# Browse All Articles

Here is an alphabetical list of all Physics Forums Insights grouped by format and then discipline. It is auto updated as new Insights are published. Enjoy!

### Articles

Physics Articles

- 11d Gravity From Just the Torsion Constraint
- 15 of the Best PF 2017 Eclipse Photos
- It Was 20 Years Ago Today — the M-theory Conjecture
- 3 Possible Models For Why Uranus Spins on Its Side
- 9 Reasons Quantum Mechanics is Incomplete
- A Beginner Physics Guide to Baryon Particles
- A Classical View of the Qubit
- A First Idea of Quantum Field Theory – 20 Part Series
- A Numerical Insight for the Fundamental Theorem of Calculus
- A Physics Misconception with Gauss’ Law
- A Principle Explanation of the “Mysteries” of Modern Physics
- A Black Hole Problem From Greg Egan’s “Incandescence”
- Intro to AC Power Analysis: Learn System Basics
- Intro to AC Power Analysis: Network Analysis
- AC Power Analysis: The 4 Levels of Cyber Resilience
- Accurate Fluid Dynamics By Video Analysis
- Acoustic ‘beats’ from Mismatched Musical Frequencies
- How to Manage TCP/IP In Automation or Measurement Networks
- Against “interpretation”
- Learn All About Earth’s Gravity
- An Example of An Accurate Hooke’s Law Laboratory
- Why Road Capacity Is Almost Independent of the Speed Limit
- Exploring the Anatomy of Compton Scattering
- Answering Mermin’s Challenge with the Relativity Principle
- Learn The Main Conceptual Ideas of Anyon Particles
- Approximate LCDM Expansion in Simplified Math
- Approximate LCDM Expansion in Simplified Math (Part 2)
- Approximate LCDM Expansion in Simplified Math (Part 4)
- Are Electromagnetic Waves Always Transverse?
- Are Magnetic Field Lines Real?
- Assessing the Physics in Edmond Hamilton’s “The Second Satellite”
- Learn Inflation Balloon Analogy Misconceptions
- Learn the Basics of Positron Emission Tomography (PET)
- Exploring Bell States and Conservation of Spin Angular Momentum
- Intro to the Big Bang and Infinity Concepts
- Black Holes and the Properties of In-Falling Radial Plungers
- Black Holes Are Not Empty Voids. A Black Hole at the Heart!
- The Block Universe – Refuting a Common Argument
- Blockworld and Its Foundational Implications: Time Dilation and Length Contraction
- Blockworld and Its Foundational Implications: The Relativity of Simultaneity and Blockworld
- Blockworld and its Foundational Implications: General Relativity and the Big Bang
- Blockworld and its Foundational Implications: General Relativity and Closed Timelike Curves
- Blockworld and its Foundational Implications: Delayed Choice and No Counterfactual Definiteness
- Learn about the Big Bang and the Expansion of the Universe
- Calculating the Balmer Alpha Line: Atomic Hydrogen
- Can We See an Atom?
- Can We Do Better Than Mechanical Energy Conservation?
- Introduction to Causal Perturbation Theory
- Intro to Centrifugal Force Reversal in Kerr Spacetime
- The What and Why of Circuit Analysis Assumptions
- Clarifying Common Issues with Indistinguishable Particles
- Addressing the “Classical Physics Is Wrong” Fallacy
- Thoughts on the Complexity of Modern Science
- Explore Coordinate Dependent Statements in an Expanding Universe
- Learn Damped Motion in Classical and Quantum Mechanics
- Dark Energy Part 1: Einstein-deSitter Cosmology
- Dark Energy Part 2: LCDM Cosmology
- Dark Energy Part 3: Fitting the SCP Union 2.1 Supernova Data
- Demystifying the Often Misunderstood Bernoulli’s Equation
- Differential Equation Systems and Nature
- The Diffraction Limited Spot Size with Perfect Focusing
- Direct Echo-Based Measurement of the Speed of Sound
- Does the Block Universe of Physics Mean Time is an Illusion?
- Either the Sun Is Getting Smaller or Gravity Is Getting Weaker
- Emergence From the Superpoint
- Lesson on Entanglement Entropy in Quantum Field Theory
- Learn Entanglement Entropy in Quantum Mechanics
- Epsilontic – Limits and Continuity
- Equations of State for Photon Gas and Relativistic Electron Gas
- Examples of Prequantum Field Theories I: Gauge Fields
- Examples of Prequantum Field Theories II: Higher Gauge Fields
- Examples of Prequantum Field Theories III: Chern-Simons-type Theories
- Examples of Prequantum Field Theories IV: Wess-Zumino-Witten-type Theories
- Exploring the Spectral Paradox in Physics
- Exploring the Energies in the Large Hadron Collider
- Exploring the Math in Killing Fields and Black Holes
- Explosion-Generated Collapsing Vacuum Bubbles Reach 20,000 Kelvin
- Frames of Reference: A Skateboarder’s View
- Learn Frenet Equations in 2-D Which Result in the Cornu Spiral
- Fun with Self-Avoiding Walks Simulations
- The Fundamental Difference in Interpretations of Quantum Mechanics
- Learn the Fundamentals of the Diffraction Grating Spectrometer
