# Science and Math Articles

Here is the collection of expert science and math articles that span all the sciences and mathematics. Some examples include physics, mathematics, biology, chemistry, cosmology and earth sciences. For math we cover algebra to advanced calculus.

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### The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations

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In this Insight, I will show how the Popescu-Rohrlich (superquantum)…

### A Simplified Synthesis of Financial Options Pricing

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

### Why the Quantum | A Response to Wheeler's 1986 Paper

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Wheeler's opening statement in his 1986 paper, How Come the…

### The 10 Commandments of Index Expressions and Tensor Calculus

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Having more than 10 years of experience in teaching vector and…

### Direct Echo-Based Measurement of the Speed of Sound

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Figure 1: Distance vs. time a firecracker report echoed off…

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### Intro to Algorithms for Programming

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Many threads here at PF include some question about how to learn…

### Lessons From the Bizzaro Universe

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The terms Bizarro and Bizarro World originated in Superman comics,…

### Either the Sun Is Getting Smaller or Gravity Is Getting Weaker

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Paper discussion: Solar system expansion and strong equivalence…

### Statistical Mechanics: The Ideal Gas

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Read Part 1: Equilibrium Systems The Ideal Gas: Boltzmann's…

### "Classical Physics Is Wrong" Fallacy

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One of the common questions or comments we get on PF is the claim…

### 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…

### Mathematical Quantum Field Theory - Renormalization

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This is one chapter in a series on Mathematical Quantum Field…

### Mathematical Quantum Field Theory - Interacting Quantum Fields

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This is one chapter in a series on Mathematical Quantum Field…

### Mathematical Quantum Field Theory - Free Quantum Fields

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This is one chapter in a series on Mathematical Quantum Field…

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### The Fundamental Difference in Interpretations of Quantum Mechanics

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A topic that continually comes up in discussions of quantum mechanics…

### Mathematical Quantum Field Theory - Quantization

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The following is one chapter in a series on Mathematical Quantum…

### Coordinate Dependent Statements in an Expanding Universe

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In this Insight we will discuss the general Robertson--Walker…

### The Schwarzschild Metric: A Newtonian Comparison

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A Short Proof of Birkoff's Theorem derived the Schwarzschild…

### The Schwarzschild Metric: The Photon Sphere

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A Short Proof of Birkoff's Theorem derived the Schwarzschild…

### Mathematical Quantum Field Theory - Gauge Fixing

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The following is one chapter in a series of Mathematical Quantum…

### The Schwarzschild Metric: GPS Satellites

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A Global Positioning System (GPS) device gives your…

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### Mathematical Quantum Field Theory - Reduced Phase Space

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The following is one chapter in a series on Mathematical Quantum…

### Work Ethic Is a Key to Success for Science Majors

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After earning a 4.0 GPA in his first semester as a…

### Intransitive Dice with a Twist

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

### Mathematical Quantum Field Theory - Gauge Symmetries

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This is one chapter in a series on Mathematical Quantum Field…

### Mathematical Quantum Field Theory - Propagators

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This is one chapter in a series on Mathematical Quantum Field…

### Mathematical Quantum Field Theory - Phase Space

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The following is one chapter of a series on Mathematical Quantum…

### Mathematical Quantum Field Theory - Observables

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The following is one chapter in a series on Mathematical Quantum…

### New Research on Untying Knots in Polymers

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A joint computational-experimental paper that I worked on was…

### Mathematical Quantum Field Theory - Symmetries

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The following is one chapter in a series on Mathematical Quantum…

### Mathematical Quantum Field Theory - Lagrangians

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This is one chapter in a series on Mathematical Quantum Field…

### Mathematical Quantum Field Theory - Field Variations

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This is chapter 4 of a series on Mathematical Quantum Field Theory.The…

### Using the Spaghetti-Twist to Align DNA

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A new paper from a collaboration of Canadian physicists has demonstrated…

### Mathematical Quantum Field Theory - Fields

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The following is one chapter in a series on Mathematical Quantum…

### Mathematical Quantum Field Theory - Spacetime

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The following is one chapter in a series on Mathematical Quantum…