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that was the end of my engineering career. i stopped doing homework pretty much entirely, so i didn't do well on tests and i didn't really learn anything :ut-oh:

good thing i changed my major. i'm still trying to recover my GPA after that mess
 
psi said:
And Nootch that's a hoot putting up a 2nd order....was it linear? Did they solve it?
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Yes it was linear and no they didn't really try very hard to solve it. They just made guesses like "seven!" and a few said they knew what the "plus" means, but in the end they were more interested in seeing pictures of themselves at the zoo (which were also on the site, and are arguably more interesting than differentials at times ;) ).

psi said:
So Nootch you go for a degree in math?
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Computer Science and [Electrical] Engineering.
 
nootch said:
Computer Science and [Electrical] Engineering.
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Ah yes from what I know of some engineer friends you're required to go up to including Differential Equations usually but some colleges want that Calculus III with Linear Algebra which can be taken after ODE's (the Linear Algebra that is). I take it you didn't have to go any higher than. Other then Infinite Series? I know one guy who took Modern Geometry (Abstract) that was an EE but he wanted to change mid-drift his major to teaching high school mathematics.

Unfortunately for me I'm at point I have to decide whether I want to complete my courses as "pure" or "applied". I've been focused on the pure mathematics but I do enjoy some applied methods. Nothing is really stopping me from doing both since I do plan to do some post-doctorate work as well or I just might just teach post-secondary mathematics and know it all.

By the way just for knowledge sake advanced chemistry works wonderous through linear algebra on chemical equations. And yes Nootch physics works ideally through calculus.

Sometime I'll post link to the chart of what mathematics are required to each career. Every career out there pretty much requires some math. Depending on career it shows what math level you should attain. (any one going into a Physics career needs to know every type of number: irrational, radical, integer, real, complex, etc. ) Even a house-wife as a career you should know decimals for currency. But as far as I remember every single major through college requires at least College Algebra. So if you are avoiding this thread because you don't like math and you have yet to fulfill major in college look forward to at least some algebra.
 
Exterior Algebra (part 2)

Okay I wrote more in Word with Mathtype tool so it looks nicer for your benefit. Here's part deux of Exterior Algebra. Enjoy!


GAHHHH! the last "y to power of p" or "y^p" in summation should be "y^q". Hey even I make mistakes!
 
Links

Here are some links that might help those wanting to study higher math get a foothold.

Mathematical Atlas - atlas of some higher math
Mathematics Web Sites - large linksource towards mathematics
MathWorld - Largest resource of math online

My honest opinion is to first go via TEXTBOOKS, then WRITTEN BOOK, then lastly INTERNET. There is that slim possibility the information on the internet from even an honest website is wrong! You really get information at your risk. Try to justly get information from university or math organizational like MAA or AMS sites only and/or government sites like the NIST. To view textbooks attend the class or visit a school library. Even hand me down textbooks that you see at booksales can help you start. I myself even use books from the 60's (I collect hundreds of math books).

Next up....math and graphics...Art!!!
 
first off a discussion (feel free to join in especially if partial to either subject) about art and mathematics. Comparing and Contrasting:

Mathematics is a science of patterns and structures.
Art involves patterns and structures.
Math is beautiful in deduction being unique to the solver (in a methodical way).
Art is creative in reflection and integrity of an individual artist.

Math uses the right brain and is rational, analytical, logical, and practical. Art uses left brain and is creative, reflective, harmonic, and aesethic.

Math is precise and limited within the bounds of a numeric algebraic structured language. One is layered atop the other to explain each other. A formal code is required to relay information.

Art however is less precise and can use practically any medium and can go under any form to get a message across.

But the one thing they share is beauty. A unique aura of being pleasing. Even if we subjected to only geometry as being visually stimulating in mathematics we include it as art and vice versa. However even long equations proofed out in equate a beauty of a quilt. The first and last points holding the hemline. Fractals, physical applications, shapes, engineering schematics, number lines, scales, graphes all share a coherent form of design that can relate to art. Some famous artists who shared a scientific view as a form of ratio to art: Leonardo Da Vinci, Durer, Ernst, Seurat, Mondrian, and Le Corbusier.

