1. Mathematical Formulas
Ing. Jaroslav Bernkopf

2. Expressing uncertainty
Mathematical Formulas
Objectives
Math symbols
Math operations
Expressing uncertainty

3. Vocabulary Mathematical Formulas
English
Czech
addition
percentage
approximate
piece
avoid
pile
cause
population
circle
result
circumference
root
common
sign
degree
square
diameter
stack
distance
stick
divide
string
division
subtract
double
subtraction
equal
uncertainty
express
fold
geometric progression
infinite
infinity
irrational
math operation
multiplication
multiply
percent

4. Math Symbols Math Symbols http://www.youtube.com/watch?v=CG0Q0jo2v6k
Mathematical Formulas
Math Symbols
Math Symbols

5. The most basic symbols are + - x ÷ =.
Mathematical Formulas
Math Symbols
We will avoid numbers and stick to the language.
The most basic symbols are + - x ÷ =.

6. = The first of the common symbols is the equal sign.
Mathematical Formulas
Math Symbols =
The first of the common symbols is
the equal sign.
We say this as equals or is equal to.
1 + 1 = 2

7. This is the addition sign.
Mathematical Formulas
Math Symbols +
This is the addition sign.
We say it as plus or add.
1+2, 4+9

8. - The next one is the subtraction sign.
Mathematical Formulas
Math Symbols -
The next one is the subtraction sign.
We say it as minus, or subtract, or take.
1-2, 13-12, 99-7

9. x , ∙ Then we have the multiplication sign.
Mathematical Formulas
Math Symbols
x , ∙
Then we have the multiplication sign.
We say this as times or multiplied by.
3x8, 26∙3

10. ÷ , / The next is the division sign. You can also show division as /.
Mathematical Formulas
Math Symbols
÷ , /
The next is the division sign.
You can also show division as /.
We say this as divided by, or over.
3 ÷ 1, 10 ÷ 5, 6 / 3

11. This one is the square root. We say the square root of.
Mathematical Formulas
Math Symbols √
This one is the square root.
We say the square root of.
√4 = 2

12. This one is the percentage sign.
Mathematical Formulas
Math Symbols %
This one is the percentage sign.
We say percent.
67%
(per cent = out of 100)

13. The circumference of a circle
Mathematical Formulas
Math Symbols 𝜋
This one is Pi.
This is a constant which begins This is an irrational number.
c = 𝜋 x d
The circumference of a circle
equals
𝜋 times its diameter.

14. The next symbol is the degree symbol.
Mathematical Formulas
Math Symbols
The next symbol is the degree symbol.
We say degrees.
90° 360°

15. Then we have the symbol for infinity.
Mathematical Formulas
Math Symbols ∞
Then we have the symbol for infinity.

16. Lastly, we have the plus minus sign.
Mathematical Formulas
Math Symbols
Lastly, we have the plus minus sign.
We say plus or minus.
6 ± 2

17. Math Symbols Mathematical Formulas
Today’s Daily Dose of English is a request from Albert, in Catalunia, Spain. Albert has written: I recently saw the "Computer Symbols" video and thought it'd be really interesting [to have] a video about mathematic operations. For example, it took me some time to find out that 3 x 4 was read "three times four" (in Spanish we say "three by four"). There are plenty of them: 3+3, 3-3, 3*3, 3/3, 3^3, sqrt(3), 3! and a lot more which I don't know how to write their symbols now. Many thanks for your videos!!! :-)
Albert Mata.
And many thanks to you, Albert, for making the request. It’s an excellent question and one that I’m sure many students are also unsure about. Unfortunately, Math was never my strong point. I’ve always been very good with English and always very bad with mathematics. However, if we avoid numbers and stick to the language, I should manage to explain this one reasonably well.
From school, I remember the basic symbols that most people are familiar with, even if we're not particularly good at manipulating them. The most basic of these are x ÷ = Let's start with the first one. This is the addition sign. We say it as plus or add. 1+2, 4+9. The next one is the subtraction sign. We say it as minus, or subtract, or take. 1-2, 13-12, Then we have the multiplication sign. We say this as times or multiplied by. 3x8, 26x3 The next is the division sign. I discovered that this is also called the obelus. You can also show division as /. We say this as divided by, or over. 3 ÷ 1, 10 ÷ 5, 6 / 3 The last of the common symbols is the equals sign. We say this as equals or is equal to. Other symbols I remember from my schooldays are... √ % π ° ∞ ± so we can look at these, too. This one is the square root. We say the square root of. √4 = 2 This one is the percentage sign. We say percent. 100% This one is Pi. This is a mathematical constant which begins and apparently has no end. This is an irrational number, apparently, though I have always been of the opinion that all numbers are irrational. People seem to be fascinated by Pi for the reason that it has no end. The only thing I remember about it is that the circumference of a circle equals π times its diameter, or something like that. The next symbol is the degree symbol. We say degrees. 90° 360° Then we have the symbol for infinity. That's about all I know of this one. Lastly, we have the plus minus sign. We say plus or minus. 6 ± 2. I have absolutely no idea why anyone would want to do this, but then again I teach English. My dislike of mathematics stems from my teacher making me stay in class at playtime because I couldn't memorize my multiplication tables when I was about 7 years old. I'm 7x7 now and I still don't know the multiplication tables by heart and I still don't like mathematics. So, I'm afraid that's the extent of my knowledge of mathematical symbols and the end of this Daily Dose of English. I hope you enjoyed it and I'll see you again soon for another one. Goodbye for now.

