Table Of ContentThe Speed Math Bible
written by Yamada Takumi, with the special collaboration of Danilo Lapegna
Transform your brain into an electronic calculator and master the mathematical
strategies to triumph in every challenge!
"The 101 bibles" series
I - The Speed Math Bible
I'm quite sure we could all agree about a fact: the traditional way to teach
mathematics has a lot of structural problems, and in most of cases it doesn't
really help students to get confident with the subject. In fact, too many students
finish their schooling still having a real "mathematical illiteracy", united with a
burning hatred of everything concerning numbers and operations.
In particular, talking about classic method of teaching mathematics, I'm strongly
of the opinion that:
It's really poor incentive for individual creativity: in fact, too many
times school will teach you that the proper method for performing a set of
calculations is "rigidly" one, and that everything should always be made in
the same way. This obviously can't do much more than boring every student
and generating the feeling that the matter itself, rather than improving one's
mental skills, actually shrinks them, gradually transforming him/her into
something that's more similar to an industrial machine.
This book, however, is designed to go far beyond this restricted vision and
will teach you that the classic approach is not the only possible approach
and that every set of mathematical calculations can be transformed into a
deeply creative challenge.
The idea of mathematical "trick" is unjustly "demonised": very few
people know that they could perform very complex calculations just by
using extraordinarily rapid and effective numerical tricks.
And although it's widely accepted that learning the right balance between
tricks and rigour, creativity and structure, quick solutions and harder
solutions would be ideal for any student, schools usually continue to prefer
following a "complexity at all costs" that of course does not nothing but
alienating people from the matter.
It's promoted very little self-expression: too many people feel that they
have "nothing to share" with some mathematical concepts even because the
rigidity of the taught method prevents everyone from expressing himself
according to his talent, his wishes and his natural predispositions.
But this book presents a completely different approach, since everything
among its pages will be deeply self-expression oriented, and the methods
shown here will teach you not just one, unquestionable method to solve
everything, but will give you the freedom to act according to what you feel
to be easier and more compatible with your natural attitude.
It's promoted very little curiosity and "researching spirit": math, as
taught from some very bad teachers, is presented as a grey and squared
world, made of endless repetitions and very few interesting things. But
thanks to this book you will start an original journey through the
singularities and the curiosities of the numbers world and you'll soon find
out how many interesting and beautiful things are hidden into its deep
harmony.
They speak very little about the real utility of mathematics: beyond the
ability to calculate your restaurant bill in an instant, the enormous
advantage you will gain in every official test or exam, or the awesome
progression of your logical and deductive faculties, you will discover that
mathematics has extraordinary strategic and creative applications that will
help you very often in your everyday challenges, giving you that extra
oomph in the administration of your personal finance, your work, your
studies, your health, your self-confidence and your strategic intelligence
when dealing with any kind of challenge.
Math is also vital engine and fuel for every little technological wonder in
the modern world. Computers and tablets could never exist today if two
mathematicians like John von Neumann and Alan Turing didn't write the
mathematical principles behind the first calculators. Internet would never
have existed if no one had developed the mathematical principles the
networks theory is based on. And the search engines and social networks
could never be born without the equations and algorithms allowing each
user to track, retrieve and organize documents, web pages and profiles
directly from a set of chaotic data. Moreover, the inventors of Google and
revolutionaries of the modern world, Larry Page and Sergey Brin, are both
graduates in mathematics.
What I'm trying to tell with this? Well, I'm not sure that every reader of this
book will end up founding the new Google, but I'm sure that a greater
mathematics competence in a world tuned on these frequencies can help
each of us to be more a protagonist and less a bare spectator of it.
In other words, this book will not simply be a set of strategies for impressing
someone or increasing your academic performance, but will let you start a
journey through a pleasant and intriguing path of personal growth, along which
you'll learn to be more effective, creative, confident and, why not, more
intelligent.
In addition to that, I would like to give you a last advice: do not immediately try
to learn every method explained here, but go slowly, make notes, select the
techniques you like most and train yourself calmly and always taking your time.
This will help your mind to learn everything with much more ease and less
effort.
Enough said: now I can't do anything but wishing you all the best and, of course,
to enjoy your reading!
Yamada Takumi
About the authors:
Yamada Takumi and Danilo Lapegna are two Software Engineers working in
London as software developers and freelance writers. Their series of books,
"The 101 bibles", has been a great sales success in the self-publishing sector in
Italy, engaging thousands of electronic readers even in a moment of economic
instability for the Italian market. Now they're constantly expanding their series
with new books about personal and professional self-development and their
work represents an important reference point in the market.
For any kind of questions, help requests or, most of all, feedbacks, you can write
them at
"The moving power of mathematical invention is not reasoning, but
imagination."
