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Mathematics - Under construction


This "wonders of mathematics" resource is dedicated to my grandchildren

Advances in mathematical understanding can lead to sudden spurts of innovation and technological discontinuities. Mathematical insight can therefore lead to strategic surprise that can provide economic, scientific and technological breakthroughs which can have profound geopolitical significance. For example, the global economy, and with it the security of billions of people, is dependent on the security of "unbreakable" (mathematical) codes. But are they unbreakable?

This is why the major global players as well as some of the smaller ones place such emphasis on mathematics research and why the job title algorithm engineer has come into existence.

There are several possible developments that might lead to the Singularity - a mathematics breakthrough is one of them.

And then there is just the mystery, beauty and elegance of this lens on the universe and perhaps what lies beyond.

A central goal of this page is to answer the question: "Where is this going and why?" that is so often never explained to the student up front and which is so central to creating excitment and the will to wrestle with the problems of deepening one's mathematical insights and using the tools it provides.

Mathematics is central to the digital economy and to economic security at the individual and the state level now and going forward.

    

Mathematics Overview

  Wiki: Lists of mathematics topics
  
  A new method for boosting the learning of mathematics (December 23, 2019)
  
  Wiki: Project Mathematics
  
  The Times Higher Education: Top Mathematics and Statistics Universities
  
  University of Waterloo - Mathematics Course List
  
  Stanford Mathematics Course list
  
  Quanta Magazine: The Map of Mathematics
  
  EthnoMathematics
  
  Wolfram Alpha
  

Mathematical Notations - "Math, too, is like a foreign language. Expressions are words and equations are sentences. There are precise rules for notating mathematical thought."

  Notation Guide for Precalculus and Calculus Students - Sean Raleigh
  
  Wiki: Mathematical Notation - a system of symbolic representations of mathematical objects and ideas
  
  Basic Math Symbols
  
  Type mathematical symbols online keyboard
  
  MathJax - a cross-browser JavaScript library that displays mathematical notation in web browsers, using MathML, LaTeX and ASCIIMathML markup
  
  MathML is a low-level specification for mathematical and scientific content on the Web and beyond.
  
  LaTeX is a high-quality typesetting system; it includes features designed for the production of technical and scientific documentation.
  
  AsciiMath is an easy-to-write markup language for mathematics
  

Branches of Pure Mathematics

  Algebra:
  
  Calculus: Calculus studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change.
  
  Probability theory is a mathematical framework for representing uncertainstatements
  
  Wiki: Probability Theory
  
  Information theory enables us to quantify the amount of uncertainty in a probability distribution
  
  Geometry and topology
  
  Logic
  
  Number Theory
  
  Combinatorics
  

Branches of Applied Mathematics

  Dynamical systems and differential equations
  
  Mathematical physics
  
  Computation
  
  Information Theory and signal processing
  
  Probability and statistics
  
  Game theory
  
  Operations Research
  

Branches of Applied Mathematics - Other

  Mathematical Economics
  
  University of Waterloo Mathematical Economics - What can you do with a degree in Mathematical Economics?
  

Mathematics Talks

  Lex Fridman interview with Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare (December 30, 2019)
  
  Lex Fridman interview with Donald Knuth: Algorithms, Complexity, Life, and The Art of Computer Programming | AI Podcast (December 30, 2019)
  

Mathematics Software

Matlab, Mathematica, Maple, PARI and SAGE

  Matlab
  
  Mathematica
  
  Maplesoft
  
  PARI
  
  SAGE
  
  Google General Search - Mathematics Software Reviews
  

British Columbia Mathematics

  
  

Mathematics Contests

  Canadian Senior and Intermediate Mathematics Contests
  
  
  

Mathematics Institutes

  Quantum Algorithms Institute at SFU
  
  The Banff International Research Station (BIRS)
  
  Institute for Pure & Applied Mathematics (IPAM)
  
  Pacific Institute for the Mathematical Sciences (PIMS, Canada) Twitter: @pimsmath
  
