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.

Maupertuis Principle

A Pure Hamiltonian Proof of the Maupertuis Principle

/
Here is another version of proof of Maupertuis's principle. This…
Kerr Spacetime

Fermi-Walker Transport in Kerr Spacetime

/
In the last two posts in this series, we developed some tools…
create a universe story

How to Create a Universe - Instructions for an Apprentice God

/
(-: ##~~~## A fantasy to be read at leisure time ##~~~## :-) Written…
quantum qubit

A Classical View of the Qubit

/
This Insight article is part of my paper Foundations of quantum…
Minkowski_Spacetime_2

Fermi-Walker Transport in Schwarzschild Spacetime

/
In the first post in this series, we introduced the concepts…

Aiming High and Managing Distractions as Keys to Success for Science Majors

/
Over the years, I've noticed some distinct trends among the physics…
The Sum of Geometric Series from Probability Theory

The Sum of Geometric Series from Probability Theory

/
Here I present a simple (but to the best of my knowledge, new)…
quantum mechanics is incomplete

9 Reasons Quantum Mechanics is Incomplete

/
I argue that all interpretations of quantum mechanics (QM) are…
against quantum interpretations

Against "interpretation"

/
I am against "interpretations" of Quantum Mechanics (QM) in a…
lie algebra representations

Lie Algebras: A Walkthrough The Representations

/
  Part III: Representations  10. Sums and…
abacus introduction

An Introduction to the Traditional Abacus of China and Japan

/
Introduction Abacuses are commonly seen in ancient civilizations…
Hooke's Law Experiement

An Accurate Hooke's Law Laboratory

/
Learning Objectives * Gain confidence and experimental care…
Lie Algebra Structure

Lie Algebras: A Walkthrough The Structures

/
  Part II: Structures5. Decompositions.Lie…
lie algebra basics

Lie Algebras: A Walkthrough The Basics

/
  Part I: Basics 1. Introduction. This article is…
Bernoulli's equation

Demystifying the Often Misunderstood Bernoulli's Equation

/
Introduction Bernoulli's equation is one of the most useful…
Magnetic Field Lines

Are Magnetic Field Lines Real?

/
We recently had a question in the relativity forums that mentioned…
vehicle power

When Vehicle Power Dictates Acceleration

/
One interesting problem when dealing with a vehicle of a certain…
Quantum Eraser

The Quantum Mystery of Wigner's Friend

/
In this Insight I will introduce the quantum mystery called ``Wigner's…
Calculus Therom

A Numerical Insight for the Fundamental Theorem of Calculus

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

The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations

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

A Simplified Synthesis of Financial Options Pricing

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

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

/
Wheeler's opening statement in his 1986 paper, ``How Come the…
tensor calculus

The 10 Commandments of Index Expressions and Tensor Calculus

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

Direct Echo-Based Measurement of the Speed of Sound

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

How to Better Define Information in Physics

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

Intro to Algorithms for Programming

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

Lessons From the Bizzaro Universe

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

Either the Sun Is Getting Smaller or Gravity Is Getting Weaker

/
Paper discussion: Solar system expansion and strong equivalence…
statmech2

Statistical Mechanics: The Ideal Gas

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

"Classical Physics Is Wrong" Fallacy

/
One of the common questions or comments we get on PF is the claim…
hilbertspaces2

Hilbert Spaces And Their Relatives: Operators

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

Hilbert Spaces and Their Relatives: Basics

/
  Basics Language first: There is no such thing as…
qft_renormalization

Mathematical Quantum Field Theory - Renormalization

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

Mathematical Quantum Field Theory - Interacting Quantum Fields

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

Mathematical Quantum Field Theory - Free Quantum Fields

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

Intro to Big Bang and Infinity Concepts

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

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

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

The Fundamental Difference in Interpretations of Quantum Mechanics

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

Mathematical Quantum Field Theory - Quantization

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

Coordinate Dependent Statements in an Expanding Universe

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

The Schwarzschild Metric: A Newtonian Comparison

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

The Schwarzschild Metric: The Photon Sphere

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