# 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