exist? It's just another form of logic.The ball goes so far when I throw it, what if I throw it farther?I see the same number of fingers up as apples on the tree,I can tell someone how many apples there are on the tree byshowing them my positioned hand. Yes, in its purest form itis language but I have to question you on the philosophy part.Hmm... I don't think raising the cannon 10 more degrees or5 degrees is a matter of philosophy. Same thing with the apples.I don't see any in [a+b]^x = P/\{x} where P/\ is Pascal's Triangleand x the "line" of it from the top.By the way, anyone found a way to note [a+b]^x without Pascal's?and for those wondering why I'm using brackets, b and ) make a

[s243a 0]

By the way, anyone found a way to note [a+b]^x without Pascal's?

and for those wondering why I'm using brackets, b and ) make a

I believe this is what you are looking for is the binomial theorem

 

 

 

I think you can use principles of statistical concept of a Combination to prove the binomial theorem. If you replace the factorial with the gamma function

you can get a non integer generalization of the binomial theorem.

[osknockout 0]

Thanks for the summations... I'll need to spend some time
on that gamma function but I'm busy now.

I've been working on Fermat's Last Theorem:
a^x + b^x ?= c^x where x>3 and a,b,c are
nonzero numbers (integers only perhaps?)

Heard it's been proved by Andrew Wiles, but I'm
still looking for an explanation.

I thought this up but I can't

find what's wrong with it (same theorem):

[/br]xlog(a + xlog(b = xlog(c[br]x[log(a + log(b] = x log(c[/br]log(a + log(b = log(c[br]a + b = c[/br]

N....NO. That's not always the case. But what's wrong here?
Sorry for my ignorance

[s243a 0]

Fermats last theorem. Wow, ambitious. Some day I may read the proof but I think it is over a hundred pages. I also havent studied much number theory but that may change. Partly because of its relevance to encryption and partly because of the connection between number theory and abstract algebra. My main interest in algebra is systems of polynomial equations. I havent studied much of it yet because it doesnt relate too closely to electrical engineering. The only area where I know it relates is roboustnuss plots A.K.A parameter mapping.

 

xlog(a + xlog(b = xlog(c

x[log(a + log(b] = x log(c

log(a + log(b = log(c

a + b = c

 

Anyway your mistake is in the first line.

log(a+ does not equal log(a)+log(

functions that have this property are known as linear functions. Functions with the property f(a+=k+f(a)+f( are known as affine functions. Anyway keep up the good work. I dont think I even knew what fermats last theorem was when I was 16.

[Zenchi 0]

Okay, I'm sorry. I'm only in Geometry (Grade 8.), so I don't know anything besides Linear Functions. Is there anyway you could give me a quick runthrough what exactly these functions are, the definition of this math, and possibly without strange greek characters? :rolleyes:I can *SOMEWHAT* comprehend it off that website earlier stated (can't remember it.. I'm on my laptop). Thanks. :3

[X3r0X 0]

Yes.... i understand

[Dooga 0]

WHAT???? I was going to chatter about the fermat's last thereom because it was supposedly the "Most Famous Mathematic Problem"... took 200 pages to prove it and over 300 years to find the proof! How smart is Fermat? I bet he didn't even prove his thereoms!

[osknockout 0]

Fermat's last theorem. Wow, ambitious. Some day I may read the proof but I think it is over a hundred pages.

I think it's one or two thousand pages. Something about a Goldbach

transformation. Looked it up, stopped at the first page Indeed,

ambitious, but it's always worth a try. I should have seen that...

 

Okay, I'm sorry. I'm only in Geometry (Grade 8.), so I don't know anything besides Linear Functions. Is there anyway you could give me a quick runthrough what exactly these functions are, the definition of this math, and possibly without strange greek characters?

heh, I understand. Just looked at the gamma & affine functions.

s243a, not all of us took calculus

 

Anyways, here you go:

 

Gamma function - [correct me if I'm wrong people]

 

Ok, you know factorials right? 3! = 3 * 2* 1, 4! = 4 * 3 *2 * 1

 

ok, there's a calculus version of that also basically, Euler played around

with that and found a way to use it for numbers like the square root of two.

Ever heard of i? sqrt(-1)? Quite possible in algebra. so you can have numbers like

2 + 7i. The gamma function is this little magic equation that can sum all the above.

 

Affine functions -

 

relative to x, y=2x is a linear function

relative to x, y=2x+7 is an affine function

 

an affine function is one where there is some constant term which allows for a

result not wholly based on independent variables.

 

The binomial theorem:

 

 

You mean this thing? Ha, not that hard!

(x+a)^n = the sum of the variables x^k + x^n - k where

k is the current term and n is the total number of terms times

n!/(n-k!)k! So basically,

 

[a+b]^2 =

[2!/((2-0)!)(0!)]a^2 * b^0 + --comment-- 0! = 1

[2!/((2-1!))(1!)]a^1 * b^1 + --brackets used for your eyes,

[2!/((2-2!))(2!)]a^0 * b^2 --not proper math grammar I think.

 

...or also known as a^2 + 2ab + b^2

 

Get used to the Greek symbols, the Greeks did a lot to math and

hence, they get some additions to mathematical language.

 

Yes.... i understand

Here, the link to the Oraculatory Digests, enjoy yourself and be enlightened.

 

By the way Dooga, I heard that Fermat had a proof involving the area

of a triangle... which he later disproved wrong so he had no proof for

it himself.