Books : Science & Nature : Mathematics : Geometry & Topology : Algebraic Topology

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Books : Science & Nature : Mathematics : Geometry & Topology : Algebraic Topology

• The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots

  Colin Adams

  
  In February 2001, scientists at the Los Alamos National Laboratory announced that they had recorded a simple knot untying itself. Crafted from a chain of nickel-plated steel balls connected by thin metal rods, the three-crossing knot stretched, wiggled, and bent its way out of its predicament--a neat trick worthy of an inorganic Houdini, but more, a critical discovery in how granular and filamentary materials such as strands of DNA and polymers entangle and enfold themselves.

  A knot seems a simple, everyday thing, at least to anyone who wears laced shoes or uses a corded telephone. In the mathematical discipline known as topology, knots are anything but simple: at 16 crossings of a "closed curve in space that does not intersect itself anywhere", a knot can take one of 1,388,705 permutations, and more are possible. All this thrills mathematics professor Colin Adams, whose primer The Knot Book offers an engaging if often challenging introduction to the mysterious, often unproven, but, he suggests, ultimately knowable nature of knots of all kinds--whether nontrivial, satellite, torus, cable or hyperbolic. As perhaps befits its subject, Adams's prose is sometimes... well, tangled ("A knot is amphicheiral if it can be deformed through space to the knot obtained by changing every crossing in the projection of the knot to the opposite crossing.") but his book is great fun for puzzle and magic buffs, and a useful reference for students of knot theory and other aspects of higher mathematics. --Gregory McNamee

  
   

• Introduction to Operator Space Theory (London Mathematical Society Lecture Note) (London Mathematical Society Lecture Note Series)

  Gilles Pisier

  
  
   

• Matrix Groups for Undergraduates (Student Mathematical Library) (Student Mathematical Library)

  Kristopher Tapp

  
  
   

• Algebra: Finite Groups of Lie Type. Finite-dimensional Fivision Algebras: v. 9 (Encyclopaedia of Mathematical Sciences): Finite Groups of Lie Type. Finite-dimensional ... 9 (Encyclopaedia of Mathematical Sciences)

  
  
   

• Introduction to Topology and Modern Analysis

  George F. Simmons

  
  
   

• Combinatorial Topology (Dover books on mathematics)

  A.S. Alexandrov

  
  
   

• K-Theory for Operator Algebras (Mathematical Sciences Research Institute Publications) (Mathematical Sciences Research Institute Publications)

  Bruce Blackadar

  
  
   

• Homotopy Theoretic Methods in Group Cohomology (Advanced Courses in Mathematics CRM Barcelona) (Advanced Courses in Mathematics CRM Barcelona)

  William G. Dwyer, Hans-Werner Henn

  
  
   

• Representations of Algebraic Groups (Mathematical Surveys & Monographs) (Mathematical Surveys and Monographs)

  
  
   

• Geometry of Differential Forms (Translations of Mathematical Monographs (Iwanami Series in Modern Mathematics)) (Translations of Mathematical Monographs (Iwanami Series in Modern Mathematics))

  Shigeyuki Mortia

  
  
   

• Global Theory of Minimal Surfaces (Clay Mathematics Proceedings) (Clay Mathematics Proceedings)

  
  
   

• A Course in Homological Algebra (Graduate Texts in Mathematics)

  Peter J. Hilton, Urs Stammbach

  
  
   

• Foundations of Topology: An Approach to Convenient Topology

  G. Preuss

  
  
   

• Classification and Orbit Equivalence Relations (Mathematical Surveys and Monographs)

  Greg Hjorth

  
  
   

• Representations and Cohomology: Basic Representation Theory of Finite Groups and Associative Algebras v. 1 (Cambridge Studies in Advanced Mathematics): ... (Cambridge Studies in Advanced Mathematics)

  D. J. Benson

  
  
   

• The Geometry of Four-manifolds (Oxford Mathematical Monographs)

  S. K. Donaldson, P. B. Kronheimer

  
  
   

• Introduction to Topology (Student Mathematical Library) (Student Mathematical Library)

  Vassiliev

  
  
   

• Lectures on the Orbit Method (Graduate Studies in Mathematics) (Graduate Studies in Mathematics)

  Kirillov

  
  
   

• Supersymmetry for Mathematicians: An Introduction (Courant Lecture Notes): An Introduction (Courant Lecture Notes)

  V. S. Varadarajan

  
  
   

• Fourier-Mukai Transforms in Algebraic Geometry (Oxford Mathematical Monographs)

  Daniel Huybrechts