学习笔记《Higher Mathematics outline》

这是我在 youtube 上找到的一个 Higher Mathematics 系列课程，讲的非常的系统，这里摘录一下这个课程的大纲，方便以后自己查阅和复习：
https://www.youtube.com/watch?v=CMWFmjlB8v0&list=PLZzHxk_TPOStgPtqRZ6KzmkUQBQ8TSWVX

这套课程属于一个叫做 project polymath 的项目，Slogan 是 One da Vinci changed the world. Let's create thousands：
http://projectpolymath.org/

An old East Indian legend tells of six blind men exploring an elephant by touch, with the goal of discovering what the elephant looked like. Because each man touched a different, very specific part of the elephant, they failed to see the “big picture” of the whole elephant. This was captured perfectly in the verse of John Godfrey Saxe's poem “The Blind Men And The Elephant”: “Each in his own opinion, Exceeding stiff and strong/Though each was partly in the right, [A]ll were in the wrong!”

Current education paradigms are very much like those blind men. Most schools and universities encourage students to “feel the elephant” in only one very specified subject field, while discouraging or even preventing them from learning about other subjects in depth, though the desire and ambition are there on the students' part. This leaves metaphorically blind graduates who are often unable to move out of the narrow, arbitrarily defined box of their field, and thus they often fail at attempting to solve problems in their field that require more subject integration or a broader knowledge base.

The Project Polymath Trustees have all experienced the frustration of narrow, hyper-specialized educations when they sought a wider base of knowledge and experience in their academic careers. While their stories are varied, common themes thread through all: frustration with a status quo that seeks to narrowly define students' life ambitions, discouragement, perseverance, and the desire for setting a new paradigm that better paves the way toward educational triumph and a better society.

Founder 是 Michael Barnathan：

A programming prodigy, Computer Science PhD, former Googler, successful entrepreneur, education reformer, and aspiring polymath, the ultimate goal of all of my endeavors is to spark a new renaissance.
个人网站：http://michael.barnathan.name/
Twitter：https://twitter.com/mbarnath

大纲

Introduction to Higher Mathematics - Lecture 1: Problem Solving 101
https://www.youtube.com/watch?v=CMWFmjlB8v0

Introduction to Higher Mathematics - Lecture 2: Introduction to Proofs
https://www.youtube.com/watch?v=_x65OJU8Uq4

Introduction to Higher Mathematics - Lecture 3: Propositional Logic
https://www.youtube.com/watch?v=3kzhDsSzKCU

Introduction to Higher Mathematics - Lecture 4: Proof Techniques
https://www.youtube.com/watch?v=WSb9q4Rj2Bg

Introduction to Higher Mathematics - Lecture 5: Set Theory
https://www.youtube.com/watch?v=HoWC0GQWGaA

Introduction to Higher Mathematics - Lecture 6: Predicate Logic
https://www.youtube.com/watch?v=YbNmPievBak

Introduction to Higher Mathematics - Lecture 7: More Proof Techniques
https://www.youtube.com/watch?v=0UgID8C9RvE

Introduction to Higher Mathematics - Lecture 8: Relations
https://www.youtube.com/watch?v=j5cj_4Mk9_M

Introduction to Higher Mathematics - Lecture 9: Functions
https://www.youtube.com/watch?v=Tk5_B7w5fiY

Introduction to Higher Mathematics - Lecture 10: Number Theory
https://www.youtube.com/watch?v=yPrbArbhPxk

Introduction to Higher Mathematics - Lecture 11: Modular Arithmetic
https://www.youtube.com/watch?v=8SHnXUcQ2Nc

Introduction to Higher Mathematics - Lecture 12: Infinity
https://www.youtube.com/watch?v=RZL5bKk9IHs

Introduction to Higher Mathematics - Lecture 13: Construction of the Real Numbers
https://www.youtube.com/watch?v=YW3EDsmj9bo

Introduction to Higher Mathematics - Lecture 14: Topology
https://www.youtube.com/watch?v=FHL4udeLf9Q

Introduction to Higher Mathematics - Lecture 15: Sequences and Functions
https://www.youtube.com/watch?v=rMe8YaoyDBA

Introduction to Higher Mathematics - Lecture 16: Group Theory
https://www.youtube.com/watch?v=WwndchnEDS4

Introduction to Higher Mathematics - Lecture 17: Rings and Fields
https://www.youtube.com/watch?v=syHBApgJhsA

Introduction to Higher Mathematics - Lecture 18: Morphisms
https://www.youtube.com/watch?v=yuzoHGEYWaU

Introduction to Higher Mathematics - Lecture 19: Epilogue
https://www.youtube.com/watch?v=1EfJICPJPMI
第19课是对整个课程的回顾，所以没有大纲