Mathematics
Mathematics is not what most people take it to be. It is a vaste and evolving field with the likelihood of more future than past.
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 deepening one's mathematical insights and using the tools it provides to appreciate the mysteries of reality.
The aspiration here is to lead the learner child, teen and adult into a innate and intuitive understanding of mathematical relations and to begin the process of thinking like a mathematician, and a physicist, and a philosopher. Mathematics is essential to being able to understand how the world actually works. The reality of the universe, from the cosmological horizon of the Big Bang to infinitly miniscule dimension of Planks length, requires a mathematical appreciation. It requires 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 origins and importance. Another part is to relate mathematics to the central physics problems of our time. The approach is tops down, smorgasbord way of enticing the explorer further into the clearest explorations of the very fabric of the universe.
Mathematics is central to the digital economy and to economic security at the individual level, the state level and world level - now and going forward.
Mathematics is fundamental to machine learning and quantum computing and seems likely to determine the future of our species.
Advances in mathematical understanding can lead to sudden spurts of innovation and technological discontinuities. Mathematics is worthy of more public and private investment than our current cultural matrix permits. Mathematical insight can lead to strategic surprises that 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 our species.
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.
One way to advance your mathematical understanding is to make a commitment to yourself to spend an hour a day reading what you find here. Start by bookmarking this page. Put this item on you morning To Do List and keep it near the top. Fair warning - recreational mathematics can be addictive, and with time you may find that your worldview changes and with it conversation discontinuities with friends and family may also occur. :-) Persist.
Mathematics Study Skills and Character
Scholastic Aptitude Testing -
Proficiency in mathematics is achieved by being given early and rigourous mathematics opportunities. It is the doorway to a broad array of careers and life experiences. Poor early instruction can be a barrier to entry into higher education.
The SAT (Scholastic Aptitude Test) is a standardized test widely used for college admissions in the United States. It assesses students' readiness for college by evaluating their skills in reading, writing, and math. The test is typically taken by high school juniors and seniors, and the scores are used, along with high school GPA, to help colleges make admissions decisions.
Many students prepare for the SAT using books, classes, online courses, and tutoring, which are offered by a variety of companies and organizations.
STEP (Sixth Term Examination Paper) is a challenging mathematics exam in the UK used by universities, particularly Cambridge University, as part of conditional offers for mathematics and related degrees. It assesses problem-solving skills and the ability to tackle undergraduate-level mathematics.
"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 - Symbols and conventions
"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 Wordprocessing
To bring your calculations to the screen elegantly a specialized typesetting system is required.
Typesetting mathematics on a computer has always been a challenge. The mathematical community almost universally accepts a typesetting language called LaTeX.
Mathematics is a language all its own.
Branches of Pure Mathematics
Branches of Applied Mathematics
Branches of Applied Mathematics - Other
Mathematics Software and Tools
Matlab, Mathematica, Maple, PARI, SAGE and Excel
British Columbia Mathematics
Mathematics Contests and Introductions
International Mathematical Organizations
Canadian Mathematical Society
"Popular" Mathematics News Sources
Mathematics Channels on You Tube
Metrology - the science of measurement
Mathematics, metrology and physics have marched hand in hand since the beginning of mathematics
Mathematics for Machine Learning and Machine Learning for Mathematics
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YT: Interview: Why Machines Learn: The Elegant Math Behind AI with Anil Ananthaswamy (March 21, 2025)
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YT: Talk: Yann LeCun "Mathematical Obstacles on the Way to Human-Level AI" (March 21, 2025)
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Epoch AI - FrontierMath — benchmarking AI against advanced mathematical research
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Nature: Deep learning:Yann LeCun, Yoshua Bengio & Geoffrey Hinton (See references fo history) (May 27, 2015)
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YT: Math Encounters: "Under the Hood: The Mathematics of AI" with Rebecca Willett (June 4, 2025)
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PNNL: How Math Reveals the Bleeding Edge of AI. Formal mathematics is a natural partner of AI (May 5, 2025)
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Book: Mathematics for Machine Learning
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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.
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The Mathematics of Machine Learning (July 8, 2016)
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The Deep Learning textbook MIT Press by Ian Goodfellow and Yoshua Bengio and Aaron Courville
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Mathematics for Machine Learning full Course || Linear Algebra || Part-1
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You Tube General search Mathematics for Machine Learning
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MIT OpenCourseware: Lecture: Mathematics of Big Data and Machine Learning (November 9, 2018)
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Via Github: Draft: Mathematics for Machine Learning pdf (February 27, 2020)
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Github: NuminaMath-CoT: NuminaMath, a very large database of mathematical problems and proofs (860,000 entries)
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Project Numina
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Mathematics Spacial Concepts
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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 Open Courseware from Universities
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, Computer Science and Energy Consumption
Talks by Professor Raymond Flood - mathematician, historian, communicator, champion of adult learners and part time students
The Fields Medal is awarded every four years on the occasion of the International Congress of Mathematicians to recognize outstanding mathematical achievement for existing work and for the promise of future achievement.
Mathematical Concepts: Blowing up, Mathematical Limits,and Singularities
Calculus Courses for Students, Professionals and Teachers
Mathematics Links to be organized
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