  Mathematical Sciences Research Institute (MSRI, Berkeley, USA)
  
  Institute of Applied Mathematics (UBC, Canada)
  
  Simons Foundation - Advancing Research in Basic Science and Mathematics
  
  Clay Mathematics Institute
  

International Mathematical Union

  International Mathematical Union
  

Canadian Mathematical Society

  Canadian Mathematical Society Twitter: Canadian Mathematical Society @canmathsociety
  

"Popular" Mathematics News Sources

  Science Daily - Mathematics News
  
  Phys.org - Mathematics News
  
  MIT Mathematics News
  
  Independent UK - Mathematics News
  
  NYT: Mathematics News
  
  Plus Magazine - Mathematics News
  
  The 10 Biggest Math Breakthroughs of 2019
  
  arXiv.org > math - arXiv is a free distribution service and an open-access archive for scholarly articles in multiple fields including mathematics, physics, and computer science
  

Mathematics Channels on You Tube

  Numberphile
  
  Khan Academy Math
  
  Worldwide Center of Mathematics
  

History of Mathematics

  Wiki: Hisory of Algebra
  
  Your Tube General Search History of Mathematics
  
  Google General Search History of Mathematics
  
  Kurt Godel: A postard from Vienna - Kurt Godel was one of the greatest mathematicians of the 20th century
  

Mathematics for Machine Learning

  Coursera: Imperial College London: Mathematics for Machine Learning. Getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science.
  
  The Mathematics of Machine Learning (July 8, 2016)
  
  The Deep Learning textbook MIT Press by Ian Goodfellow and Yoshua Bengio and Aaron Courville
  
  Mathematics for Machine Learning full Course || Linear Algebra || Part-1
  
  You Tube General search Mathematics for Machine Learning
  
  MIT OpenCourseware: Lecture: Mathematics of Big Data and Machine Learning (November 9, 2018)
  
  Via Github: Draft: Mathematics for Machine Learning pdf (Februar 27, 2020)
  

Online Mathematics Courses, Tutors and Coaching

  Oppia Mathematics - Learning Library
  
  The 10 Biggest Math Breakthroughs of 2019
  
  Mathematics - U Waterloo - Centre for Education in Mahematics and Computing Courseware
  
  Vedantu
  
  Brillant.org
  
  Socratica What is a Vector Space? (Abstract Algebra)
  
  3Blue1Brown Vectors, what even are they? | Essence of linear algebra, chapter 1
  
  3Blue1Brown Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2
  
  The Trev Tutor: [Discrete Mathematics] Introduction to Sets
  
  Brilliant Courses
  

Mathematics Resources

  Wolfram MathWorld
  
  MIT Open Courseware - You Tube
  
  Stanford University YOUCUBED inspire, educate and empower teachers of mathematics
  
  
  

Mathematics Syllabus (an outline of the subjects in a course of study or teaching)at various institutions

You might note the degree of user friendliness in the outline. Does it explain what each area of mathematics is useful for so that prospective students can make informed decisions?

  The British Columbia Mathematics curriculum
  
  The Ontario Elementary Mathematics Curriculum
  
  UBC Math Twitter: UBC Math Department @ubcmath
  
  University of Waterloo Faculty of MathematicsWaterloo Mathematics @WaterlooMath
  
  Ontario Elementary Mathematics Curriculum
  
  Waterloo Mathematics Twitter: Waterloo Mathematics @WaterlooMath
  
  Oxford Mathematics Twitter: Oxford Mathematics @OxUniMaths
  
  
  

Quantum Algorithms

  arxiv: Quantum Algorithm Implementations for Beginners (April 10, 2018)
  
  Google Books: An Introduction to Quantum Computing Algorithms (April 10, 1999)
  
  Microsoft Research: Workshop on Quantum Algorithms and Devices - Afternoon Sessions I (August 11, 2017)
  
  Google Search Quantum Algorithms
  
  YT:Quantum Algorithms
  
  Institute for Quantum Computing: A Universal Training Algorithm for Quantum Deep Learning (October 15, 2018)
  

