An American mathematician Harold Calvin Marston Morse, formulated a famous theory which stands as one of the landmarks of 20th century mathematics, and generated tremendous strides in variational analysis and in other related fields (Themistocles. M, 1983, p. 3). He is best known for his work on the calculus of variations where he introduced the technique in the field of global analysis, now known as Morse Theory. His theory concerned with the algebraic topology, the Betti numbers which used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes. Another kind of quantities is the set of critical points of the function, separated into connected sets that are classified analytically and algebraically or by local homological properties (Pitcher, 1994, p. 223). In the most elementary version, these are isolated non-degenerate critical points that are classified by index and are counted (Pitcher, 1994, p. 224). The relation in general is group theoretic but in elementary case, the Morse inequalities relate the Betti numbers and the numbers of critical points of various indices (Pitcher, 1994, p. 224).
The role that Morse theory played in the study of various problems of pure and applied mathematics is well-known (Themistocles. M, 1983, p. 8). Not only he made the single greatest contribution of American mathematics from this theory, he also wrote papers and books on a whole range of topics including on minimal surfaces, theory of functions of a complex variable, papers on differential topology, mathematical physics and on dynamical systems. His theory had a tremendous impact in many areas of Mathematics.
The Morse theory of critical points arose at approximately the beginning of the twentiet...
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...such abrupt changes in a system’s behavior is that we usually observe a dynamical system when it’s at or near its steady-state, or equilibrium, position (Casti, 1996, p. 116). When critical points are non-degenerate, Morse’s Theorem applies (Casti, 1996, p. 108).
There are a number of classical applications of Morse theory, including counting geodesics on a Riemann surface and determination of the topology of a Lie group (Bott 1960, Milnor 1963) (Eric W). Morse theory has received much attention in the last two decades as a result of the paper by Witten (1982) which relates Morse theory to quantum field theory and also directly connects the stationary points of a smooth function to differential forms on the manifold (Eric W). Morse’s achievement in mathematics is singular and monumental, and will remain visible for years to come (Themistocles. M, 1983, p. 3).
As a boy Johannes worked and studied with his father and learnt lessons from books with his mother, with whom he would play ?four-hands? at the piano, ?just for fun.? There were never any doubts as to his becoming a musician. From early childhood he learn everything his father could teach him, read everything he could lay hands on, practiced with undeviating enthusiasm, and filled reams of paper with exercises and variations. The soul of the child went out in music. He played scales long before he knew the notes, and great was his joy when at the age of six he discovered the possibility of making a melody visible by placing black dots on lines at different intervals, inventing a system of notation of his own before he had been made acquainted with the method which the musical world had been using for some centuries.
... relationship in one problem that doesn’t appear in others. Among all of this, there is such vastness in how one person might approach a problem compared to another, and that’s great. The main understanding that seems essential here is how it all relates. Mathematics is all about relationships between number and methods and models and how they all work in different ways to ideally come to the same solution.
Samuel F. B. Morse was one of the greatest inventors of the 19th century; he was the invention of the singled-wire telegraph machine that influenced the Industrial Revolution in America and the Morse code led way to many future innovations. Samuel Morse was not just an inventor; he was also a painter that did works such as The Chapel of the Virgin at Subiaco and The Gallery of the Louvre 1831 – 1833 to portraits of famous politicians such as John Adams.
During the years of 1665 and 1667 he worked out the essentials of calculus, he hit upon the crucially important optical law and most significantly grasped the principle o...
Samuel Finley Breese Morse was born on April 27, 1791 in Charleston, Massachusetts. He was born into a wealthy family with two younger brothers named Sidney and Richard. His father, Jedidiah Morse was a minister, writer, geographer and a congregational clergyman. His mother was Elizabeth Ann Breese. When Samuel got older, he married a woman named Lucrece. Together they had three children, Susan (the oldest), Charles (the middle child), and Finley (the youngest) who was named after Samuel. Soon after having Finley, Lucrece died and Samuel later was remarried to one of his cousins. She was only twenty-six years old but he married her because she was deaf and dumb so he felt she could be dependent on him. Morse's family grew with several more children. When Samuel was eight years old, he attended Phillip's Academy in Andover, Massachusetts where his father was a trustee. Samuel was an unsteady student that was always getting in trouble for drawing and not paying attention. In 1805 he entered Yale College and graduated in 1810. Soon after, he convinced his parents to send him to London to study painting. He lived in England from 1811 to 1815 getting into Royal Academy in 1813. Samuel first began working after he graduated from Yale College as a clerk for Boston book publisher. Another job he had was painting which he studied in the U.S. and in Europe. He opened a studio to paint portraits, but was not very successful. People would go to his studio to look at his artwork but not to buy it. Soon after, he went from house to house asking people if they wanted their portrait painted for $15 but he was not successful in this either. Later in his life, he taught art at the University of the City of New York. He also ran for mayor of New York several times but always lost.
Samuel Finley Breese Morse was born on April 27, 1791, in Charlestown, just outside of Boston, Massachusetts. He was the son of Jedidiah Morse, a pastor who was as well known for his geography as Noah Webster, a friend of the family, was known for his dictionaries.
2. The motion of these quanta are governed by a set of materialistic principles constituting the
16 Pierre-Daniel Templier, Erik Satie (Cambridge & London, MIT Press, 1969, trans. Elena L. French and David S. French), pp. 102
Johnson, J. S., & Newport, E. L. (1991). Critical period effects on universal properties of
Rosenblum, Bruce, and Fred Kuttner. "Chapter 4: Our Newtonian Worldview." Quantum Enigma: Physics Encounters Consciousness. Oxford: Oxford UP, 2008. 23-37. Print.
Newman, James R., The World of Mathematics. Vol. 1, New York: Simon and Schuster, c1956.
Leibniz, Gottfried Wilhelm., and J. M. Child. The Early Mathematical Manuscripts of Leibniz. Mineola, NY: Dover Publ., 2005.
So, in conclusion these are all of the mathematical and scientific discoveries and accomplishments of Sir Isaac Newton. He influenced the world as we know today in so many ways. A great man on so many levels. It is simply unimaginable to me how a single man was able to coo all of this in just eighty four years. But amazingly enough he did. And I believe that the whole should be eternally grateful, because without him, we do not know where we would be or how far we would be behind in this world. So, thank you so much Sir Isaac Newton for opening our eyes about the world around us and letting us know what we are capable of. This is the life and story of Sir Isaac Newton.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
Abstractions from nature are one the important element in mathematics. Mathematics is a universal subject that has connections to many different areas including nature. [IMAGE] [IMAGE] Bibliography: 1. http://users.powernet.co.uk/bearsoft/Maths.html 2. http://weblife.bangor.ac.uk/cyfrif/eng/resources/spirals.htm 3.