Jacob Bronowski The Ascent Of Man Pdf' title='Jacob Bronowski The Ascent Of Man Pdf' />Great Thinkers, Great Theorems The Great Courses. Mathematics is filled with beautiful theorems that are as breathtaking as the most celebrated works of art, literature, or music. They are the Mona Lisas, Hamlets, and Fifth Symphonys of the fieldlandmark achievements that repay endless study and that are the work of geniuses as fascinating as Leonardo, Shakespeare, and Beethoven. Here is a sample Pythagorean theorem Although he didnt discover the Pythagorean theorem about a remarkable property of right triangles, the Greek mathematician Euclid devised an ingenious proof that is a mathematical masterpiece. Plus, its beautiful to look at Area of a circle The formula for the area of a circle, A r. Greek thinker Archimedes. His argument relied on the clever tactic of proof by contradiction not once, but twice. Basel problem The Swiss mathematician Leonhard Euler won his reputation in the early 1. The solution was delightfully simple the path to it, bewilderingly complex. Larger infinities In the late 1. The relationship between the Roman Catholic Church and science is a widely debated subject. Historically, the Church has often been a patron of sciences. German mathematician Georg Cantor blazed the trail into the transfinite by proving that some infinite sets are bigger than others, thereby opening a strange new realm of mathematics. You can savor these results and many more in Great Thinkers, Great Theorems, 2. Approaching great theorems the way an art course approaches great works of art, the course opens your mind to new levels of math appreciation. And it requires no more than a grasp of high school mathematics, although it will delight mathematicians of all abilities. Your guide on this lavishly illustrated tour, which features detailed graphics walking you through every step of every proof, is Professor William Dunham of Muhlenberg College, an award winning teacher who has developed an artists eye for conveying the essence of a mathematical idea. Through his enthusiasm for brilliant strategies, novel tactics, and other hallmarks of great theorems, you learn how mathematicians think and what they mean by beauty in their work. As added enrichment, the course guidebook has supplementary questions and problems that allow you to go deeper into the ideas behind the theorems. An Innovative Approach to Mathematics. Professor Dunham has been taking this innovative approach to mathematics for over a quarter centuryin the classroom and in his popular books. With Great Thinkers, Great Theorems you get to watch him bring this subject to life in stimulating lectures that combine history, biography, and, above all, theorems, presented as a series of intellectual adventures that have built mathematics into the powerful tool of analysis and understanding that it is today. In the arts, a great masterpiece can transform a genre think of Claude Monets 1. Impression, Sunrise, which gave the name to the Impressionist movement and revolutionized painting. The same is true in mathematics, with the difference that the revolution is permanent. Once a theorem has been established, it is true forever it never goes out of style. Therefore the great theorems of the past are as fresh and impressive today as on the day they were first proved. What Makes a Theorem Great A theorem is a mathematical proposition backed by a rigorous chain of reasoning, called a proof, that shows it is indisputably true. F-r8s.jpg' alt='Jacob Bronowski The Ascent Of Man Pdf' title='Jacob Bronowski The Ascent Of Man Pdf' />Explore the most aweinspiring theorems in the 3,000year history of mathematics. This course reveals how great minds like Pythagoras, Newton, and Euler crafted. As for greatness, Professor Dunham believes the defining qualities of a great theorem are elegance and surprise, exemplified by these cases Elegance Euclid has a beautifully simple way of showing that any finite collection of prime numbers cant be completethat there is always at least one prime number left out, proving that the prime numbers are infinite. Dr. Dunham calls this one of the greatest proofs in all of mathematics. Surprise Another Greek, Heron, devised a formula for triangular area that is so odd that it looks like it must be wrong. Its my favorite result from geometry just because its so implausible, says Dr. Dunham, who shows how, 1. Isaac Newton used algebra in an equally surprising route to the same result. Great Thinkers, Great Theorems includes many lectures that are devoted to a single theorem. In these, Professor Dunham breaks the proof into manageable pieces so that you can follow it in detail. When you get to the Q. E. D. the initials traditionally ending a proof, signaling quod erat demonstrandum Latin for that which was to be demonstratedyou can step back and take in the masterpiece as a whole, just as you would with a painting in a museum. In other lectures, you focus on the biographies of the mathematicians behind these masterpiecesgeniuses who led eventful, eccentric, and sometimes tragic lives. For example Cardano Perhaps the most bizarre mathematician who ever lived, the 1. Italian Gerolamo Cardano was a gambler, astrologer, papal physician, convicted heretic, and the first to publish the solution of cubic and quartic algebraic equations, which he did after a no holds barred competition with rival mathematicians. Newton and Leibniz The battle over who invented calculus, the most important mathematical discovery since ancient times, pitted Isaac Newtonmathematician, astronomer, alchemistagainst Gottfried Wilhelm Leibniz mathematician, philosopher, diplomat. Each believed the other was trying to steal the credit. Euler The most inspirational story in the history of mathematics belongs to Leonhard Euler, whose astonishing output barely slowed down after he went blind in 1. Like Beethoven, who composed some of his greatest music after going deaf, Euler was able to practice his art entirely in his head. Cantor While Vincent van Gogh was painting pioneering works of modern art in France in the late 1. Georg Cantor was laying the foundations for modern mathematics next door in Germany. Unappreciated at first, the two rebels even looked alike, and both suffered debilitating bouts of depression. Describing a common reaction to the theorems produced by these great thinkers, Professor Dunham says his students often want to know where the breakthrough ideas came from How did the mathematicians do it The question defies analysis, he says. Its like asking Why did Shakespeare put the balcony scene in Romeo and Juliet What made him think of it Well, he was Shakespeare. This is what genius looks like And by watching the lectures in Great Thinkers, Great Theorems, you will see what equivalent genius looks like in mathematics. Tvgenial 4.10 Serial. Hide Full Description.