Mathematics
This "wonders of mathematics" resource is dedicated to my grandchildren - it is a work in progress like mathematics itself
A central goal 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.
The aspiration here is to lead the learner child, teen and adult into a innate and intuitive understanding of mathematical relations. To begin the process of thinking like a mathematician, and like a physicist, and a philosopher - to being able to understand how the world actually works. The reality of the universe from the Big Bang to Planks length requires a mathematical appreciation. It requires complex and subtle reasoning divorced from the simplistic view that our senses alone provide.
Part of the strategy here is to set the broad outline of mathematics - its orgins, goals and domains - to create a global appreciation of its importance.
Mathematics is central to the digital economy and to economic security at the individual and the state level and beyond - now and going forward.
Mathematics is central to machine learning and quantum computing and seems likely to determine the future of our species.
Advances in mathematical understanding 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.
The global economy - and with it the security of billions of people, - is dependent on the platform that mathematics provides for our standard of living and for solving the existential issues that lie before us.
Governments at all levels are focusing on fostering mathematics skills and research.
Central to mathematics is abstraction. Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
The relationship between mathematics and physics has been long and fruitful. It will be discussed below.
And then there is just the mystery, beauty and elegance of this lens on the universe and perhaps what lies beyond.
"Elementary arithmetic is the branch of mathematics that involves the basic operations of addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathematics, elementary arithmetic is generally the first branch of mathematics taught in schools."
Mathematical Notation
"Math, too, is like a foreign language. Expressions are words and equations are sentences. There are precise rules for notating mathematical thought."
We need to start when young to understand the vocabulary of mathematics if we are to escape the memorization trap that leads to non comprehension and ultimately the mathematical thinking offramp.
Mathematics Acronyms and Symbols
Branches of Pure Mathematics
Branches of Applied Mathematics
Branches of Applied Mathematics - Other
Mathematics Software
Matlab, Mathematica, Maple, PARI, SAGE and Excel
British Columbia Mathematics
International Mathematical Organizations
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Wiki: List of Mathematics Journals
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Taylor & Francis on line: Mathematics and Statistics
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Wiki: Mathematics journals
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arXiv Mathematics - Open Access
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Open Access Mathematics Journals
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Canadian Mathematical Society
"Popular" Mathematics News Sources
Mathematics Channels on You Tube
Mathematics for Machine Learning
Online Mathematics Courses, Tutors and Coaching
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?
Mathematics for young children - and teens
The Lean mathematical library, mathlib
"The Lean mathematical library, mathlib, is a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. "
Mathematics Links to be organized
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