- Gaia and the Race to Detect More Gravitational Waves
- Exploring General Relativity as a Gauge Theory
- Does Gravity Gravitate? Part 2
- Does Gravity Gravitate: The Wave
- Learn About the Greenberger-Horne-Zeilinger Experiment
- What Planck Length Is and It’s Common Misconceptions
- High Temperature and Low Duality for the Ising Model on an Infinite Regular Tree
- Why Higher Category Theory in Physics?
- Higher Prequantum Geometry II: The Principle of Extremal Action – Comonadically
- Higher Prequantum Geometry III: The Global Action Functional – Cohomologically
- Higher Prequantum Geometry IV: The Covariant Phase Space – Transgressively
- Higher Prequantum Geometry I: The Need for Prequantum Geometry
- Higher Prequantum Geometry V: The Local Observables – Lie Theoretically
- What is the Homopolar Generator: An Analytical Example
- Homotopy Lie-n Algebras in Supergravity
- How Can We Jump When the Ground Does No Work?
- How Quantum Information Theorists Revealed the Relativity Principle at the Foundation of Quantum Mechanics
- How Quantum Information Theory Solves “the only mystery” of Quantum Mechanics
- How to Better Define Information in Physics
- How to Create a Universe – Instructions for an Apprentice God
- The Essential Guide to Self Study Mathematics
- How to Zip Through a Rotating Tunnel Without Bumping Into the Walls
- I Know the Math Says so, but Is It Really True?
- Inflationary Misconceptions and the Basics of Cosmological Horizons
- How to Initiate Research Work As a Physics Major
- The Interaction of Sound and Light
- Introduction to Electric Vector Potential and Its Applications
- Introduction to Pitot-Static Systems in Gliders
- Intro to the Ionization Energy of Atomic Hydrogen
- Is Mechanical Energy Conservation Free of Ambiguity?
- Is Pressure A Source Of Gravity?
- Is Science an Authority? How to View Announcements from Scientists
- Learn About the FLRW Metric and The Friedmann Equation
- Learn About the Friedmann Equation and the Cosmos
- Learn About Knut Lundmark and the Prehistory of Dark Matter
- The LCDM Cosmological Model in Simplified Math (Part 3)
- Lessons From the Bizzaro Universe
- LHC Part 2: Commissioning
- LHC Part 3: Protons as Large as a Barn
- LHC Part 4: Searching for New Particles and Decays
- Massive Meets Massless: Compton Scattering Revisited
- Maxwell’s Equations in a Static, Spherically Symmetric Spacetime
- How to Scientifically Measure How Many Days Are in a Year
- Can You Measure Quantum Entanglement?
- Learn a Misconception of the Heisenberg Uncertainty Principle
- Learn the Top Misconceptions about Virtual Particles
- Modern Physics Understood as an Unrecognized Kuhnian Revolution
- Understand the Acoustic Modulation vs. Beating Confusion
- Why the Need of Infinity in Physics
- What are Negative Absolute Temperatures
- Learn About Neutrino Masses and Speed
- Learn the Fields of Mathematical Quantum Field Theory
- Learn Field Variations in Mathematical Quantum Field Theory
- Learn Free Quantum Fields in Mathematical Quantum Field Theory
- Learn Gauge Fixing in Mathematical Quantum Field Theory
- Learn Gauge Symmetries in Mathematical Quantum Field Theory
- Learn the Geometry of Mathematical Quantum Field Theory
- Learn Interacting Quantum Fields in Mathematical Quantum Field Theory
- Learn Lagrangians in Mathematical Quantum Field Theory
- Learn Observables in Mathematical Quantum Field Theory
- Learn Phase Space in Mathematical Quantum Field Theory
- Learn Propagators in Mathematical Quantum Field Theory
- Learn Quantization in Mathematical Quantum Field Theory
- Learn Reduced Phase Space in Mathematical Quantum Field Theory
- Learn Renormalization in Mathematical Quantum Field Theory
- Learn Spacetime in Mathematical Quantum Field Theory
- Learn Symmetries in Mathematical Quantum Field Theory
- Learn Why Ohm’s Law Is Not a Law
- What Thermodynamics and Entropy Means
- Opinion: When Pro Scientists Explain Using Pop Science
- Oppenheimer-Snyder Model of Gravitational Collapse: Implications
- Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details
- Introduction to Perturbative Quantum Field Theory
- Permanent Magnets Explained by Magnetic Surface Currents
- Learn the Physics of Hand-to-Hand Combat
- Learn the Physics of Virtual Particles in Quantum Mechanics
- Plus/minus What? How to Interpret Error Bars
- A Poor Man’s CMB Primer: Orientation of the Universe
- A Poor Man’s CMB Primer: The Birth of a Cosmic Background Radiation
- A Poor Man’s CMB Primer: Bumps on a Blackbody
- A Poor Man’s CMB Primer: Cosmic Acoustics
- A Poor Man’s CMB Primer: Quantum Seeds
- Posterior Predictive Distributions in Bayesian Statistics
- Learn About Quantum Amplitudes, Probabilities and EPR
