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Solving The Mathematics Of Life

Tosin Afolayan, a public speaker, youth coach and good friend of mine made an excellent illustration while describing the power of the human brain in one of his training sessions with my team members and me at Unstoppables International a few weeks back. He painted a picture of a young man who thinks he isn't intelligent, drops out of school because he consecutively got bad results and proceeds to become a cab driver because he founds it easier to learn how to drive a car.

He pointed out how that driving a car requires far more use of the brain than solving the most difficult mathematical problems! All you need to solve mathematical problems is to apply formulas, but driving a car safely demands so much more. Just imagine you want to make a u-turn. You will have one of your legs on the clutch and the other on the break, your hands controlling the steering wheel, your eyes looking where you are going, while you check for oncoming vehicles from the sides and watch your rare mirror too. You might have to horn and change the gears in just few seconds! Imagine how many things you are required to do simultaneously.

As Tosin went on with his training, I was reminded of how difficult I found mathematical problems. I particularly hated algebras in junior school. I couldn't just wrap my little brain around how that a(a-b)+(a+b)b equals to a2+b2! Whenever I complained to my teacher, she said, "I've always told you to learn from worked examples." I would sadly sink my head and wished there was nothing like mathematics.

Life seems to be designed to test our ability to learn, endure and survive. It grows tougher as the year adds. Whether or not we like to tackle problems or not, we are expected to live triumphantly, resolving every difficulty along the way. That is why the greatest and most enviable form of power in human experience is the staying power. Life's algebras are not to be avoided, but worked out.

Solutions will not jump out like a rabbit from a magician's hat. Just like you need the right formulas to solve mathematical problems, life's problems have to be fixed using the right principles. Principles are fundamental truths, generic denominations which are changeless. You need to learn the principles that govern a successful life. Principles do not change; our understanding does. The following will help you solve you life's problems:

1. RESOLVE YOUR TASK

The quality of every life is measured by result! Good or bad, our results reveal our means. A crystal clear end in view helps to resolve focus and fine-tune the process to the highest degree of precession. In the game of life, the goal-minded player reduces stress incited by distractions by having a clear end in view at all times. We are called to a purpose-driven life. The first most important question to ask yourself is, "What am I living for?" before you answer the question, think on the words of Charles Mays, "Make sure the thing you're living for is worth dying for."

2. DEFINE YOUR METHODS

If you know WHAT, the HOW will follow. Once the destination has been defined, the course must be charted. This is extremely important because our lives are time-bound and we are limited. Isn't it a painfully futile mission to climb a very tall and fragile ladder just to get to the zenith and discovers it was leaning against a wrong wall? Always analyze your tasks and evaluate your abilities. You must evolve as much as you can to develop sufficient "muscles" to tackle your tasks effectively. Learn the methods that work with your personality, acquire the needed skills and employ the right hands in getting your work done. This will minimize waste and accelerate productivity.

You might also want to heed my mathematics teacher's advice "... learn from worked examples." It is true that "experience is the best teacher." But you don't have forever to make all the mistakes, creating the "experiences" to learn from. It is only smart to learn from "worked examples" - people who have done what you are trying to do, and even those who have failed at it. Learn from their mistakes, learn from their successes.

3. MASTER YOUR TIME:

If you are given an algebra equation to solve, you will also be given the time duration to do it, which is why it is called a problem. In case you haven't noticed, every second gone is an irreversible reduction from our thin lives. I'm not trying to make you feel like an endangered species, but I'm afraid the gift of life that you have depletes per second. Therefore, a mastered time is a mastered life. Everyone has equal hours for a day, but not everyone has equal years in their lives. You have to be conscious of this and maximize the time you have to the fullest. Jesus said, "I must work the works of him that sent me, while it is day: the night cometh, when no man can work."

Gideon Banks is the founder/CEO of Unstoppables International. He is an artist, entrepreneur, business consultant and writer who believes life is an art and every waking moment must be lived in style without losing touch on individuality, creativity and humanity. "Some people find me crazy, others, amazing; but I'm categorically unconventional. I figured I can only be the best by being myself."

Read more articles by Gideon Banks on his personal website, http://gideonbanks.com

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Set Theory: Constructing The Rational Numbers


Terminology

The term rational in reference to the set Q refers to the fact that a rational number represents a ratio of two integers. In mathematics, the adjective rational often means that the underlying field considered is the field Q of rational numbers. Rational polynomial usually, and most correctly, means a polynomial with rational coefficients, also called a "polynomial over the rationals". However, rational function does not mean the underlying field is the rational numbers, and a rational algebraic curve is notan algebraic curve with rational coefficients.

