# Mathematics Articles

### Hilbert Spaces And Their Relatives: Operators

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Operators. The Maze Of Definitions. We will use…

### Hilbert Spaces and Their Relatives: Basics

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Basics Language first: There is no such thing as…

### 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…

### How to Tell Operations, Operators, Functionals and Representations Apart

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All these concepts belong to the toolbox of physicists.…

### Simple Geometry, Deep Math

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Introduction It is a remarkable fact that consideration of…

### Representations and Why Precision is Important

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

### Can Angles be Assigned a Dimension?

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

### Exploring the Relationship Between Group Theory and Geometry

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

### An Interesting Ramsey Theory Riddle

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

### Scientific Inference: Balancing Predictive Success with Falsifiability

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Bayes' Theorem: Balancing predictive success with…

### Perfect Secrecy and the Unbreakable Cipher

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

### The Monographic Substitution Cipher: From Julius Caesar to the KGB

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A monographic substitution cipher works by replacing individual…

### The Case for Learning Complex Math

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

### Things Which Can Go Wrong with Complex Numbers

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

### Intro to the Millennium Prize Problems

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

### Axioms for the Natural Numbers

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

### A Forward on Real Numbers and Real Analysis

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

### 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…

### Teaching Math and the Obvious

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

### 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…

### Is Zero a Natural Number?

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

### What is a Property Formally

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