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Topic: Marston Morse

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	Morse
		Morse taught briefly at Harvard before entering military service for the period of World War I. For the duration of the war he served as a private in the U.S. Army in France and for his outstanding work in the Ambulance Corps he was awarded the Croix de Guerre with Silver Star.
		This is now called Morse theory and it grew out of a major discovery which Morse made not long after returning to mathematics after the war and published in his important paper Relations between the critical points of a real function of n independent variables in 1925.
		Morse theory is important in the field of global analysis which is the study of ordinary and
	www.educ.fc.ul.pt /icm/icm2003/icm14/Morse.htm (967 words)

	Amazon.ca: Morse Theory. (AM-51): Books: John Milnor (Site not responding. Last check: 2007-10-10)
		Morse theory was developed in the 1920s by mathematician Marston Morse.
		Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory.
		Morse theory is about finding geometric information about manifolds using analysis of functions(smooth functions) having these manifolds as their domain.
	www.amazon.ca /Morse-Theory-Am-51-Willard-Milnor/dp/0691080089 (933 words)

	Schlumberger Fellowship Awarded to Student Studying Morse Theory
		Original Morse theory, which applied to a class of mathematical objects called smooth manifolds-such as a plane, a circle and the surface of a sphere-provides a general tools of attacking this problem.
		In the 1930s, Marston Morse proved a major result that generalize the straightforward result that the lowest-order nonvanishing term in the Taylor series describes the local behavior of a smooth function of single variable (function with derivatives of up to order n) to functions of many variables.
		And when it does, it means that strange things are going on with the physical or biological or sociological phenomenon that the function represents, such as the buckling of a beam or the outbreak of ecological catastrophe or the outbreak of a political revolution.
	hypatia.math.uri.edu /~kulenm/mth381pr/morseth/morseth.html (656 words)

	Thue-Morse L-system
		Marston Morse rediscovered the same sequence in 1917 [Mor21] in studying the dynamics of ``geodesics'' on surfaces.
		In fact, Morse proved a slightly stronger theorem stating that there is no string of the form EEe where E is a given string and e is the first symbol in E.
		On the other hand, the original reason (see [Mor21] that Morse introduced this sequence is that, without being periodic, it still has a large degree of redundancy.
	www.math.okstate.edu /mathdept/dynamics/lecnotes/node16.html (569 words)

	Crystallographic Topology - Critical Nets 1
		The first application of Morse theory to crystal physics was by van Hove (1953), who showed that certain singularities in lattice dynamics originate from crystallographic symmetry.
		Some formal results concerning Morse functions on orbifolds are also starting to appear in the mathematical preprint literature (e.g., Lerman and Tolman, 1995), but these are primarily based on symplectic rather than Euclidean geometry (cf., Kirwan, 1984), which is beyond our mathematical capabilities to extend into algebraic geometry.
		The crystallographic case closest to the general Morse inequality limits is the diamond structure in space group #227 with basic unit critical point counts of (1,2,2,1) and unit cell counts (8,16,16,8).
	www.ornl.gov /sci/ortep/topology/critnet.html (2573 words)

	Morse
		Samuel Morse, the supervisor of Alfred Vail and the developer of Morse code.
		Morse code or continuous wave is a method of coding messages into long and short beeps.
		Morse, the name for the large buckle on the Cope one of the vestments of the Roman Catholic church.
	www.knowledgefun.com /book/m/mo/morse.html (122 words)

	Morse theory
		Morse's theory of critical points would play a decisive role throughout Bott's career, notably in his work on homogeneous spaces, the Lefschetz hyperplane theorem, the periodicity theorem, and the Yang-Mills functional on a moduli space.
		In the Twenties Morse had initiated the study of the critical points of a function on a space and its relation to the topology of the space.
		Classical Morse theory deals only with functions all of whose critical points are nondegenerate; in particular, the critical points must all be isolated points.
	www.math.harvard.edu /history/bott/bottbio/node9.html (526 words)

	Crystallographic Topology 101 - Overview
		The geometric topology of interest is the topological properties of crystallographic groups, represented as orbifolds, and the Morse theory global analysis of critical points in symmetric functions.
		Critical nets are based on the concepts of Morse functions, Morse theory (i.e., critical point analysis), and hyperplane arrangements in topological complexes, which are classic topics in the mathematical topology and global analysis literature.
		Morse functions on orbifolds constitute a relatively new aspect of equivariant (i.e., group orbit compatible) topology.
	www.ornl.gov /ortep/topology/overview.html (2580 words)

