A01=John Milnor
Affine connection
Author_John Milnor
Banach algebra
Betti number
Bott periodicity theorem
Calculus of variations
Category=PB
Cauchy sequence
Compact space
Conjugate points
Coordinate system
Corollary
Covariant derivative
Critical point (mathematics)
Curvature
Diagram (category theory)
Differentiable function
Differentiable manifold
Differential topology
Dimension (vector space)
Dirichlet problem
Elementary proof
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euclidean space
Euler characteristic
First variation
Fundamental lemma (Langlands program)
General position
Geometry
Hilbert space
Homomorphism
Homotopy
Homotopy group
Inclusion map
Infimum and supremum
Jacobi field
Lie algebra
Lie group
Line segment
Linear map
Loop space
Manifold
Mathematical induction
Metric connection
Metric space
Morse theory
N-sphere
Orthogonal group
Orthogonal transformation
Path space
Ricci curvature
Riemannian geometry
Riemannian manifold
Sard's theorem
Second fundamental form
Sectional curvature
Simply connected space
Skew-Hermitian matrix
Smoothness
Square-integrable function
Subgroup
Submanifold
Subset
Tangent space
Tangent vector
Theorem
Topological space
Topology
Unit sphere
Unit vector
Vector bundle
Vector field
Vector space
Product details
- ISBN 9780691080086
- Weight: 227g
- Dimensions: 152 x 235mm
- Publication Date: 21 May 1963
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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 more than forty years. Morse theory was developed in the 1920s 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 1947.) 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 1962 for his work in differential topology.
He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c 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 re.ection that this ease is the mark of a master." Milnor has published five books with Princeton University Press.
