Notes on various mathematical topics An Interesting Integral Involving The Golden Ratio \pi^\pi = ? A Few Notes on Harmonic Oscillators and Fields (WIP) A Few Notes on Functional Analysis (WIP) A Few Notes on the Brachistochrone Problem A Few Notes on the Principle of Least Action and Newton’s Second Law of Motion A Useful Mathematical Trick, Telescoping Series, and the Infinite Sum of the Reciprocals of the Triangular Numbers A Few Notes on Euler’s Formula and Euler's Identity A Few Notes on Euler’s Product Formula and the Riemann Zeta Function A Few Notes on Euler's Solution of the Basel Problem A few notes on the Dirac Delta Function and the Laplace Transform Why do parallel lines appear to meet in the distance? A few notes on Projective Geometry A bit on a structural correspondence between rings and groups Is i^i a real number? A bit on infinite series Proof that the sqaure root of 2 is irrational A Few Notes on the Division Algorithm (WIP) Notes on Groups, Rings, and Fields A Few Notes on Cayley's Theorem A Few Notes on Group, Ring and Field Theory (warning: WIP) A Few Notes on Change of Basis A Few Notes on Algebriac Structures (WIP) Some notes on Density Operators, Expectation Values, and Matrix Shapes A Few Notes on Bell States, Superdense Coding, and Quantum Teleportation Notes on the Bloch Sphere Notes on the Dual Beam Splitter Experiment Just for fun Can You Spot The Error? Happy New Year 2022! What is the difference in our ages? Happy New Year 2021! Fermat's Christmas Theorem Merry Christmas! Last Update: 01.23.2022 by dmm@1-4-5.net