Math Articles

Here is the collection of expert Insights that deal with all mathematics disciplines. These cover all areas of math and all skill ranges from algebra to advanced calculus.

stock options math

A Simplified Synthesis of Financial Options Pricing

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Financial options (the right to purchase ("call") or sell ("put")…
hilbertspaces2

Hilbert Spaces And Their Relatives: Operators

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  Operators. The Maze Of Definitions. We will use…
hilbertspaces

Hilbert Spaces and Their Relatives: Basics

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  Basics Language first: There is no such thing as…
dice

Intransitive Dice with a Twist

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Intransitive dice are sets of dice that don't follow the usual…

A Journey to The Manifold SU(2): Differentiation, Spheres and Fiber Bundles

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Part 2  Differentiation, Spheres and Fiber Bundles Image…
mathoperators

How to Tell Operations, Operators, Functionals and Representations Apart

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 All these concepts belong to the toolbox of physicists.…
geometrysimple

Simple Geometry, Deep Math

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IntroductionIt is a remarkable fact that consideration of…
representations

Representations and Why Precision is Important

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First of all: What is a representation? It is the description…
angledimensions

Can Angles be Assigned a Dimension?

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1. Some Background on Dimensional Analysis ... if you are…
groupsandgeometry

Exploring the Relationship Between Group Theory and Geometry

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There is a very deep link between group theory and geometry.…
computers

An Interesting Ramsey Theory Riddle

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This insight will be about Ramsey theory. Ramsey theory has its…
logicp3

Scientific Inference: Balancing Predictive Success with Falsifiability

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  Bayes' Theorem: Balancing predictive success with…
encryption

Perfect Secrecy and the Unbreakable Cipher

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Is it possible to design an unbreakable cipher? Do methods of…
cipher

The Monographic Substitution Cipher: From Julius Caesar to the KGB

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A monographic substitution cipher works by replacing individual…
complexmath

The Case for Learning Complex Math

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Resistance to complex math seems to never die out.  I see it…
complexnumbers

Things Which Can Go Wrong with Complex Numbers

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At the first sight, there are many paradoxes in complex number…
MillenniumPrize

Intro to the Millennium Prize Problems

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In this Insight, I will go over the background information…
micro2

Axioms for the Natural Numbers

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** Bloch Chapter 1.2The Peano system in Bloch has a special…
micro3

A Forward on Real Numbers and Real Analysis

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It is important to realize that in standard mathematics, we attempt…
physicsturnedmath

Trials and Tribulations of a Physicist who Became a Math Geek

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How did I go from the brink of changing my major from physics…
math obvious

Teaching Math and the Obvious

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My #1 goal, when I teach a math class, is to convey a certain…
subway

A Brachistochrone Subway Is Not a Cost-effective Idea

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It is apparent that a subway tunnel could be built without the…
abstract_algebra

Is Zero a Natural Number?

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Using: Anderson-Feil Chapter 1.1Is zero a natural number?This…
micro1

What is a Property Formally

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** Hrbacek-Jech Chapter 1.2Hrbacek and Jech do not go into…