User:J D Bowen
Hi there! I'm a graduate of the University of San Francisco, BS Mathematics, and a graduate student and TA at San Francisco State.
I'm particuarly interested in topology, and it is in this area I intend to contribute to Proofwiki.
Pages and Such
I've done a lot of topology, some number theory, differential geometry... just a bunch of stuff.
Projects
I'm working on putting all of my lecture notes in topology up here, drawing heavily on 3 reference texts: Guillemin and Pollacks Differential Topology, Bredon's Topology and Geometry, and Hocking and Youngs Topology.
I hope to get cracking on knot theory soon-ish.
Pages I've Written
I keep this for my own reference, so I can keep track of what I should finish and what I've abandoned and what I would like to still do.
Complex Functions
Analytic Continuation of Riemann Zeta Function
Trivial Zeroes of Riemann Zeta Function are Even Negative Integers
Equivalence of Definitions of Riemann Zeta Function
Derivative of Riemann Zeta Function
Reciprocal of Riemann Zeta Function
Square of Riemann Zeta Function
Equivalence of Definitions of Gamma Function
Analytic Function Theory
Zeroes of Analytic Function are Isolated
Uniqueness of Analytic Continuation
Equivalence of Definitions of Analytic Function
Fundamental Theorem of Algebra
Multivariate Calculus
Differential Geometry
Implications of Stokes' Theorem
Existence of Local Coordinates
Manipulation of Exterior Derivative
Series
Manipulation of Absolutely Convergent Series
Product Form of Sum on Completely Multiplicative Function
Ingham's Theorem on Convergent Dirichlet Series
Number Theory
Euler Phi Function in terms of Möbius Function
Order of Divisor Count Function
Knot Theory
Alexander Polynomial is a Knot Invariant
Measure Theory
Equidecomposability is an Equivalence Relation
Existence of Non-Measurable Subset of Real Numbers
Equidecomposability Unaffected by Union
Countable Set has Measure Zero
Measurable Sets form Algebra of Sets
Combinatorics
Topology
Weak Whitney Immersion Theorem
Classification of Compact One-Manifolds
Classification of Compact Two-Manifolds
Classification of Compact Three-Manifolds Supporting Zero-Curvature Geometry
Rokhlin's Theorem on Bounded Manifolds and Induced Spin Structures
List of Fundamental Groups for 2-Manifolds
Fundamental Group is Independent of Base Point for Path-Connected Space
Homotopy Group is Homeomorphism Invariant
Extendability Theorem for Intersection Numbers
Relative Homotopy is Equivalence Relation
Algebra
Classification of Groups of Order up to 15
Dicyclic Group is Non-Abelian Group
Fundamental Theorem of Finite Abelian Groups
Integration Theory
Lebesgue Integral is Extension of Darboux Integral
Assorted and Uncategorized
Properties of Algebras of Sets