18. Symbol Name Read as Example
Mathematical Formulas
Math Symbols
Symbol
Name
Read as
Example +
addition sign
plus
2 + 5 = 7 -
subtraction sign
minus
5 - 3 = 2
x, ∙
multiplication sign
times
4 x 3, 4 ∙ 3 = 12
÷, /
division sign
divided by
8 ÷ 2, 8 / 2 = 4 =
equal sign
equals
A = B √
square root sign
square root of
√4 = 2 %
percentage sign
percent
75% 𝜋 Pi
[páj]
c = 𝜋 ∙ d
degree symbol
degrees
90°
plus minus sign
plus or minus
6 ± 2
power
2 to the power of 8 28

19. List of mathematical symbols
Mathematical Formulas
Math Symbols
List of mathematical symbols

20. I give you a large piece of paper. Fold the paper over.
Mathematical Formulas
The Tipping Point
I give you a large piece of paper.
Fold the paper over.
Take that folded paper and fold it over again.
Refold the original paper 50 times.
How tall is the final stack?
Most people guess:
The pile would be as thick as a phone book, or
it would be as tall as a refrigerator.
The real height of the stack approximates the distance to the Sun.
Folded it over one more time.
The stack would be as high as the distance to the sun and back.
This is called a geometric progression.
Epidemics are another example of geometric progression.
A virus spreads through a population.
It doubles and doubles again.
We have a hard time with this kind of progression.
The end result is far out of proportion to the cause.

21. Malcolm Gladwell: The Tipping Point
Mathematical Formulas
The Tipping Point
Malcolm Gladwell: The Tipping Point
Consider, for example, the following puzzle. I give you a large piece of paper, and I ask you to fold it over once, and then take that folded paper and fold it over again, and then again, and again, until you have refolded the original paper 50 times. How tall do you think the final stack is going to be? In answer to that question, most people will fold the sheet in their mind's eye, and guess that the pile would be as thick as a phone book or, if they're really courageous, they'll say that it would be as tall as a refrigerator. But the real answer is that the height of the stack would approximate the distance to the Sun. And if you folded it over one more time, the stack would be as high as the distance to the sun and back.
This is an example of what in mathematics is called a geometric progression. Epidemics are another example of geometric progression: when a virus spreads through a population, it doubles and doubles again, until it has (figuratively) grown from a single sheet of paper all the way to the Sun in fifty steps. As human beings we have a hard time with this kind of progression, because the end result — the effect — seems far out of proportion to the cause.

22. Jak vysoký by byl stoh, kdybychom papír přeložili 51x?
Mathematical Formulas
The Tipping Point
Odpovězte anglicky:
Jak vysoký by byl stoh přeložených papírů, kdybychom jeden papír přeložili 50x?
Jak vysoký by byl stoh, kdybychom papír přeložili 51x?
Popište, jak se množí virus.
Přeložte do angličtiny:
Dám ti velký kus papíru.
Stoh by byl vysoký jako lednička.
Znovu se zdvojnásobuje a zdvojnásobuje.
6x3

23. Paper Magic Paper Magic http://www.youtube.com/watch?v=N1sOcD2vITQ
Mathematical Formulas
Paper Magic
Paper Magic

24. How long is a piece of string?
Mathematical Formulas
A piece of string
How long is a piece of string?

25. How long is it going to take to get there?
Mathematical Formulas
A piece of string
Hello, how long is a piece of string? Here is a piece of string, a long piece of string. Here is another piece of string, so a medium length piece of string. And here is another piece of string, it's a short piece of string, or pieces of strings of different length.
There‘s an expression in English which is „How long is a piece of string?" if you ask a question about a quantity, but given the information we have, there is no way to give an accurate answer:
How long is it going to take to get there?
How long is a piece of string?
How much do you love me?

26. Thank you. Questions? Q & A Mathematical Formulas

27. Container Mathematical Formulas
beta times higher current – beta-krát větší proud
calculate the current - vypočítat proud
calculate the values – vypočítejte hodnoty
Can you derive the equation? - Umíš odvodit ten vzorec?
derive the equation - odvodit vzorec
explain the equation - vysvětlit vzorec
given the following conditions – jsou-li dány následující podmínky
given the values - s danými hodnotami
it consists of the sum skládá se ze součtu ...
many times - mnohokrát
minus sign - znaménko mínus
plus sign - znaménko plus
resistance is equal to - odpor je roven
resistance is zero – odpor je nulový
simplify the above explanations – zjednodušit výše uvedená vysvětlení
solve the task – řešit úlohu
substitute the known values - dosadit známé hodnoty
the gain is equal to zero – přenos je roven nule
The gain is never lower than 1. - Zesílení není nikdy menší než 1.
the gain is reduced by 3 dB − přenos je nižší o 3 dB
The output polarity is the same. - Výstupní polarita je ta samá.
the output voltage is the same as the input voltage − výstupní napětí je stejné jako vstupní napětí
the resistance is equal to - odpor je roven
the resistance is practically infinite - odpor je prakticky nekonečný
the voltage gain is equal to unity − napěťový přenos je roven jedné
The voltage gain is infinite. - Napěťové zesílení je nekonečné.
the voltages add together - napětí se sčítají
this implies that - z toho vyplývá, že
Children learn multiplication tables by heart.
numbers_cardinal_ordinal.ppt
model_numbers.ppt