The Path of Mathematics

This is a list of math resources collected from the college STEM students. In case you don't know what is STEM, it is short for Science, Technology, Engineering and Mathematics :) 1. All Level Resources (K12 - College) There are some pretty organized math websites, which covers most of the topics from basic arithmetic to college math, such as Algebra or Precalculus. Khan Academy  Feature: Videos, cover all level of math topics, have good quizes https://www.khanacademy.org/math/precalculus/trig-equations-and-identities-precalc/using-trig-identities-precalc/a/trig-identity-reference Math is Fun Feature: Text file & pictures, easy to understand https://www.mathsisfun.com/ 2. College Math Paul's Online Math notes Feature: Nice class handout, cover first two years college math classes such as calculus, linear algebra and differential equations. http://tutorial.math.lamar.edu/ 3 Blue 1 Brown Feature: Videos, connect abstract math concept to g...

April 30 Claude Shannon and Information Theory      Claude Shannon, “the father of information theory”, was born on April 30, 1916. Shannon was an American mathematician, electrical engineer and cryptographer. His most famous theory, the information theory, is used widely nowadays in data compression, information encryption and quantum computing. You may use the word “bit” a lot and wondering where this strange word comes from. Well, it comes from Shannon! In 1948, Shannon published a famous paper, A Mathematical Theory of Communication, and used the “bit”, short for “binary digits”, to describe the size of information. After that, this unit of information was accepted and used all over the world. Thanks to Shannon, now we can use math to measure information. The word “entropy” is used to describe the uncertainty of the information. The higher the entropy, the more possible combinations we have, which means it is harder to guess the “real” combination. This concept is ...

You might feel math is difficult. Well, yes and no. Math is difficult because you have to understand everything to move on, rather than just dump them in your brain without chewing. However, math is approachable. Math is not a magic, but a systematic subject. There's clear paths. The Path of Math: Stage 1: Math before college Arithmetic Algebra Geometry Trigonometry Precalculus Stage 2: First two years college (aka lower level math) Calculus (3-4 courses) Differential Equation Linear Algebra Statistics Stage 3: Third and Fourth college (aka upper level math) Introduction to proof Algebra  Analysis Other topics such as Topology, Differential Equations, depends on the program The earlier subjects are usually prerequisite for later subjects. For example, Analysis is proof based. So taking a proof class will help you success in Analysis.  There are many good resources to help learning, I have shared some website I personally like on another blog named Useful Math Reso...