PinnedNick SchotThe Synergy of Computational Physics, AI, and Complex SystemsThis article delves into my current field of study as a Master’s student, offering insights into the fascinating intersection of physics…Sep 7, 2023Sep 7, 2023
PinnedNick SchotThe Sum of Powers —New Equations and A Unique Derivation of Faulhaber’s Formula1¹²+2¹²+3¹²+4¹²+5¹²+ · · · + n¹²= ?Jan 11, 20231Jan 11, 20231
PinnedNick SchotQuantum Mechanics Decoded: A Math-Friendly Guide (I)“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” —…Jun 20, 2023Jun 20, 2023
PinnedNick SchotinPhysicsFromScratchLet’s Derive The Catenary Equation With CalculusWhat is a catenary?Nov 19, 2021Nov 19, 2021
Nick SchotUnderstanding the Otto Cycle: The Heart of Your Car’s EngineThe Otto cycle, named after Nikolaus August Otto who invented it in the 1870s, is a set of processes used by typical four-stroke internal…Apr 10Apr 10
Nick SchotUnraveling the Coin Toss: Probability, Independence, and the Gambler’s FallacyThe toss of a coin is one of the simplest experiments one can perform to understand the fundamentals of probability and statistics. This…Apr 9Apr 9
Nick SchotSimple Derivation Faulhaber’s Formula — Taylor Expansions and Generating Functions1¹⁰⁰+2¹⁰⁰+3¹⁰⁰+…+n¹⁰⁰=?Apr 29, 2023Apr 29, 2023
Nick SchotinPhysicsFromScratchSo You Want To Teach Yourself Physics . . . ?““How long will it take me to master physics?” a prospective student asks. “How long do you expect to live?” is the only respectable…Nov 29, 20212Nov 29, 20212
Nick SchotinPhysicsFromScratchDerivation Catenary Equation With Calculus of VariationsSometimes it’s useful to directly apply the Calculus of Variations to physical systems. A common example is the application to the…Nov 19, 20212Nov 19, 20212
Nick SchotinPhysicsFromScratchIntroduction to the Philosophy of Physics — A Study Guide“I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many…Nov 16, 20212Nov 16, 20212