	Morse Theory Online Text - Physics Forums Library
		morse theiry give you a forlmula for how it chnages in terms of the index of the second order term of the taylor series, thought of as a quadratic form.
		morse's theory has many more applications than just to proving lefschetzs results but perhaps we owe to morse the clarification and substantiation of lefschetz's theory of pencils on an algebraic variety.
		According to my father and grandmother (Marston Morse's wife), there was tension between professors at Princeton and those involved with the Institute.
	www.physicsforums.com /archive/index.php/t-128460.html (1407 words)

	Orometry: Theory of Surface Networks
		Two important early papers on the subject were written by Arthur Cayley (1859), one of the founders of topology, and by James Clerk Maxwell (1870) the eminent Scottish physicist who also developed famous theories of electromagnetic fields and light.
		Maxwell's observations on terrain were further developed mathematically by Marston Morse (1925, 1968).
		What Maxwell and Morse developed mathematically, we may derive independently as a function of mountain prominence: That every summit (except the highest one) corresponds to a saddle.
	www.peaklist.org /theory/orometry/article/Orometry_3.html (1927 words)

	AMS Presidents: A Timeline
		After serving in the military during World War I, Morse taught at Harvard University, Cornell College, and Brown University, then spent the rest of his academic career at Harvard University (1926-1935) and at the Institute for Advanced Study (1935 until his retirement in 1975).
		He developed what became known as Morse theory, a powerful tool in the field of global analysis, and an important contribution of American mathematics.
		Morse won the National Medal of Science in 1965, and was a member of the American Academy of Arts and Sciences, the U.S. National Academy of Sciences, and of academies in Italy and France.
	www.ams.org /ams/26-morse.html (134 words)

	The Newton History Museum: Rediscovering Newton Artists 1850-1950 (Site not responding. Last check: 2007-10-10)
		Mary Morse, the subject of Giovanni Troccoli's painting, never married and supported herself as a teacher.
		She and her sister Carrie also did wood carving to supplement their income and showed their work at the Arts and Crafts Society in Boston, where they studied with Troccoli.
		This photograph of Mary Morse was taken inside the Morseland Avenue studio used by Troccoli.
	www.ci.newton.ma.us /Jackson/newton-artists/intro/mary-morse.html (77 words)

	Park City Mathematics Institute (Site not responding. Last check: 2007-10-10)
		In 1925, Marston Morse introduced a powerful tool, now known as Morse theory, for studying the topology of smooth manifolds using gradient flows.
		The first half of this course will be an introduction to a discrete analogue of Morse theory that has proved useful for the study of spaces.
		We will see how this theory can be applied to some combinatorial problems arising in graph theory, complexity theory, and algebraic combinatorics.
	www.admin.ias.edu /ma/2004/gss2004.htm (1651 words)

	Math Forum (Site not responding. Last check: 2007-10-10)
		I doubt my one brief meeting with Morse would be of any interest,
		Marston Morse was the first research mathematician whom I ever met.
		I am looking for stories about and/or reminiscences of Marston Morse.
	mathforum.org /kb/rss/rssmessages.jsp?threadID=383370 (105 words)

	Colby College Mathematics: Senior Prizes (Site not responding. Last check: 2007-10-10)
		The Marston Morse Prize in Mathematics goes to an outstanding senior Mathematics major, and the Senior Prize in Mathematical Sciences goes to an outstanding Mathematical Sciences major.
		The senior prize in Mathematics is named for Marston Morse, a Waterville native and Colby graduate from the class of 1914 who went on to get a PhD at Harvard and became one of the leading lights in American mathematics.
		He taught at Harvard, Cornell, and Brown before becoming (in 1935) a member of the Institute for Advanced Study in Princeton, where he studied mathematics until his death in 1977 at age 85.
	www.colby.edu /math/program/prizes.html (234 words)

	AMCA: Hilbert Space and Variational Methods for Singular Quadratic Functionals Applied to Singular Second Order Linear ... (Site not responding. Last check: 2007-10-10)
		The purpose of this paper is to develop a unified theory for the study of singular second order linear differential equations.
		Other studies of singular quadratic functionals include those of John Chellevold in 1951 (Ph.D. thesis) and 1952, Edmond C. Tomastik in 1965 (Ph.D. thesis) and 1966, Junior Stein in 1971 (Ph.D. thesis) and 1973, Marston Morse in 1973, and Zuzana Doslá and Ondrej Doslý in 1995.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/q/o/66.htm (269 words)

	DMT-Overview01
		Digital Morse Theory (DMT) explains the properties and behavior of families of contour lines in n-dimensions.
		Digital Morse Theory enables many properties that traditional continuous Morse theory predicts (Reeb graphs).
		DMT insight is that by finding all of the Criticalities, we can understand (graph) all of the regions we wish to understand.
	www.casi.net /D.DMT/D.Overview/DMT-Overview01.html (473 words)