Even the Egyptians formulated a "Sacred Geometry" to their architecture and artwork. As many ancient civilizations. Even Texaco stations of years gone were formulated into a precise shape. Washington D.C. is a mathematical city in its design. (more on that later).

Next post will be some art work (all my own done by math programs).
 
i think a fundamental difference is the fact that math IS and we're constantly trying to discover it and understand it, and art is our creation, which we can add to indefinitely. pretty neat though
 
I personally love math. It has always been easy for me because it makes sense and I can rember formulas functions ect. This makes me good at math and so i took algebraaaa 1 in eigth grade and now i'm taking 10th grade math as a freshman. but my main strength with math is maniplating equations which makes me very good at trick questions in math. Now admitedly i havn't gotted to algebra 2 yet even so my opion might change after i get math that is actually challenging
 
Lissajous Figures

Well I'm gathering up some cool pictures and will probably limit it to five to show a variety of themes, I will discuss one type of figure that mixes sound with mathematics. Jules Lissajous put a mirror on tip of tuning fork and aimed a light beam at it. It made a wave shape on a screen showing the vibration. But then he put another tuning fork "orthogonal" to the other fork with another mirror and presto a beautiful design showed up. These are perhaps some of the most fascinating figures to see "sound". Here is a link to some preset Lissajous Figures

Anyone that has heard of this or made their own designs let us know! If this is new to you and you love it let us know too! I think it is cool to see beautiful figures as art and science!
 
Density Plot

Okay here is first figure of Math and Art! I might add more than 5 but I'll post them along over the month.

This is a random generation of overlapping rectangular data sets. The color that is situated depends on the number of rectangles covering that area. This is known as a density plot. Looks Cubist in formation eh?
 
Something wrong?????
 
Density Plots

Maybe the picture didn't come out right. If you could see the above one it was 40 randomly placed rectangles.

I posted another one with 10 rectangles here also so it's easy to see the color scheme and I put it .gif form instead of .jpg now.

EDIT - added the original in .gif form again so you can see 40 rectangles too (-> Density Plot 1.gif)
 
wow, funky-cool. it's better than a lot of the "art" i got to see in my recent modern art class ;)
 
Okay I deleted the bad .jpg from post 31. And since you can see the above ones all is good. I'm still narrowing down what looks artistic that nobody really has seen before that's also mathematical.
Coming soon...
 
Reversible Cellular Automata

As initial conditions are different for the three systems below given you can instantly tell the ones that quickly become chaotic and random. However choosing a point within as initial point we can reverse and see the initial conditions (that way we know what the initial conditions are). If we couldn't change initial conditions to have different outcomes we wouldn't be able to fulfill the Second Law of Thermodynamics and have reversiblility.

The artistic quality here is like the unravelling of something simple to complex like the focus is moving along the columns of each system on 73 and 222. However we see a geometric pattern in 26 that seems to repeat and repeat. These three systems are known as Reversible Cellular Automata.
 
I think for benefit of knowing what I used to make graphics I'll name the program(s) I used. All pictures though end up in Adobe Photoshop and ImageReady for touch up and sizing.

for the Density Plots I used Mathematica
for the Reversible Cellular Automata I used NKS Explorer

Probably going to add an animated one in here sometime.
More to come all!
 
Moebius Strip

MC Escher (famous artist that played a lot with topological figures)
view link of MC Escher to see some artwork of his.

A Moebius Strip is easy to make with paper. Just grab a long rectangular strip of paper. Have each end meet but twist once and then tape. Imagine you're an ant walking on surface of one side. Well it's all one side as you can see. In math programs it's beautiful to see the shadings as you turn the strip. Kind of like a hue of watercolour.... Same exact strip below just turned at different angles. This was made in Maple.
 
Graphic Matrix representation

Here are matrices with randomly generated values graphically represented in a hot map setting (temperature to values).
Each matrix is of 10, 100, and 1000 for n so matrix is n x n in size.
The squares become specks as the n gets larger for the approximately same size canvas (graphing area).

It's almost like the pixelating effect in some art programs or the speckling effect with a brush. Sometimes it's the way comic books are made with different shades of a pixel to render the whole picture.

Here though is randomly generated art made in Matlab.... :nod:
 
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