- Quantum Computing for Beginners
- The Quantum Liar Experiment: An Instantiation of the Mermin Device
- Quantum Mechanics and the Famous Double-slit Experiment
- Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics
- Learn the Top 5 Misconceptions About Infinity
- Exploration into the Physics of Rainbows
- Relativistic Treatment of the DC Conducting Straight Wire
- Learn the Relativistic Work-Kinetic Energy Theorem
- Relativity on Rotated Graph Paper (a graphical motivation)
- When Renewable Energy Meets Power Grid Operations
- How Representative is the Night Sky?
- Find Out the Results Shown at 2017 CERN EPS Conference
- Understanding Retrocausality and Blockworld
- Retrocausality: How Fundamental is the Arrow of Time?
- Reversible vs Irreversible Gas Compression and Expansion Work
- The Revival of Newton-Cartan Theory in General Relativity
- Roger Babson’s Anti-Gravity Contest
- Exploring a Paper on Scaling Laws and the Speed of Animals
- The Schwarzschild Geometry: Spacetime Diagrams
- The Schwarzschild Metric: GPS Satellites
- The Schwarzschild Metric: The Photon Sphere
- The Schwarzschild Metric: A Newtonian Comparison
- Should You Do Science for Love or for Money
- Scientific Inference: Logical Induction Ain’t Logical
- Scientific Inference: Do We Really Need Induction?
- Introduction to the Secondary Forces in Physics
- Have Scientists Seen an Electron?
- How to Self-Study Basic High School Mathematics
- Signature of the Sun: Analyzing the Solar Balmer Series Lines
- Explore Some Sins in Physics Didactics
- Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime
- Learn About Spacetime Diagrams of Light Clocks
- Spectral Standard Model and String Compactifications
- Learn About the Speed of Light and Galilean Relativity
- Learn Statistical Mechanics: The Ideal Gas
- How the EPR Paradox Fits Between Entanglement and Nonlocality
- How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics
- Struggles with the Continuum: Spacetime Conclusion
- Struggles With the Continuum: Is Spacetime Really a Continuum?
- Struggles With The Continuum: Quantum Mechanics of Charged Particles
- Struggles With the Continuum: Point Particles and the Electromagnetic Field
- Struggles with the Continuum – Relativity and Quantum
- Struggles with the Continuum: Quantum Electrodynamics
- Struggles with the Continuum – Freeman Dyson and QED
- Struggles with the Continuum: General Relativity
- Super p-Brane Theory Emerging from Super Homotopy Theory
- Superdeterminism and the Mermin Device
- Garrett Lisi’s Superparticle Bet With Frank Wilczek
- Learn About Supersymmetry and Deligne’s Theorem
- Symmetry Arguments and the Infinite Wire with a Current
- The 10 Commandments of Index Expressions and Tensor Calculus
- The 7 Basic Rules of Quantum Mechanics
- Revisiting The Deuterium Lyman Alpha Line Experiment
- The Einstein Field Equation in a Static, Spherically Symmetric Spacetime
- The Evolution of the Universe, Cosmic Web and Connections
- What are the Fates of Massive Stars
- The Last Man On The Moon | A Look Back at Previous Missions
- The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview
- The Poor Man’s Milli-Ohm Meter
- The Reappearance of Supernova (SN) Refsdal
- Learning the Twin Paradox for Freely-falling Observers
- The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations
- Learn Time Dilation and Redshift for a Static Black Hole
- Learn Time Synchronization Across Switched Ethernets
- Tolman Law in a Nutshell
- Tools to Enrich our Quantum Mechanics Interpretations Discourse
- Understanding Bohr’s Helium Lines
- Understanding Buoyancy: The Limits of Archimedes
- Understanding the General Relativity View of Gravity on Earth
- Understanding Superposition Physically and Mathematically
- Some Useful Integrals In Quantum Field Theory
- How to Use the Spaghetti-Twist Method to Align DNA
- Explore The Vacuum Fluctuation Myth in Quantum Theory
- Learn About Vacuum Fluctuations in Experimental Practice
- “Violating” Einstein’s Photoelectric Effect Model
- Weak Values Part 1: Asking Photons Where They Have Been
- Weak Values Part 2: The Quantum Cheshire Cat Experiment
- What Are Tensors and Why Are They Used in Relativity?
- What Happens When You Flip the Light Switch – From Zero Seconds to 20 Years
- What is Energy? A Definition and Controversy
- When Discussing the Twin Paradox: Read This First
- When Science is Not Enough: Legal and Health Implications of Questions
- When Vehicle Power Dictates Acceleration
- Why Bother Teaching Mechanical Energy Conservation?
- Why the Quantum | A Response to Wheeler’s 1986 Paper
- Why There Are Maximum Mass Limits for Compact Objects
- The Quantum Mystery of Wigner’s Friend
- Yardsticks to Metric Tensor Fields

