User:Anghel/Projects

Projects

 * do the $R$-module.
 * Elements of Module with Equal Images under Linear Transformations form Submodule - prove without Submodule Test
 * Directed Smooth Curve Relation is Equivalence - Generalizes to $\R$ without problems.
 * Definition:Piecewise Continuously Differentiable Function - add complex definition, add closed interval at Definition:Complex-Differentiable Function
 * Path Homotopy is Equivalence Relation - add proof, special case of relative homotopy
 * Definition:Adjoint (Norm Theory) - add definition from Meise & Vogt
 * Definition:Neighborhood (Complex Analysis) - merge with Definition:Open Complex Disk, and merge the disks with the balls, match definition with Definition:Neighborhood (Topology), cite AMS: Joshua Bowman
 * Derivative of Complex Composite Function - correct proof
 * Triangle Inequality/Vectors in Euclidean Space - proof from Cauchy-Schwarz, and refactor
 * Angle Between Non-Zero Vectors Always Defined - add link to above, correct Definition:Angle Between Vectors
 * Contour Integration by Substitution - add simply connected domain => primitive
 * Integration by Substitution/Definite Integral - add case where integral is negative.
 * Weierstrass M-Test - add complex case
 * Epsilon-Function Differentiability Condition/Complex Case - add claim of continuous differentiability
 * Definition:Path (Topology) - add page Closed Real Intervals are Homeomorphic
 * Norm is Continuous - merge
 * Definition:Unit Ball - merge with Definition:Closed Unit Ball
 * Definition:Compact Space/Real Analysis - add equivalence theorem
 * Three Regular Tessellations/Squares - add proof
 * Heine-Borel Theorem/Real Line - explain example
 * Charles Babbage's Conjecture - counterexample ^2
 * Absolutely Convergent Generalized Sum Converges - simple clarification
 * Inverse of Matrix is Scalar Product of Adjugate by Reciprocal of Determinant - add proof based on Matrix Product with Adjugate Matrix
 * Definition:Contour/Simple - add example link to parameterization of $\map {N_1} 0$, to show simple and closed contour.
 * Definition:Measure (Measure Theory)
 * Inverse Function Theorem - proof from Wikipedia
 * Separated Sets are Clopen in Union
 * Uniform Convergence is Hereditary - add proof?
 * Equivalence of Definitions of Boundary - create proof
 * All Normal Vectors of Simple Closed Contour Cannot Point into Interior/Lemma 1 - Borsuk Lemma, combined with line between vectors, Also, Corner Smoothening Lemma.
 * Arzelà-Ascoli Theorem
 * Definition:Pi - check up on various theorems about the periodicity of pi
 * Note on Definition:Quotient Mapping
 * Definition:Rotation (Geometry) - correct definition, add matrices proof