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Call Number: 41 Mu
This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures.
Algebraic Topology by
Call Number: ONLINE and 43 Ha
This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition.
Foundations of Differentiable Manifolds and Lie Groups by
Call Number: 45 Wa
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds.
The Knot Book by
Call Number: 48 Ad
"What are the different properties and classifications of knots? How do you determine whether a knot is actually knotted or can be untangled? What is the appropriate measure of the complexity of a knot? What does knot theory research offer to other sciences? In The Knot Book Colin Adams describes and illustrates the work being done to answer these questions. Starting with the simplest knot (the trivial knot or unknot), Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians now can solve, as well as those that remain open. He also looks at how knot theory is providing important insights in biology, chemistry, physics, and other fields."
Ergodic Theory by
Call Number: 49 Ei
This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic.
Recurrence in Ergodic Theory and Combinatorial Number Theory by
Call Number: ONLINE and 49 Fu
Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory.
מיון הנושאים 40-49
41 Point set topology. General topological spaces
42 Topological analysis. Theory of functions on a topological space
43 Algebraic and combinatorial topology. Homology. Co-Homology. Homotopy. Co-Homotopy. Fibre spaces. Differential topology
44 Topological groups. Continuous groups. Lie groups. Compact groups. Continuous transformations groups. Automorphic representations
45 Manifolds. Bundles. Differential topology. Differential manifolds. Catastrophe. Low dimensional topology. Global analysis
46 Graph theory. Weaves. Design theory
See also: 81.2 Combinatorics
47 Dimension theory
49 Dynamical systems. Topological dynamics. Ergodic theory. Chaos. Complex systems