Math Articles

- 10 Math Things We All Learnt Wrong At School
- A Pure Hamiltonian Proof of the Maupertuis Principle
- Learn a Simplified Synthesis of Financial Options Pricing
- Is Zero a Natural Number?
- An Overview of Complex Differentiation and Integration
- Learn Axioms for the Natural Numbers
- A Brachistochrone Subway Is Not a Cost-effective Idea
- Can Angles be Assigned a Dimension?
- Hear the Case for Learning Complex Math
- Classification of Mathematics by 42 Branches
- Counting to p-adic Calculus: All Number Systems That We Have
- Differential Equation Systems and Nature
- An Intro on Real Numbers and Real Analysis
- Exploring Frequentist Probability vs Bayesian Probability
- An Interesting Ramsey Theory Riddle
- Exploring the Relationship Between Group Theory and Geometry
- Learn the Basics of Hilbert Spaces and Their Relatives
- Learn the Basics of Hilbert Spaces and Their Relatives: Operators
- How Bayesian Inference Works in the Context of Science
- How to Write a Math Proof and Their Structure
- How to Get Started with Bayesian Statistics
- Learn About Intransitive Dice with a Twist
- Évariste Galois and His Theory
- Introduction to the World of Algebras
- A Journey to The Manifold SU(2): Differentiation, Spheres, and Fiber Bundles
- Learn Lie Algebras: A Walkthrough The Basics
- Lie Algebras: A Walkthrough The Representations
- Learn Lie Algebras: A Walkthrough The Structures
- Mathematician Mary Somerville Features in Google Doodle
- Lessons From My Experience Teaching Math
- Intro to the Millennium Prize Problems
- The Monographic Substitution Cipher: From Julius Caesar to the KGB
- P vs. NP and what is a Turing Machine (TM)?
- Is It Possible to Design an Unbreakable Cipher?
- Beginners Guide to Precalculus, Calculus and Infinitesimals
- Probabilistic Factors Involved in Disease and Virus Testing
- Linear Representations and Why Precision is Important in Math
- Scientific Inference: Balancing Predictive Success with Falsifiability
- Series in Mathematics: From Zeno to Quantum Theory
- When Simple Geometry Unveils Deep Math
- How to Tell Operations, Operators, Functionals, and Representations Apart
- The Amazing Relationship Between Integration And Euler’s Number
- The History and Importance of the Riemann Hypothesis
- The Sum of Geometric Series from Probability Theory
- Things Which Can Go Wrong with Complex Numbers
- Trials and Tribulations of a Physicist who Became a Math Geek
- What Are Infinitesimals – Advanced Version
- What Are Numbers?
- What is a Property Formally in Mathematical Logic
- When Lie Groups Became Physics
- Yardsticks to Metric Tensor Fields

Engineering Articles

Other Science Articles

- 5 Pieces of Evidence that Support Theory of Evolution
- Atomic Positioning with DNA Hinges
- Can Gene Editing Eliminate Alzheimer’s Disease?
- What Causes Cancer: Bad Luck or Bad Lifestyles?
- Differential Equation Systems and Nature
- Why CRISPR Technologies Won’t Lead to Designer Babies
- Frequently Made Errors in Climate Science – The Greenhouse Effect
- Learn About History’s First Science Experiments
- Want to Tell One Wood from Another? Learn Basic Wood Anatomy
- Learn About New High Performance Ultra-wide Angle Camera Lenses
- Learn the Amazing New Research on Untying Knots in Polymers
- Probabilistic Factors Involved in Disease and Virus Testing
- Why Your Software is Never Perfect
- Studio in a Box: Learn About Digital Modeling Amplifiers
- The New Bioethics: A 21st Century Overview
- What is Evolution: A Beginner’s Guide
- Polymer Physics and Genetic Sequencing
- When did Mitochondria Evolve?

