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.

Quantum Eraser

The Quantum Mystery of Wigner's Friend

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♦ Please note this Insight is currently being edited. Please…
Calculus Therom

A Numerical Insight for the Fundamental Theorem of Calculus

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The purpose of this article is not to provide some rigorous statement,…
Super Quantum

The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations

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

A Simplified Synthesis of Financial Options Pricing

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

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…
tensor calculus

The 10 Commandments of Index Expressions and Tensor Calculus

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

Direct Echo-Based Measurement of the Speed of Sound

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

How to Better Define Information in Physics

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When I ask questions about conservation of information I frequently…
algorithms

Intro to Algorithms for Programming

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

Lessons From the Bizzaro Universe

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

Either the Sun Is Getting Smaller or Gravity Is Getting Weaker

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Paper discussion: Solar system expansion and strong equivalence…
statmech2

Statistical Mechanics: The Ideal Gas

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

"Classical Physics Is Wrong" Fallacy

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

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…
qft_freequantum

Mathematical Quantum Field Theory - Free Quantum Fields

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This is one chapter in a series on Mathematical Quantum Field…
bb_infinity2

Intro to Big Bang and Infinity Concepts

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This article is part of our student writer series. The writer…
journeycosmos3

A Journey Into the Cosmos - FLRW Metric and The Friedmann Equation

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This article is part of our student writer series. The writer…
qm_interpretations

The Fundamental Difference in Interpretations of Quantum Mechanics

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

Mathematical Quantum Field Theory - Quantization

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

Coordinate Dependent Statements in an Expanding Universe

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In this Insight we will discuss the general Robertson--Walker…
gps3

The Schwarzschild Metric: A Newtonian Comparison

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A Short Proof of Birkoff's Theorem derived the Schwarzschild…
gps2

The Schwarzschild Metric: The Photon Sphere

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

Mathematical Quantum Field Theory - Gauge Fixing

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The following is one chapter in a series of Mathematical Quantum…
gps1

The Schwarzschild Metric: GPS Satellites

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 A Global Positioning System (GPS) device gives your…
cosmosintro

A Journey Into the Cosmos - The Friedmann Equation

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 This article is part of our student writer series.…
qtf_phased_space

Mathematical Quantum Field Theory - Reduced Phase Space

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

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…
dice

Intransitive Dice with a Twist

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

Mathematical Quantum Field Theory - Gauge Symmetries

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

Mathematical Quantum Field Theory - Propagators

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

Mathematical Quantum Field Theory - Phase Space

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

Mathematical Quantum Field Theory - Observables

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

New Research on Untying Knots in Polymers

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

Mathematical Quantum Field Theory - Symmetries

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

Mathematical Quantum Field Theory - Lagrangians

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This is one chapter in a series on Mathematical Quantum Field…
qtf_field_variations2

Mathematical Quantum Field Theory - Field Variations

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

Using the Spaghetti-Twist to Align DNA

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

Mathematical Quantum Field Theory - Fields

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

Mathematical Quantum Field Theory - Spacetime

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