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#Pure Mathematics

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Maths Explained

A-Level Exams - Sample Assessment

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Comprehensive practice with sample A-level Pure Mathematics and Statistics & Mechanics exams, aligned with Edexcel's new specification, to prepare students for the rigorous assessment format.
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3 Lesons
6 hours
On-Demand
Free-Video
University of Oxford

Knotty Problems - Marc Lackenby

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Explore knot theory, topology, and unsolved mathematical problems with Professor Marc Lackenby in this engaging lecture on the fascinating world of knots and their applications.
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12 Lesons
52 minutes
On-Demand
Free-Video
Maths Explained

A-Level 2021 Practice Exams

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Practice exams for A-level Pure Mathematics and Statistics & Mechanics, featuring Edexcel-style questions to prepare students for 2021 examinations.
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3 Lesons
4 hours 30 minutes
On-Demand
Free-Video
Institute for Advanced Study

Combinatorial Invariance: A Case Study of Pure Math / Machine Learning Interaction - Geordie Williamson

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Explore the intersection of pure mathematics and machine learning through the lens of combinatorial invariance, featuring insights on neural networks and their application to mathematical conjectures.
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16 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Multivariate Method of Moments: From Sample Complexity to Implicit Computations - 2023

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Explore o método de momentos multivariados, sua complexidade amostral e cálculos implícitos na matemática aplicada e industrial, com insights da teoria pura.
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1 Lesons
53 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Mathematical and Computational Challenges in Quantum Computing - IPAM UCLA

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Explore mathematical and computational challenges in quantum computing through workshops and collaborations, focusing on empowering mathematics to impact quantum information science and vice versa.
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7 Lesons
20 minutes
On-Demand
Free-Video
Insights into Mathematics

The Big Mathematics Divide - Between "Exact" and "Approximate" - Sociology and Pure Maths

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Explores the divide between exact and approximate theories in pure mathematics, challenging conventional views on arithmetic, algebra, topology, and number theory, including the Riemann Hypothesis.
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7 Lesons
41 minutes
On-Demand
Free-Video
Insights into Mathematics

Is Pure Mathematics Logically Viable? Five Challenges - Sociology and Pure Maths

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Exploring five challenges to pure mathematics' logical viability, this talk critically examines the field's foundations and encourages reevaluation of its core principles and practices.
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6 Lesons
22 minutes
On-Demand
Free-Video
Insights into Mathematics

The One Dimensional Random Walk Hypergroup - Diffusion Symmetry

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Explore affine transformations, representation theory, and random walks on a 1D lattice. Learn about hypergroups and calculate probabilities in this advanced mathematics lecture.
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10 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

Curt Jaimungal Interview and Theories of Everything - Sociology and Pure Maths

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Exploring diverse topics from physics and mathematics to consciousness and UFOs, this wide-ranging interview delves into theories of everything, sociological aspects of science, and the intersection of academic disciplines.
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20 Lesons
1 hour 20 minutes
On-Demand
Free-Video
Insights into Mathematics

Particle Collisions, Hypergroups and Quadratic Residues - Diffusion Symmetry 3

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Explore particle collision models, hypergroups, and quadratic residues in algebraic structures. Learn about fusion rule algebras, complete graphs, and primitive roots in prime fields.
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11 Lesons
41 minutes
On-Demand
Free-Video
Insights into Mathematics

History of Geometry IV - The Emergence of Higher Dimensions - Sociology and Pure Maths

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Explore the emergence of higher dimensions in 19th-century geometry, including projective geometry, cyclography, and spaces of lines and curves, revolutionizing our understanding of mathematical spaces.
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7 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

The S3 Character Table - A New Meaning - Diffusion Symmetry

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Explore the S3 character table from a diffusion symmetry perspective, uncovering new interpretations in group theory, combinatorics, and algebraic structures.
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12 Lesons
45 minutes
On-Demand
Free-Video
Insights into Mathematics

Emile Borel - Real Number Enthusiast or Skeptic? - Sociology and Pure Mathematics

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Explore Emile Borel's contributions to measure theory and his skepticism about real numbers, including normal numbers and the intriguing concept of a "know-it-all" number.
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5 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Euclid Book 1 Props I - V - A Critical Review - Sociology and Pure Mathematics - N J Wildberger

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Critical review of Euclid's Book 1 Propositions I-V, examining logical foundations and constructions. Explores historical significance and questions modern interpretations of Euclidean geometry.
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8 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

