Calculation in most cases, can be easy or straightforward. But what to calculate, which relationships to quantify is a matter of imagination
Caffeine induced mathematical thinking..
How come math and politics can have anything in common? What is it? Answer: our moral CPU examines math results then make political decisions
From logic, p AND q => s. The "p" is your complex math calculation, while "q" can be anything from real world. Try it, see what "s" can be.
You may ask why you need to calculate anything. Well some significant political decision may depend on that very calculation.
Stochastic function is continuous but nowhere differentiable. Integrate that!! (hint, Ito's lemma :-)
Integration should be introduced with a stochastic function, showing students limit in probability first, and then limit in Riemann sense.
Forget about polynomials! You can create ANY type of functions in math, you are allowed (by ZFC axioms). If they interest you, even better.
Polynomials are created from this air (from ZFC axioms). You are not required nor it's possible within math, to justify their introduction
In math, you are free to create any function! No proof required! Then, since you created it, you may well be interested in their properties.
When You Can Start Developing New Concepts Airplane, my blog http://tiny.cc/m5s1l
Directional thinking supported by related systems of axioms.
Combustion is, in its essence, an ELECTRICAL reaction between the fuel and oxygen molecules. From my blog http://tiny.cc/fboud
The moment you find when a stack of bricks becomes architecture, you will find out when numbers and operations in math become beauty.
Proof in math is like a proof in any other field. Logic of proof is same. The only difference is math has well defined starting assumptions.
Word "IF" is a Magical Wand of Math. Using "IF" you can generate vast quantity of numbers, functions, patterns with no reference to reality.
Can you have debates, opinions in Engineering? Yes, but not on Physics Laws. You can debate initial and boundary conditions!
p AND q => s. Your "p" is your strong will, motivation, decision. You decide what is "q" from your world of ideas. Then "s" will follow :-)
Math should help you think more freely. Math shouldn't prohibit all your other thoughts and thinking in order to correctly add two numbers.
When writing a fiction story, remember, human values are at stake and not physics laws. Work the story events backwards.
Formula for good acting. Get into your character weeks before the scenes. Then, your response to the scene events will be almost unconscious
Formula for good acting. Always gesture first, even for a second, then say a line. It will look like you are fully in character..
Good acting can make any difficult, artificial part of movie plot work.
I would let students write an essay why they don't like math, and then work with him or her on case by case basis.
Women Mathematicians. Danica McKellar, Hollywood star (IMDB: http://tiny.cc/lwhrh) and published math author (J. Phys.) http://tiny.cc/cwrk8
Where math comes from and origins of fundamental math concepts for better understanding mathematics.Blog http://tiny.cc/lyah8
The confusion in applying math is that in math you have only one number 2, while in field of app. you have to keep track where 2s come from.
Track to creativity. Chose world of interest. Axiomatize it. Chose world where you interpret results. Axiomatize it. Play with both worlds.
When my world of axioms clashes with your world of axioms, fallacies will fly like sparks!
Social values, moral, ethics and engineering brain circuitry - my Blog, http://tiny.cc/ckbdq
The first course in calculus should include Ito's Lemma and Ito's calculus, to show other kind of limits (limit in probability)..
Finding patterns within facts in any subject of study, even very boring ones, can make that subject way more interesting.
Comedians not only discover what properties are the same between two objects or concepts, but they also select those which are funny!
Mathematics doesn't need to know nor does it care what are you quantifying! Language describing way of quantification doesn't belong to math
Quantification is broader term than measurement. You can quantify by simply assigning a number, sometimes even without counting.
Never trust the other side of a logical connective. :-)
Can you learn to play chess? No. You can only learn rules. How to play it will be up to you.
I think logically. It's just that my assumptions are wrong.
Think logically! Don't let the emotions, feelings, sex, intuition, love interfere with your decision...whom you are going to marry.
The difficulty of being creative is in the fact that you don't know what should be on the other side of a logical connective.