	Norbert Wiener article by Leon Tabak (Site not responding. Last check: 2007-10-10)
		These names may not yet be familiar to you, but you will surely encounter them as you continue your studies in mathematics, physics, philosophy, anthropology, electrical engineering, et cetera.
		The war ended in November of 1918; in 1919, Wiener joined the faculty of mathematics at M.I.T. The Massachusetts Institute of Technology had just moved from the Boston side of the Charles River into newly constructed buildings on the Cambridge side.
		As it happened, he shared the prize that year with Colby College alumnus Marston Morse.
	people.cornellcollege.edu /ltabak/publications/articles/wiener.html (4960 words)

	Environmental Math - Annotated Bibliography
		The author poses a startling question: "Why should those mathematicians who reason and discover in private using visual representations always have to try to describe their work using solely linguistic representations, only to have the reader decode the result to rediscover the visual representations that led to the discovery in the first place?"
		Raoul Bott, Marston Morse and his mathematical works, Amer.
		Davis, Visual geometry, computer graphics, & theorems of perceived type, Missoula Conference on the Influence of Computing on Mathematical Research & Education, Aug. 1973, 27 pp.
	home.comcast.net /~benfusaro/Book/bibliography.html (977 words)

	RJFcrit (Site not responding. Last check: 2007-10-10)
		The Drama of John Marston : Critical Re-visions, edited by T.F. Wharton: Cambridge University Press, 2000.
		John Marston of the Middle Temple: An Elizabethan Dramatist in His Social Setting, Philip J. Finkelpearl: Harvard University Press, 1969.
		The Satire of John Marston, Morse S. Allen: Haskell House, 1965.
	home.earthlink.net /~sa.pe/AN2.html (101 words)

	Presidential Inauguration
		Marston Morse: The Man, the Mathematician, the Humanist
		Marston Morse, one of the great mathematicians of the 20th century, was one of the first members of the Institute for Advanced Study at Princeton.
		Initial research on Morse's life and work took the professors to the archives at Harvard, the Institute for Advanced Study, and to the home of his widow, Louise Morse.
	www.saintmarys.edu /Inauguration/SISTARCOSTAR.html (539 words)

	NDSU Club Math Page (Site not responding. Last check: 2007-10-10)
		Abstract: In this talk we will prove the famous result of Axel Thue that there is an infinite cube-free word on a two letter alphabet.
		This result was independently discovered by Marston Morse and Gustav Hetlund 38 years later in there fundamental paper on symbolic dynamics.
		Application of Thue's results lead to a negative resolution of the Burnside Conjecture in 1964 by Golod.
	www.ndsu.nodak.edu /ndsu/coykenda/math/mathclub/juras.html (116 words)

	University of Louisville Math Club
		Marston Morse Quoted in S Gudder A Mathematical Journey.
		Morse Theory: Basic concepts, Formal development, The Morse inequalities, Further reading
		Morse Theory: Introduction, Discussion of Morse Function and Theorem, brief mention of
	www.louisville.edu /~swwhit01/math_club/Morse_Theory.html (652 words)

	DMT Research Update
		Others who have done or are doing Morse Theory Research:
		The Calculus of Variations in the Large, by H. Marston Morse
		Morse Theory for Implicit Surface Modeling, by J. Hart
	www.casi.net /D.DMT/D.ProgressReport2/recentdmt.html (30 words)

	IAS School of Math: Marston Morse Conference
		Marston Morse Conference on Gauge Theory and Symplectic Theory
		Princeton University and the School of Mathematics, Institute for Advanced Study will be holding a mini-conference on Gauge Theory and Symplectic Geometry in conjunction with the Marston Morse Memorial Lectures on Monday, Tuesday and Thursday, March 29, 30 and April 1, 1999.
		Marston Morse Lecture - Tomasz Mrowka, Massachusetts Institute of Technology
	www.math.ias.edu /~warfield/Marston.html (323 words)

	The Calculus of Variations in the Large (American Mathematical Society Colloquium Publications Volume XVIII) - Marston ... (Site not responding. Last check: 2007-10-10)
		The Calculus of Variations in the Large (American Mathematical Society Colloquium Publications Volume XVIII) - Marston Morse
		The Calculus of Variations in the Large (American Mathematical Society Colloquium Publications Volume XVIII) by Morse, Marston
		Book condition: Large 8vo in blue cloth titled in gilt at the spine and front panel, 368 pp.
	www.biblio.com /books/60050987.html (167 words)

	The Mathematics Genealogy Project - H. C. Marston Morse
		The Mathematics Genealogy Project - H. Marston Morse
		According to our current on-line database, H. Marston Morse has 5 students and 455 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	www.genealogy.math.ndsu.nodak.edu /html/id.phtml?id=4926 (98 words)

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