Education Articles

- An Introduction to the Traditional Abacus of China and Japan
- Blaming Government for Teacher and Scientist Failures in Integrity
- Exploring the Problem of Fake News and Science Reporting
- False Physics Major Dichotomy: Theorist or Experimentalist?
- Why Imagination Without Knowledge Is Ignorance Waiting to Happen
- What Is The Most Important Thing That You Learned?
- Very Little Excuse To Ask A Question Cold
- Finding Niches for Publishable Undergraduate Research
- Opinion: When Pro Scientists Explain Using Pop Science
- Why Is Quantum Mechanics So Difficult?
- Real Research in Unexpected Places – Backyards, Barns, Bayous
- Real Research in Unexpected Places – Boat Ramps
- Revamping Undergraduate Introductory Physics Laboratory
- Why Study Physics? A Bit Goes a Long Way!
- The Most Important Thing You Can Learn from Physics Forums
- Why Bother Teaching Mechanical Energy Conservation?
- Why ChatGPT Is Not Reliable
- Why You Should Not Use Wikipedia As Your Primary Source
- Why Work Ethic Is a Key to Success for Science Majors

### FAQs

Physics FAQs

- 7 Basic Space Law Questions Explored
- How Does an Airplane Wing Work? A Primer on Lift
- Where Did the Big Bang Happen?
- Do Black Holes Really Exist?
- Can I Send a Signal Faster than Light by Pushing a Rigid Rod?
- Can We Tell Whether the Universe Is Rotating?
- Do Photons have Mass?
- Do Photons Move Slower in a Solid Medium?
- Does Gravity Gravitate?
- Does the Heisenberg Uncertainty Principle Imply Energy Nonconservation?
- Why Don’t Electrons Crash into the Nucleus in Atoms?
- Was the Early Universe in a Disordered State?
- Learn About Energy Gained by Charge in an Electrostatic Field
- Is there Evidence for the Big Bang?
- A Geometrical View of Time Dilation and the Twin Paradox
- How Fast Do Changes in the Gravitational Field Propagate?
- Lenses and Pinholes: What Does “In Focus” Mean?
- PF’s policy on Lorentz Ether Theory and Block Universe
- Radius of the Observable Universe in Light-years Is Greater than Its Age
- Could Redshifts Be Intrinsic Rather than Cosmological?
- Why Is the Speed of Light the Same in All Frames of Reference?
- What Is the Steady-state Model and Why It’s No Longer Viable
- Is the Universe a Black Hole?
- At What Velocity Does the Universe Expand and Can It Be Faster than Light?
- What Are Tensors and Why Are They Used in Relativity?
- What Are the Thermodynamics of Black Holes? A 5 Minute Introduction
- What are Virtual Particles? A 10 Minute Introduction
- How to Build a Definition for Heat
- What is Impedance? A 5 Minute Introduction
- What is Mass Inflation? A 5 Minute Introduction
- What is Potential Energy? A 5 Minute Introduction
- What is relativistic mass and why it is not used much?
- What Is the Bell Spaceship Paradox, and How Is It Resolved?
- What is the Double Slit? A 5 Minute Introduction
- What is the Moment of Inertia? A 10 Minute Introduction
- Why Does C Have a Particular Value, and Can It Change?
- Why Is Acceleration Due to Gravity a Constant?
- Why We Don’t Discuss Perpetual Motion Machines (PMM)
- Will All Matter Be Converted to Photons?
- Why Won’t You Look at My New Theory?
- Why You Can’t Quantum Tunnel Through a Wall

Math FAQs

- How to Find Potential Functions? A 10 Minute Introduction
- What Proofs are in Mathematics and Why Bother?
- The History and Concept of the Number 0
- What are Significant Figures? A 5 Minute Introduction
- What is a Fibre Bundle? A 5 Minute Introduction
- What Is a Limit of a Function? A 5 Minute Introduction
- What is a Linear Equation? A 5 Minute Introduction
- What is a Parabola? A 5 Minute Introduction
- What is a Real Number? A 5 Minute Introduction
- What is a Tangent Line? A 5 Minute Introduction
- What Is a Tensor? The mathematical point of view.
- What is Integration By Parts? A 5 Minute Introduction
- What is Lie algebra? A 5 Minute Introduction
- Why Do People Say That 1 And .999 Are Equal?

### Guides

Physics Guides

- A Layman’s Guide to: Lies, Damned Lies and Pseudoscience
- Learn Advanced Astrophotography Tips
- An Accurate Simple Harmonic Oscillator Laboratory
- Learn Intermediate Astrophotography Tips
- Corrections to the Australian Physics Olympiad Questions and Solutions
- Getting Started with Solar System Imaging
- Guide to Buying Your First Telescope
- How to Avoid Breaking Physics With Your “What If” Question
- Introduction to Astrophotography for Beginners
- Physics Blogs You Need to Be Reading
- Physics Forums Crackpot Index and Bingo
- Learn Solar Eclipse Viewing Basics
- What Are Your Favorite Science or Math Blogs?