AI impact on Mathematics

  Using neural networks to solve advanced mathematics equations (January 14, 2020)
  
  Nature: Simple artificial-intelligence problem puts researchers up against a logical paradox discovered by famed mathematician Kurt Godel.(January 8, 2019)
  
  
  

Mathematics Links to be organized

  Differentiable Programming (December 2015)
  
  Why Machine Learning needs statistics(December 2015)
  
  Causal Thinking in the Twilight Zone Judea Pearl (July 2015)
  
  Claimed Breakthrough Slays Classic Computing Problem; Encryption Could Be Next (November 2015)
  
  Critical Algorithm Studies: a Reading List (November 2015)
  
  New general-purpose optimization algorithm promises order-of-magnitude speedups on some problems (October 2015)
  
  P vs. NP and the Computational Complexity Zoo
  
  UBC Presentation: STOCHASTIC LOCAL SEARCH FOUNDATIONS AND APPLICATIONS Introduction: Combinatorial Problems and Search (Holger H. Hoos & Thomas Stutzle)
  
  Avi Wigderson on the "P vs. NP" problem - Efficient computation, internet security & the limits to human knowledge
  
  Major advance reveals limits of computation - Maybe?
  
  Sebastian Seung's Quest to Map the Human Brian - Mathematics
  
  Algorithms for the Satisfiability (SAT) Problem: A Survey (1996)
  
  Amoeba-inspired computing system outperforms conventional optimization methods
  
  Complexity No Bar to AI
  
  Stephen Wolfram: Computation and the Future of Mathematics
  
  Stephan Wolfram: Is Mathematics Invented or Discovered
  
  Stephan Wolfram:The Background and Vision of Mathematica
  
  Aaron Sloman: "Evolution, robots and mathematics"
  
  Common Probability Distributions: The Data Scientist�s Crib Sheet (December 2015)
  
  Gunnar Carlsson: The Shape of Data - Topological Mapping (September 2015)
  
  Austin Fowler: Quantum computing and the need for new algorithms
  
  The Achampong Theorem and national security
  
  Unconventional Computing - beyond Von Neuman and Turing - MULTI-level logic variables
  
  Method to shortcut simulations to reach previously unreachable timescales & ID practicable problems
  
  Godel's Lost Letter and P=NP (with Blogroll)
  
  Efficient discovery of overlapping communities in massive networks
  
  The Baffling and Beautiful Wormhole Between Branches of Math - Euler�s identity
  
  Live Fourier Transform demo, showing small-angle scattering patterns for some structures
  
  Look at Nothing - Blog on small-angle scattering
  
  Stanford University: Lecture 1 | The Fourier Transforms and its Applications
  
  Scott Aaronson - Thought experiments: Is There Anything Beyond Quantum Computing?
  
  Primes - a visual tribute The Riemann Hypothesis
  
   Perhaps we can rigorously develop a science of when large sections of proofs can be effectively handwaved
  
  The real 10 algorithms that dominate our world
  
  Algorithmia - Open Marketplace for Algorithms
  
  Axiomatic method is not fully adequate to the current mathematical practice argued
  
  SF: Dusa McDuff
  
   The research interests of Henry Cohn
  
  Gil Press - A short history of digitization
  
  Encyclopedia of Integrer Sequences (OEIX) - Sloane
  
  The OECD Learning Framework 2030
  
  Inquiry based learning
  

Mathematics for kids

  Math Symbols - the words of a language
  
  Wiki: Math Symbols, Explanations & Examples
  
  MATH & GEOMETRY Vocabulary and Terminology in English
  

Mathematics Calculators and Tools

  You Tube: A quick tutorial on how to enter and use numbers in scientific notation with the google online calculator
  
  Google Calculator Guide
  
  Common Sense.org TOP PICKS | 20 Digital Graphing Tools
  
  Online math calculators and solvers for mathematical calculations
  
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