Mathematics In The Modern World PDF

 In 18th century mathematics is already a modern science  Mathematics begins to develop very fast because of introducing it to schools  Therefore everyone have a chance to learn the basic learnings of mathematics  Thanks to that, large number of new mathematicians appear on stage ...

 In 18th century mathematics is already a modern science  Mathematics begins to develop very fast because of introducing it to schools  Therefore everyone have a chance to learn the basic learnings of mathematics  Thanks to that, large number of new mathematicians appear on stage  There are many new ideas, solutions to old mathematical problems,researches which lead to creating new fields of mathematics.  Old fields of mathematics are also expanding.  He was a Swiss mathematician.  Johann Bernoulli made the biggest influence on Leonhard.  1727 he went to St Petersburg where he worked in the mathematics department and became in 1731 the head of this department.  1741 went in Berlin and worked in Berlin Academy for 25 years and after that he returned in St Ptersburg where he spent the rest of his life..  Euler worked in almost all areas of mathematics: geometry, calculus, trigonometry, algebra,applied mathematics, graph theory and number theory, as well as , lunar theory, optics and other areas of physics.  Concept of a function as we use today was introduced by him;he was the first mathematician to write f(x) to denote function  He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Euler’s number), the Greek letter Σ for summations and the letter i to denote the imaginary unit  There aren't many subjects that Newton didn't have a huge impact in — he was one of the inventors of calculus, built the first reflecting telescope and helped establish the field of classical mechanics with his seminal work, "Philosophiæ Naturalis Principia Mathematica."  He was the first to decompose white light into its component colors and gave us the three laws of motion, now known as Newton's laws.  We would live in a very different world had Sir Isaac Newton not been born.  Other scientists would probably have worked out most of his ideas eventually, but there is no telling how long it would have taken and how far behind we might have fallen from our current technological trajectory.  Isaac Newton is a hard act to follow, but if anyone can pull it off, it's Carl Gauss.  If Newton is considered the greatest scientist of all time, Gauss could easily be called the greatest mathematician ever.  Carl Friedrich Gauss was born to a poor family in Germany in 1777 and quickly showed himself to be a brilliant mathematician.  You can find his influence throughout algebra, statistics, geometry, optics, astronomy and many other subjects that underlie our modern world.  He published "Arithmetical Investigations," a foundational textbook that laid out the tenets of number theory (the study of whole numbers).  Without number theory, you could kiss computers goodbye.  Computers operate, on a the most basic level, using just two digits — 1 and 0, and many of the advancements that we've made in using computers to solve problems are solved using number theory.  John von Neumann was born in Budapest a few years after the start of the 20th century, a well-timed birth for all of us, for he went on to design the architecture underlying nearly every single computer built on the planet today.  Von Neumann received his Ph.D in mathematics at the age of 22 while also earning a degree in chemical engineering to appease his father, who was keen on his son having a good marketable skill.  In 1930, he went to work at Princeton University with Albert Einstein at the Institute of Advanced Study.  Right now, whatever device or computer that you are reading this on, be it phone or computer, is cycling through a series of basic steps billions of times over each second; steps that allow it to do things like render Internet articles and play videos and music, steps that were first thought up by John von Neumann.  Before his death in 1957, von Neumann made important discoveries in set theory, geometry, quantum mechanics, game theory, statistics, computer science and was a vital member of the Manhattan Project.  Alan Turing a British mathematician who has been call the father of computer science.  During World War II, Turing bent his brain to the problem of breaking Nazi crypto-code and was the one to finally unravel messages protected by the infamous Enigma machine.  Alan Turing's career and life ended tragically when he was arrested and prosecuted for being gay.  He was found guilty and sentenced to undergo hormone treatment to reduce his libido, losing his security clearance as well. On June, 8, 1954, Alan Turing was found dead of apparent suicide by his cleaning lady.   Alan Turing was instrumental in the development of the modern day computer.  His design for a so-called "Turing machine" remains central to how computers operate today.  The "Turing test" is an exercise in artificial intelligence that tests how well an AI program operates; a program passes the  Turing test if it can have a text chat conversation with a human and fool that person into thinking that it too is a person.  Mandelbrot was born in Poland in 1924 and had to flee to France with his family in 1936 to avoid Nazi persecution.  After studying in Paris, he moved to the U.S. where he found a home as an IBM Fellow.  Working at IBM meant that he had access to cutting- edge technology, which allowed him to apply the number-crunching abilities of electrical computer to his projects and problems.  Benoit Mandelbrot died of pancreatic cancer in 2010.  Benoit Mandelbrot landed on this list thanks to his discovery of fractal geometry.  Fractals, often-fantastical and complex shapes built on simple, self-replicable formulas, are fundamental to computer graphics and animation.  Without fractals, it's safe to say that we would be decades behind where we are now in the field of computer-generated images.  Fractal formulas are also used to design cellphone antennas and computer chips, which takes advantage of the fractal's natural ability to minimize wasted space.  The modern world would not exist without maths With maths you can tell the future and save lives Maths lies at the heart of art and music Maths is a subject full of mystery, surprise and magic  Google: Linear algebra, graph theory, SVD Internet: Network theory Security: Fermat, RSA Error correcting codes: Galois theory Medical imaging: Radon Transform Communications: FFT, Shannon Medical Statistics: Nightingale Mathematicians really have made the modern world possible