A Self-educated Mathematician Established the Boolean Algebra

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George Boole (1815–1864)

The term “Boolean algebra” honors George Boole (1815–1864), a self-educated English mathematician. Boolean algebra captures essential properties of both set operations and logic operations. Boolean logic is credited with laying the foundations for the information age (computers and cell phones).

One of the puzzles on Boolean logic:

There are three balls X, Y and Z. They are colored red, white and blue, but not necessarily in this order. One, but only one, of the following statements is true:

X is red

Y is not red

Z is not blue

3 balls
How many solutions does the puzzle have?

Think yourself before checking the solution.

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Markov Chain in Every Day Life

The picture shows a subway map.  A team of inspectors verifies passengers’ tickets at a station on a line, or all lines through it if there are many lines.  Then they randomly choose the next neighboring station and move there to make their inspection.

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Subway map

How many times higher is the probability of being inspected at station C than at station A?

Are you eager to know the answer? Try yourself before reading how Markov Chain helps to solve the problem. The answer is here.

 

 

The perfect explanation is given in the PBS Infinite Series video:

Is Zero Your Hero?

Everybody has a favorite number.  What number is your hero?

Not Knowing Math Can Cost $15,000

 

A big number of people can lack basic math skills.

Follow Your Passion in Math

Grow your passion by motivating practice like the 11-year-old Math Marvel

“Chess is a mathematical poem” – Aarushi Maheshwari 

Interesting Maths Facts

 

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  • Notches (cuts or indentation) on animal bones prove that humans have been doing mathematics since around 30,000 BC.
  • Ancient Greeks used little rocks to represent numbers. The name of Calculus means pebbles in Greek.
  • The = sign (“equals sign”) was invented by 16th Century Welsh mathematician Robert Recorde, who was fed up with writing “is equal to” in his equations.
  • The word hundred is derived from the word “hundrath”, which actually means 120 and not 100.
  • Zero (0) is the only number which cannot be represented by Roman numerals.
  • Many Chinese hospitals do not have a 4th floor  because the words four in Japanese, Cantonese, Mandarin and Korean (shi, sei, si, sa) sound the same as the words in those languages for death.
  • Forty is the only number with letters in alphabetical order, while one is the only one with letters in reverse order.
  • The number 5 is pronounced as ‘Ha‘ in Thai language. 555 is also used by some as slang for ‘HaHaHa’.
  • Zero is an even number. Mathematicians remember it. Many people take longer to decide whether it is even or odd.

Mathematical Beauty

e + 1 = 0

Euler’s identity is often cited as an example of deep mathematical beauty.

Constance Reid: Euler’s identity is “the most famous formula in all mathematics”.

Euler’s Identity is a special case of his formula from complex analysis suggested by Swiss mathematician Euler in  1748.

The identity links five fundamental mathematical constants:

  • The number 0
  • The number 1
  • The number π (π = 3.141 . . .)
  • The number e (e = 2.718 . . .)
  • The number i, the imaginary unit of the complex numbers.

Euler’s Identity “is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth”. – Benjamin Peirce.

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