Math Articles

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  10. Sums and Products. Frobenius began in ##1896## to generalize Weber's group characters and soon investigated…

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

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…

There is a very deep link between group theory and geometry. Sadly, this link is not emphasized a lot in most courses of group theory, even though it is…

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…

It is important to realize that in standard mathematics, we attempt to characterize everything in terms of sets. This means that notions such as natural…

It is apparent that a subway tunnel could be built without the need for supplied energy like electricity, assuming zero friction everywhere.  The tunnel…