Math Guides

- 10 Math Tips to Save Time and Avoid Mistakes
- 5 Common MATLAB Error Messages and How to Fix Them
- In High School and Want to Do Advanced Mathematics?
- Resources for High School Math at Home
- How to Self Study Linear Algebra for Students
- How to Self Study Abstract Algebra
- How to Self Study Intermediate Analysis Math
- How to Self Study Analysis: Intro to Analysis
- A Guide to Self Study Calculus
- How to Self Study Geometry for Students
- What Are Infinitesimals – Simple Version

Education Guides

- Learn 3 Tips For Cooling Off Hot Debates and Win The Argument
- A Lesson In Teaching Physics: You Can’t Give It Away
- Aiming High and Managing Distractions as Keys to Success for Science Majors
- What are Alternative Careers for a Physics Graduate
- How to Apply for Physics Graduate School
- What Academic Advice Would You Tell Your 18 Year Old Self?
- What’s Your Most Memorable Textbook?
- How to Become a Medical Physicist in 3653 Easy Steps
- Choosing a Research Area and an Advisor As a Physics Major
- Am I Cut Out for Mathematics or Sciences?
- Dealing with Doubt as a Science Student
- Early Physics Education in High Schools For Physics Majors
- How to Enter Physics Graduate School From Another Major
- First years of Graduate School from Being a TA to the Graduate Exams
- How to Get a Physics Job!
- Guide to Publishing in Peer Reviewed Journals
- How to Avoid Breaking Physics With Your “What If” Question
- So I Am Your Intro Physics Instructor
- Mathematical Preparations For a Physics Major
- The Best Methods to Deal with Procrastination
- How to Succeed at Oral Presentations As a Physics Major
- Oral Presentations – Addendum | Physics Career
- How I Overcame Learning Challenges That I Faced Studying Science
- How to Get a Postdoctoral Physics Position
- 5 Problems with Students Self Studying Mathematics
- How to Publish in a Physics Journal As a Physics Major
- How to Publish in a Physics Journal (Addendum)
- Research Work and The Lab Book As a Physics Major
- Resources for High School Physics at Home
- Learn the Secrets of Successful Science Projects
- How to Survive the First Year of College As a Physics Major
- The Birth of a Physics Textbook: An Author’s Journey
- Explaining the Life of a Physics Major
- The US Graduate School System For Physics Majors
- A Guide to Going Back to School For Math or Science
- What Physics Majors Should Expect from Graduate School
- How to Write a Master Degree Thesis As a Physics Major
- How to Write Your Doctoral Thesis/Dissertation As a Physics Major
- Your Curriculum Vitae As a Physics Graduate
- Your Physics Thesis Defense Guide

Other Science Guides

- An Intro to the Systemless Interface of Rooting Android Phones
- Clearing Misconceptions and Some Tips on Debloating Android Phones
- An Introduction to Computer Languages
- Create an Android Ringtone Picker Using the Ringtonemanager Class
- Ultimate Digital Camera Buyer’s Guide: Compacts, DSLR and Tripods
- Digital Camera Buyer’s Guide: DSLR
- Digital Camera Buyer’s Guide: Introduction
- Digital Camera Buyer’s Guide: Bridge Cameras
- Digital Camera Buyer’s Guide: Tripods
- The LCEVC Coding Standard and 8K Television
- How to Evaluate a Camera Lens for Performance
- Programming an ATmega8A using Arduino
- Reflections on Technology Product Quality
- The Rise of AI in Classrooms, Labs and Industry – Part 3
- The Rise of Artificial intelligence in STEM Labs, Classrooms, and Industry
- What Technology or Discovery Will Be the Most Revolutionary Within 20 Years?
- Why ChatGPT Is Not Reliable

