Correction to notes on abstract distance geometry II

Distance Geometry Notes

Introduction. This paper is concerned with several disconnected developments in distance geometry. §1 deals with the congruent imbedding of metric spaces in euclidean or Hubert spaces. By showing that the validity of the Pythagorean theorem insures the essentially euclidean character of the metric, the basic role this theorem plays in euclidean geometry is seen to be fully justified. In §2 the ...

Notes on Abstract Algebra

1 Functions Definition 1.1. Given sets S and T , suppose there is a subset G ⊆ S × T with the following properties: • If (s1, t1) ∈ G and (s2, t2) ∈ G and s1 = s2 then t1 = t2; • For each s ∈ S, there is an element (s, t) ∈ G. Then for each s ∈ S, there is exactly one element α(s) ∈ T so that (s, α(s)) ∈ G. This defines a function α, with domain S and target T , which can be denoted α : S → T ....

Notes on Symplectic Geometry

1. Week 1 1 1.1. The cotangent bundle 1 1.2. Geodesic flow as Hamiltonian flow 4 2. Week 2 7 2.1. Darboux’s theorem 7 3. Week 3 10 3.1. Submanifolds of symplectic manifolds 10 3.2. Contact manifolds 12 4. Week 4 15 4.1. Symplectic linear group and linear complex structures 15 4.2. Symplectic vector bundles 18 5. Week 5 21 5.1. Almost complex manifolds 21 5.2. Kähler manifolds 24 6. Week 6 26 6....

Notes on Abstract Interpretation ∗

Notes on Noncommutative Geometry

Foreword This book is not just a survey of noncommutative geometry — later NCG; rather, it strives to answer some naive but vital questions: What is the purpose of NCG? What is it good for? Can NCG solve open problems of classical geometry inaccessible otherwise? In other words, why does NCG matter? What is it anyway? Good answer means good examples. A sweetheart of NCG called non-commutative t...