# Download ➹ Morse Theory (Annals of Mathematic Studies AM-51): Morse Theory: Based On Lecture Notes By M. Spivak And R. Wells (Annals of Mathematics Studies) Author John Milnor – Tactical-player.co.uk

The classic work on the subject, written in the incomparable style of John Milnor The difficult subject is explained with a simplicity and clarity which rivals how Richard Feynman was able to write about Physics. This is a good supplement for information on Morse Theory but be warned that it is a set of lecture notes. I gave this book a 5star because it does succeed in presenting the main ideas,theorems,and proofs in Morse theory This book was given as a reference in V.I.Arnold s Mathematical Methods Of Classical Mechanics for further information on Riemannian curvature AppendixI It turns out that Arnold s book contains much material which is prerequisite to Milnor Euler Lagrange equations,vector fields on manifolds,Poisson Brackets,and which you will encounter in Milnor are explained in Arnold Another book which helps is Bishop and Crittendon s Geometry Of Manifolds The configuration space of a mechanical system can and does in many cases translate to a Riemannian manifold with a motion of the system necessarily translating to a geodesic of the manifold An example is a double planar pendulum Since each pendulum is free to rotate 360 degrees,its configuration space is a torus or donut Geodesics are extremal paths,hopefully minimal One possible path is a closed spiral on the donut Is it a geodesic What s the motion This book answers a great many questions as to how the shape or curvature and topology of the manifold influences and determines its geodesics A knowledge of homotopy theory,deformation retracts,cw complexes,etc is needed Not easy going but rewarding I m still working on it. This is a great book, a classic Sure, the fonts and diagrams could use some modernization But if you really want to learn a subject in Math, learn from the giants.This is very easy to read assuming you are a first year in grad school in Math, or an advanced undergrad. Great quality, book came with handwritten note One Of The Most Cited Books In Mathematics, John Milnor S Exposition Of Morse Theory Has Been The Most Important Book On The Subject For Than Forty Years Morse Theory Was Developed In The S By Mathematician Marston Morse Morse Was On The Faculty Of The Institute For Advanced Study, And Princeton Published His Topological Methods In The Theory Of Functions Of A Complex Variable In The Annals Of Mathematics Studies Series In One Classical Application Of Morse Theory Includes The Attempt To Understand, With Only Limited Information, The Large Scale Structure Of An Object This Kind Of Problem Occurs In Mathematical Physics, Dynamic Systems, And Mechanical Engineering 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 Milnor Was Awarded The Fields Medal The Mathematical Equivalent Of A Nobel Prize In For His Work In Differential Topology He Has Since Received The National Medal Of Science And The Steele Prize From The American Mathematical Society Twice And In Recognition Of His Explanations Of Mathematical Concepts Across A Wide Range Of Scientic Disciplines The Citation Reads, The Phrase Sublime Elegance Is Rarely Associated With Mathematical Exposition, But It Applies To All Of Milnor S Writings Reading His Books, One Is Struck With The Ease With Which The Subject Is Unfolding And It Only Becomes Apparent After Retion That This Ease Is The Mark Of A Master Milnor Has Published Five Books With Princeton University Press