Advanced Complex Analysis - Part 1:Zeros of Analytic Functions,Analytic continuation, Monodromy, Hyperbolic Geometry and the Reimann Mapping Theorem - IIT Madras Advanced Complex Analysis - Part 2: Compactness of Meromorphic Functions in the Spherical Metric, Spherical Derivative, Normality, Theorems of...
Find the error in the "proof" of the following assertion: Theorem: Any set of n elements has the property that all n elements are identitcal. Proof: By induction on n \in N. Consider the base case o Prove the following using inductive reasoning: ...
Many proofs are geometric andintuitive, if they are given at all, and certainly very little if any progress has been made with respect to abstraction or the separation of laws and objects. In hindsight, then, we could say that in addition to the shift from practical to theoretical, mathemati...
One of my interests is inphysicalproof, or even physicaldemonstration, ofmathematicaltheorems. In many (but not all) cases these proofs can be made rigourous. But even when they cannot, they almost always give an interestingoutlookon the theorem, helping understand its relevance or its veracity...