John Keil's Preface to Euclid - Sociology and Pure Mathematics

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Exploration of John Keil's 1723 preface to Euclid's Elements, discussing its historical context and significance in geometry, including comparisons to Isaac Barrow's version.
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5 Lesons
21 minutes
On-Demand
Free-Video
Insights into Mathematics

Sociology and Pure Mathematics - Pure Mathematics Relies on a Fake Arithmetic

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Challenges modern pure mathematics' reliance on "fake arithmetic," proposing alternative approaches to calculus without infinite processes and calling for sociological analysis of mathematical practices.
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8 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

The Perspective Image of a Square III - The Solution

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Explore the solution to projecting a square onto a quadrilateral, delving into geometry, perpendicularity, and perspective. Gain insights into mathematical problem-solving and related concepts.
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8 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

Understanding Uniform Motion - Are Radians Really Necessary? - WildTrig

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Explores the concept of radians, questioning their necessity in uniform motion and examining the distinction between pure and applied mathematics in this context.
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5 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

Newton's Method for Approximating Cube Roots - Real Numbers and Limits Math Foundations

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Newton's method for approximating cube roots: explore cubes, cube roots, and techniques to find approximate solutions. Learn about Taylor expansion, tangent lines, and advanced methods like the weighted Babylonian and quadratic Newton approaches.
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8 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Cubics and the Prettiest Theorem in Calculus - Arithmetic and Geometry Math Foundations

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Explore cubic polynomials, their calculus, and tangent conics. Learn about Etienne Ghys' theorem, considered one of the most beautiful in calculus, with an elegant proof provided.
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6 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

Translating Polynumbers and the Derivative - Arithmetic and Geometry Math Foundations

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Explore polynomials and derivatives algebraically, introducing Taylor polynomials and sub-derivatives. Challenges traditional calculus views, shifting towards Euler and Lagrange's approach to mathematical foundations.
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10 Lesons
37 minutes
On-Demand
Free-Video
Michael Penn

What Is It Like to Be a Pure Mathematician?

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Explore the life of a pure mathematician, delving into abstract algebra, group theory, and partitions. Gain insights into the field's challenges, problem-solving approaches, and the beauty of elegant proofs.
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17 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vidit Nanda - Principal Components Along Quiver Representations

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Principal components analysis for quiver representations: dimensionality reduction, comparison, and optimization techniques for vector-space valued representations across pure and applied mathematics.
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14 Lesons
41 minutes
On-Demand
Free-Video
Fields Institute

The Canonical Base Property and CM-Triviality

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Explore the Canonical Base Property and CM-triviality in model theory, covering key concepts, counterexamples, and applications in Lie algebras and amalgamation.
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14 Lesons
27 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

What Can the Working Mathematician Expect From Deep Learning? - IPAM at UCLA

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Explore deep learning's impact on mathematics, its potential applications, and insights from a pure mathematician's perspective on this emerging field's role in mathematical research.
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1 Lesons
52 minutes
On-Demand
Free-Video
Insights into Mathematics

Logical Weaknesses in Modern Pure Mathematics - Real Numbers and Limits - Math Foundations 87

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Explores logical weaknesses in modern pure mathematics, focusing on inconsistent rigor and problematic definitions. Challenges conventional views and invites discussion on foundational issues in mathematics.
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9 Lesons
27 minutes
On-Demand
Free-Video
Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 112

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Explores the concept of real numbers, challenging their existence and examining how quantities like length, area, and function values are inherently approximate rather than exact 'real' values.
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8 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

MathFoundations Series - 200 Videos Milestone and Future Directions

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Celebrating 200 videos of MathFoundations, reflecting on the series' journey, addressing challenges in modern pure mathematics, and outlining future directions for critical thinking in mathematical foundations.
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7 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

The Fundamental Theorem of Algebra - Challenging Mathematical Orthodoxy

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Challenging the Fundamental Theorem of Algebra: Exploring its limitations, implications for calculus and linear algebra, and the need for a more accurate formulation in rational numbers.
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1 Lesons
23 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Geometry of Tensor Networks and Tensor Invariants

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Explore geometric aspects of tensor networks and invariants, focusing on their applications in mathematics and theoretical physics.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
TEDx

What Makes People Engage With Math

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Discover strategies to make mathematics engaging and accessible with insights from a popular math educator, covering topics from pure math to real-world applications.
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1 Lesons
19 minutes
On-Demand
Free-Video
SAIConference

Exploring the Creative Union of Artificial Intelligence and Pure Mathematics

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Explore the fusion of AI and pure mathematics, uncovering how machine learning can predict complex mathematical structures and potentially revolutionize theorem proving and scientific discovery.
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14 Lesons
34 minutes
On-Demand
Free-Video