My article that will change how math is thought :) http://tiny.cc/bvn7i
My blog for anyone who is interested what mathematics is all about and how to use math any time you want, http://tiny.cc/0nl49
How the new ideas are born by creatively combining different directions of thinking and axiomatic systems. http://tiny.cc/1ur1q
When a school claims "we'll teach you C++ so you can be a programmer" is the same as "we'll teach you English so you can be Shakespeare".
A picture is worth a thousand words - mathematics and disciplines it is applied to - http://deconstruktion.blogspot.com/
Illustration of the relationship between mathematics and disciplines it is applied to. http://tiny.cc/lbdfm #math #mathematics
Insomnia, red wine, Family Guy, iPod, Kutta-Joukowski Theorem, Panel Numerical method, aerodynamics, aviation history...those are my nights.
More Math Insights. Mathematics Axiomatic Frontier and How Outer Worlds Puncture it to Generate Numbers. http://tiny.cc/lbdfm
Where the Graphs in Math and Physics Come From. Why do we use graphs to represent functions? http://tiny.cc/coiie #math #physics
Automobile Engine Principles, from fuel chemical bonds energy to crankshaft and camshafts, now with illustration video! http://tiny.cc/38l7i
Easy to grasp, explained and illustrated by me, principles of internal combustion engines, http://tiny.cc/s97w5 #physics #cars
How emotions enter math: "Boeing wasn’t happy with the way the Air Force calculated the higher fuel costs of the A330," http://tiny.cc/fl4vx
While number 5 is only 5 in math, it really matters what, when, and where you counted, in physics. Was it meters, seconds, mass, speed..?
Our emotions are like a guitar, like strings, waiting inside us to be plucked and played into a melody not yet heard..
To be a good writer you have to know the matters very well...
You probably wondered what 2.5% meant in my previous post. That's my point! Mathematician sees just that, 2.5%. No other meaning is required
The best starting point to learn about combustion is energy calculation of oxygen splitting fuel molecule forming accelerating CO2 and H2O.
Computers work with two bits, 0, 1. Humans work with interpretation of bits. Consequently, a single bit can have billions of interpretations
A very decision whether you will add or subtract two numbers has nothing to do with math. It can come from non mathematical thinking.
Field of math application is to math is as a driver is to his car. To physicist it matters where he drives, while mathematician doesn't care
Applied math - clash and harmony between two or more axiomatic systems, one of which is in mathematics.
If math is derived from 9 axioms where teachers found all those apples, pears, giving, getting, having, and claiming these words are math.
Worse thing than making a bad decision is when others know you decided wrong yet they take advantage of it watching you sit and do nothing.
Mathematics is never used as a motivational method for a student to do something else. But student has to find another motivation to do math
Issue how math is thought is that teachers mix nonmathematical reasoning with math statements derived directly from fundamental axioms.
In order to explain to student that 2 + 3 = 5, at one point it should be signified that no examples are necessary to state the addition.
Kids should be told the fact that "Mary gave Pitter two apples" has nothing to do with math. It's sociology, psychology, economy.
For each real world example in math students should be shown that formula can be gotten from axioms.
Where numbers come from? How about from love? http://yarzabek.wikispaces.com/, "Let me Count the Ways I Love You"...
New fields with applied mathematics. Quantitative physiology, quantitative finance, quantitative biology, quantitative sailing :-) etc ....
My goal here is not to talk about stochastic PDEs, integrals, other differential equations. I want to show where they are coming from.
Mathematics and other fields and why math can be independent discipline http://tiny.cc/gwdgy
In order to make a winning invention you have to discover the right system, figure out its axioms, and generate the winning premises.
Logic deals with truth values, but, determining what is true, in the first place, has, in many cases, nothing to do with logic.
Instead of addition, subtraction, etc...I would introduce excercises with operation "pick a number" in the first five lectures in math.
You can not "apply" math in some field, simply because, in math, you do not know what are you counting. You can only "utilize" math.
No matter what direction of thinking you are taking (logical, practical, irrational) emotions are there to stop or encourage you to do that.