(A De Morgan)
II - 5 mathematical strategies that will seriously improve your life
We constantly count and make measurements in our everyday life: how many
hours must we sleep to feel really refreshed, what's our ideal body fat
percentage, how much time do we need to finish examining those documents,
after how many miles the gas tank of our car will be empty ... these are all
examples of everyday problems we constantly have to deal with, and that
obviously would require a solution as more effective as possible.
At the same time, however, we too often evaluate the factors involved in our
problems from a purely qualitative point of view rather than a quantitative one,
giving them purely empirical solutions. That is, for example, instead of trying to
understand the proper amount of sleeping hours for our body, we too often try to
sleep enough to feel relatively fit. Rather than calculating our body fat
percentage and adjusting our diet accordingly, we prefer some kind of
homemade diet that does not really pay attention to our real physiological needs.
And we do that despite it is intuitive that addressing these issues from a
quantitative point of view, and so measuring, evaluating, calculating the
quantities involved, would offer a greater efficiency to our actions, and so would
give us the ability to produce much more with many less expenses in terms of
time, money and resources.
Wait: this does not mean that you should run into some weird obsession for
rational assessments or for measuring every single aspect of reality. Your
existence of course needs even impulsively done actions, lessons learnt from
your mistakes and the coexistence with the inevitable unknown.
However, when you actually feel the need to get more results in a specific field,
a stronger mathematical "grip" on it could be a great strategy to enhance your
personal improvement. After all, the most successful companies are exactly
those doing the best in retrieving and analysing data about the consequences of
their behaviour. But how could we do that? Here's some advices we could
follow for the purpose:
Play giving marks more often. No, this has nothing to do with school. If,
for example, you really enjoy doing something, like, I don't know, eating a
particular type of food or going traveling somewhere, try giving to these
actions, or to the advantage you get from doing them, a mark. From 0 to 10,
from 0 to 100, it doesn't matter! The point is playing making quantitative
concepts out of qualitative ones, and starting making better analysis on their
basis. For example, if dedicating yourself to jogging in the morning has for
you a higher mark than going to gym, you could simply start to decide to ...
go jogging more often!
Quantity in most of cases helps you to better focus on the most important
things, and cleans your thoughts from the unnecessary stuff!
Try to make measurements where nobody else would do it. "Not
everything that can be counted really counts, and not everything that counts
can be really counted", said Albert Einstein.
This phrase not only confirms what I earlier said about the fact that
mathematics and calculations sometimes must simply be put aside (luckily),
but can help us to understand that, too much often, the most commonly used
measurement systems can deceive us, and can divert our attention from the
things that really matter.
An example I love doing about this is in the school report cards: their
obvious purpose should be giving the measurement of the performance of a
student, but we often forget that, on the other side, there could be a teacher
that simply has an awful teaching method.
And that's where we should start to "make measurements" where nobody
else would do it: letting the students evaluate the quality and the goodness
of their teacher's work could push everybody into doing better his/her work,
and consequently into producing better results for everybody.
Making measurements, evaluating, focusing on the things that other people
tend to ignore, gives you that extra oomph that will produce a significant
advantage in any kind of situation!
Increase the quantity and improve the quality of your measurement
instruments. Imagine: it's a lazy evening and you decide to go watching a
movie to the cinema. Now, you have to decide which movie buying the
tickets for, but you're hesitating between that new action movie with a lot of
old celebrities and that new horror Japanese movie about a dead woman
who comes back from the grave. Now you could take your smartphone,
read the movie reviews from some famous website and simply choose the
movie with the highest rate. But of course you would better estimate the
quality of those movies after increasing the quantity of your measurement
instruments and, for example, reading movie ratings from many different
websites instead than from only one of them.
Now there is a concept that can really come in handy: the mathematical
mean that, although is quite widely known, we'll explain in a few words,
just to make sure that everybody knows what are we talking about.
If you have multiple quantities, multiple measurements, multiple values (ex.
3, 4 and 5 stars rating for a movie on three different websites), you can sum
those numbers (ex. 3 + 4 + 5 = 12) and then divide the result by the number
of values you considered (three ratings in this case, so 12 / 3 = 4).
This will give you the mean of those quantities, which is universally
considered as a very precious value since, as in the measurements theory, as
in the probability one, it's said to be very close to the "real" value of
something (if a real value can philosophically or scientifically exist, of
course).
But now, let's add something and let's talk about quality of measurement
instruments: how many times happened that a multi-award winning movie
just left you asleep in your chair?
That simply means that those measurement instruments (the "official"
movie reviews we used to estimate the goodness of the product) weren't as
reliable as they were supposed to be. And this really happens a lot of times,
doesn't it?
But what's the solution? How could we improve the quality of our
instruments?
Well, we could, for example, browse just among the opinions of the friends
