Math Articles

Introduction: "Convenient Notation"In Dirac's Principles of Quantum Mechanics published in 1930 he introduced a "convenient notation" he referred …

The Concept A vector space is an additively written abelian group together with a field that operates on it. Vector spaces are often described as a set…

Abstract Why do we need yet another article about complex numbers? This is a valid question and I have asked it myself. I could mention that I wanted…

Introduction Series play a decisive role in many branches of mathematics. They accompanied mathematical developments from Zeno of Elea (##5##-th century…

Introduction When doing mathematics,  we usually take for granted what natural numbers, integers, and rationals are. They are pretty intuitive.   Going…

Abstract I want to shed some light on complex analysis without getting all the technical details in the way which are necessary for the precise treatments…

An entire book could easily be written about the history of numbers from ancient Babylon and India, over Abu Dscha'far Muhammad ibn Musa al-Chwarizmi (##\sim…

P or NP This article deals with the complexity of calculations and in particular the meaning of ##P\stackrel{?}{\neq}NP## Before we explain what P and…

Introduction This Insight looks at the various probabilistic factors and related terminology involved in disease and virus testing.As we all know,…

Confessions of a moderate Bayesian, part 2 Read Part 1: Confessions of a moderate Bayesian, part 1Bayesian statistics by and for non-statisticianshttps://www.cafepress.com/physicsforums.13280237 Background One…

Proofs in mathematics are what mathematics is all about. They are subject to entire books, created entire theories like Fermat's last theorem, are hard…

  Part III: Representations  Sums and Products. Frobenius began in ##1896## to generalize Weber's group characters and soon investigated…

Introduction Financial options — the right to purchase (call) or sell (put) stock or other assets at a fixed price on a future date — have been around…

Intransitive dice are sets of dice that don't follow the usual rules for "is better/larger than". If A<B and B<C, then A<C. If Bob runs faster…

Introduction It is a remarkable fact that consideration of very elementary concepts in geometry often leads quickly into deep and unexpected mathematical…

Klein's Erlangen program: groups and geometry There is a very deep link between group theory and geometry. Sadly, this link is not emphasized in most…

Is it possible to design an unbreakable cipher? Do methods of encryption exist that guarantee privacy from even the most capable and highly-resourced…

At the first sight, there are many paradoxes in complex number theory. Here are some nice examples of things that don't seem to work:Example A [itex]-1=i^2=\sqrt{-1}\cdot\sqrt{-1}=\sqrt{(-1)(-1)}=\sqrt{1}=1[/itex]Example…

Set-Theoretic Foundations of Mathematics It is important to realize that in standard mathematics we attempt to characterize everything in terms of sets.…

Introduction A subway tunnel could, in principle, operate without external energy (like electricity) if we assume zero friction everywhere. The train…