### Tutorials

Physics Tutorials

- A Formal Definition of Large-Scale Isotropy
- A New Interpretation of Dr. Walter Lewin’s Paradox
- An Alternate Approach to Solving 2-Dimensional Elastic Collisions
- An Alternative Approach to Solving Collision Problems
- An Introduction to the Generation of Mass from Energy
- Learn Basic Kinematics in Classical Mechanics
- How to Calculate the Spin of Black Hole Sagittarius A*
- An Equation for the Centrifugal Force Reversal Near A Black Hole
- Corrections to MIT Open Courseware: Systems of Varying Mass
- Elementary Construction of the Angular Velocity
- Equations of Motion Revisited
- Learn The Basics of Rolling Motion
- Fabry-Perot and Michelson Interferometry: A Fundamental Approach
- Exploring Fermi-Walker Transport in Kerr Spacetime
- Learning Fermi-Walker Transport in Schwarzschild Spacetime
- Frames of Reference: Linear Acceleration View
- Frequently Made Errors in Equation Handling
- Frequently Made Errors in Heat: Elementary Level
- Frequently Made Errors in Mechanics: Forces
- Frequently Made Errors in Mechanics – Friction
- Frequently Made Errors in Mechanics: Hydrostatics
- Frequently Made Errors in Mechanics: Kinematics
- Frequently Made Errors in Mechanics: Moments
- Frequently Made Errors in Mechanics: Momentum and Impacts
- Frequently Made Errors in Mechanics: Springs
- Frequently Made Errors: Pseudo and Resultant Forces
- Frequently Made Errors in Vectors – Elementary Use
- Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes
- How to Determine the Change in Entropy
- How to Apply Newton’s Second Law to Variable Mass Systems
- How to Master Projectile Motion Without Quadratics
- How to Measure Internal Resistance of a Battery
- How to Model a Magnet Falling Through a Conducting Pipe
- How to Model a Magnet Falling Through a Solenoid
- How to Recognize Split Electric Fields
- How to Solve Projectile Motion Problems in One or Two Lines
- Fermi-Walker Transport in Minkowski Spacetime
- How to Use Duality in Computational Electromagnetic Problems
- Learn an Integral Result from Parseval’s Theorem
- Learn the Basics of Dimensional Analysis
- LightCone 8 Tutorial Part III – How Things are Computed
- LightCone8 Tutorial Part I
- LightCone8 Tutorial Part II – Charts
- Maximizing Horizontal Range of a Projectile
- Maxwell’s Equations in Magnetostatics and Solving with the Curl Operator
- Misconceiving Mutual Inductance Coefficients
- A Numerical Electromagnetic Solver Using Duality
- Learn Orbital Mechanics in Unity Game Engine for Augmented Reality
- Learn Orbital Precession in the Schwarzschild and Kerr Metrics
- Learn a Partial “Derivation” of Gauss’s Law
- Intro to Physically Reasonable Waves on a String
- Understanding Precession in Special and General Relativity
- Quaternions in Projectile Motion
- Presenting a Rare Kinematic Formula
- Learn About Relativity on Rotated Graph Paper
- Learn Relativity Using the Bondi K-calculus
- Relativity Variables: Velocity, Doppler-Bondi k, and Rapidity
- Quantum Renormalisation Made Easy
- Why Renormalisation in Quantum Theory Needs a Cutoff
- Rindler Motion in Special Relativity: Hyperbolic Trajectories
- Rindler Motion in Special Relativity: Rindler Coordinates
- The Schwarzschild Geometry: Key Properties
- The Schwarzschild Geometry: Coordinates
- The Schwarzschild Geometry: Physically Reasonable?
- An Example of Servo-Constraints in Mechanics
- Learn A Short Proof of Birkhoff’s Theorem
- How to Solve Einstein’s Field Equations in Maxima
- Learn Statistical Mechanics: Equilibrium Systems
- Subtleties Overlooked in Friction Questions: Object Slides Down Ramp
- Learn About Tetrad Fields and Spacetime
- The Classical Limit of Quantum Mechanical Commutator
- The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors
- Understanding Entropy and the 2nd Law of Thermodynamics
- Valentine’s Reflections: Mathematical Matters of the Heart
- How to Visualize the 2-D Particle in a Box

Math Tutorials

- A Novel Technique of Calculating Unit Hypercube Integrals
- A Path to Fractional Integral Representations of Some Special Functions
- A Trick to Memorizing Trig Special Angle Values Table
- An Introduction to Theorema Primum
- Physical Applications of the “Tan Rule”
- Learn Complex and Irrational Exponents for the Layman
- Some Conceptual Difficulties in the Roles of Variables and Constants
- A Continuous, Nowhere Differentiable Function: Part 1
- A Continuous, Nowhere Differentiable Function: Part 2
- Demystifying the Chain Rule in Calculus
- Explore the Fascinating Sums of Odd Powers of 1/n
- Computing the Riemann Zeta Function Using Fourier Series
- Frequently Made Errors in Probability: Conditionals in Natural Language
- Explaining the General Brachistochrone Problem
- Geometry of Side-side-angle (SSA) and Impossible Triangles
- How to Solve Second-Order Partial Derivatives
- Informal Introduction to Cardinal Numbers
- Investigating Some Euler Sums
- Mathematical Irrationality for Dummies
- Is There a Rigorous Proof Of 1 = 0.999…?
- A Journey to The Manifold SU(2): Representations
- How to Make Units of Measurement Work for You
- Learn About Matrix Representations of Linear Transformations
- Some Misconceptions on Indefinite Integrals
- Omissions in Mathematics Education: Gauge Integration
- The Pantheon of Derivatives – Part II
- The Pantheon of Derivatives – Part III
- The Pantheon of Derivatives – Part IV
- The Pantheon of Derivatives – Part V
- Demystifying Parameterization and Surface Integrals
- Learn Partial Differentiation Without Tears
- Introduction to Partial Fractions Decomposition
- Errors in Probability: Continuous and Discrete Distributions
- Python’s Sympy Module and the Cayley-Hamilton Theorem
- Reduction of Order For Recursions
- SOHCAHTOA: Seemingly Simple, Conceivably Complex
- Trick to Solving Integrals Involving Tangent and Secant
- Learn How to Solve the Cubic Equation for Dummies
- Solving Homogeneous Linear ODEs using Annihilators
- How to Solve Nonhomogeneous Linear ODEs using Annihilators
- Learn Further Sums Found Through Fourier Series
- The Analytic Continuation of the Lerch and the Zeta Functions
- The Art of Integration
- The Extended Riemann Hypothesis and Ramanujan’s Sum
- The Pantheon of Derivatives – 5 Part Series
- Using the Fourier Series To Find Some Interesting Sums
- What Are Eigenvectors and Eigenvalues in Math?