Source:  wikipidia

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Getting the rationals from the integers

A diagram showing a representation of the equivalent classes of pairs of integers Wikipedia.


Our next task is to define the set of rational numbers from the integers using equivalence classes of pairs of integers.

The idea is clear: we think of a pair of integers (p, q) as the fraction p/q and use an equivalence relation to identify fractions that should have the same values.

The Rational Numbers by Ron Freiwald: pdf


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The field Q

In this section we are going to construct the rational number from the integers. Historically, the positive rational numbers came first: the Babylonians, Egyptians and Greeks knew how to work with fractions, but negative numbers were introduced by the Hindus hundreds of years later. It is possible to reflect this in the build-up of the rationals from the natural numbers by first constructing the positive rational numbers from the naturals, and then introducing negatives (Landau proceeds like this in his Foundations of Analysis). While being closer to history, this has the disadvantage of getting a ring structure only at the end.

The Field Q of Rational Numbers by Franz Lemmermeyer: pdf


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More understanding:

Constructing Integers and Rational Numbers by Jeff Thunder: pdf
The Rational Numbers: pdf


Where Football Meets Mathematics


Where Football Meets Mathematics

Math is all around us - at our works, homes and definitely in the sports and football predictions.

Frequently we find different connections between math and football, which are used by this game's greatest specialists. Some of them are basics of the football predictions posted on this website.

The true football fans still remember the Dutchman Dennis Bergkamp and his masterpiece goals. Sports commentators describe him as a genius, who mastered the football game to perfection and possessing extremely accurate shot, but what is he saying about himself.

"When I played in Holland I always tried to hit the ball over the goalkeeper. People always questioned me about this. Why would I want to humiliate the goalkeeper or to demonstrate arrogance? But I always explain: When the goalkeeper leaves his post he makes the angle to it less but opens the space above it. What I do isn't a show, it is mathematics."

This advice came from the coach Louis Van Gaal, who teaches strategies for success in the match based on mathematical precision and order.

As his players state about him: Van Gaal isn't one of those coaches who will repeat to them: "do this, do that". He will leave the technical part to them, but he is a master of the tactical part and knows what should everyone do in order for the whole system to work properly.

"I hope that I know well the basics of math in football and try to apply them" - Ottmar Hitzfeld as coach of Bayern Munich in 2007.

Ottmar hizfield

Ottmar Hitzfeld graduated as a math teacher and now he is the most successful German football coach at club level. He won twice the FIFA award for best coach in the world and is one of the only three coaches who won the Champions League with two different teams.(Ernst Happel and Jose Mourinho are the other two).

Unlike most Germans, Hitzfeld carried his football career as a player in Switzerland.There he quickly arose as a top striker in the country, helping Basel win the championships in 1972 and 1973. While playing for the Swiss team, Hitzfeld graduated and received his diploma as teacher of mathematics and physical education.

We believe that we have found the next evidence proving that football is mathematics.

Hitzfeld is recognized for his managerial capabilities - the ability to control units in the team to work as one and to develop and apply different tactics. The coach is taught of perfectionism and he sticks to all the details that would lead his team to success. For example, as a coach of the Switzerland national team he led the players to train in specially selected mountain resort where it is estimated that the height above sea level is most favorable to the players to adapt to the specific conditions of South Africa.

Thus, estimating all the factors, Hitzfeld is following his main coaching philosophy - "The next match is the most important match and we must do everything to win."

Bearing in mind the mathematical education of Hitzfeld, his numerous successes in the football are definitely not accidental, after all this is a game which is often described by specialists as a game of strategies.

Forebet.com - Mathematical soccer predictions "Where football meets mathematics"

Set Theory: Constructing The Integers



Introduction

Taking the finite ordinals gives a model for N. We can prove all of the standard properties of N.
Natural numbers are good for indicating the number of times you want to iterate a function. But what if you want to allow iterations of the inverse function.
How do we introduce the negative numbers?

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Step 1: Introducing equivalence relations

 In general an equivalence relation results when we wish to “identify” two elements of a set that share a common attribute. The definition is motivated by observing that any process of “identification” must behave somewhat like the equality relation, and the equality relation satisfies the reflexive (x = x for all x), symmetric (x = y implies y = x), and transitive (x = y and y = z implies x = z) properties.

Equivalence Relations by R.C.Lacher: pdf

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Step 2: Constructing integers from natural numbers


The natural numbers are designed for measuring the size of finite sets, but what if you want to compare the sizes of two sets? For example, you might want to compare the number of chairs in a classroom with the number of students to determine the number of free chairs. If there are more students than chairs, you would use negative integers to indicate the absence of free chairs.

The Integers by Wayne Aitken: pdf


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More understanding:

Constructing the Integers by Bernd Schröder: pdf