Other Science Tutorials

- An Intro to AVX-512 Assembly Programming
- AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic
- AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic Conclusion
- AVX-512 Programming: Extracting Column Subtotals from a Table
- Why Can’t My Computer Do Simple Arithmetic?
- Create an Android Ringtone Picker Using the Ringtonemanager Class
- Guide to C++ Programming For Beginners
- How to Setup a Raspberry Pi Cluster
- Intro to Algorithms for Programming
- Intro to Data Structures for Programming
- Learn Orbital Mechanics in Unity Game Engine for Augmented Reality
- P vs. NP and what is a Turing Machine (TM)?
- Parallel Programming on a CPU with AVX-512
- Parallel Programming on an NVIDIA GPU
- Python’s Sympy Module and the Cayley-Hamilton Theorem
- Recursion in Programming and When to Use or Not to Use It
- Learn Simple Python Debugging with Pdb
- Simple Python Debugging with Pdb: Part 2
- The Joy of Processing
- The Rise of AI in STEM – Part 2
- Why ChatGPT Is Not Reliable

### Interviews

Interviews

- MathJax Developer: Peter Krautzberger
- Interview with Astronomer Pamela Gay
- Interview with Biologist Jim McNamara
- Interview with a Biophysicist: Andy Resnick
- Interview with Chemical Physicist: DrClaude
- Interview with a Chemist: Borek
- Interview with an Electrical Engineer: Berkeman
- Interview with an Engineer: Russ Watters
- Interview with Instrument Engineer Jim Hardy
- Interview with a Mathematical Physicist: John Baez Part 1
- Interview with Mathematical Physicist John Baez Part 2
- Interview with Physicist David Hestenes
- Interview with Mathematician Fresh_42
- Interview with Mathematician and Physicist Arnold Neumaier
- Interview with a Mentor: Drakkith
- Interview with Physicist David J. Griffiths
- Interview with a Physicist: Doc Al
- Interview with a Physicist: Sean Carroll
- Interview with a Physicist: ZapperZ
- Interview with Physics Mentor bhobba
- Interview with a Physics Mentor: Nugatory
- Interview with a Physics Mentor: PeterDonis
- Interview with Physics Mentor: Stevendaryl
- Interview with Science Advisor DrChinese
- Interview with Theoretical Physicist Carlo Rovelli
- Interview with Theoretical Physicist Clifford V. Johnson
- Interview with Theoretical Physicist Garrett Lisi
- Interview with Theoretical Physicist: Sabine Hossenfelder
- Interview with Astrophysicist Adam Becker
- Interview with Astrophysicist D H
- Interview with Biologist Ryan_m_b
- Interview with Engineer Chestermiller
- Interview with Engineer jrmichler
- Interview with Engineer Mentor anorlunda
- Interview with Mathematician Mark44
- Interview with Mentor Evo
- Interview with Mentor Integral
- Interview with Mentor LisaB
- Interview with Niels Tuning a LHCb Run Coordinator
- Interview with Physicist Dale
- Interview with Physicist George Jones
- Interview with Physicist jtbell
- Interview with Theoretical Physicist Michio Kaku
- Q&A With Universe Today’s Astronomer Fraser Cain
- Q&A Interview with Physicist Michio Kaku

### Quizzes

Quizzes

- Ice Quiz: All About Ice Trivia
- Grab Bag Science Quiz and Trivia
- Albert Einstein Quiz: How Well Do You Know Albert Einstein?
- Inventions and Inventors Quiz and Trivia
- It’s Elemental! The Periodic Table Quiz
- Match the Scientist with the Story Quiz
- Name the Science Book Author Quiz
- Name the Science Photo Quiz
- Name the Scientist Quiz and Trivia
- PF Insight Scavenger Hunt 2
- PF Insights Scavenger Hunt
- NASA Quiz and Trivia: Test Your NASA Knowledge
- Isaac Newton Quiz: Test Yourself on Isaac Newton
- Moon Quiz: Test Yourself on the Moon
- Richard Feynman Quiz: Think You Know Richard Feynman?
- Stephen Hawking Quiz: Think You Know Stephen Hawking?
- LHC Quiz: Think You Know about the LHC?
- Pluto Quiz: Think You Know Pluto?
- Which Scientist Said What Quiz