Understanding Variable Fonts and Their Web Applications - Learn With Jason
Explore variable fonts with Jason Pamental: learn how they enhance web performance and art direction, with practical demos and implementation tips for immediate use in web projects.
A Formula for the Circumference of an Ellipse
Explore the mathematical derivation of an approximate formula for calculating the circumference of an ellipse, including its historical context and practical applications.
Oxford Calculus: How to Solve the Heat Equation
Learn to solve the Heat Equation, a fundamental PDE in calculus, with Oxford mathematician Dr Tom Crawford. Includes practice questions, interactive worksheets, and a free calculator app for comprehensive understanding.
Oxford Calculus - Separation of Variables Integration Technique Explained with Examples
Learn to solve first order separable differential equations using the separation of variables method, with worked examples and practice exercises from an Oxford mathematician.
Oxford Calculus - Jacobians Explained
Comprehensive explanation of Jacobians in 2D coordinate changes, focusing on polar coordinates. Includes derivation of general formula and practical applications with interactive exercises.
Oxford Linear Algebra - Linear Transformations Explained
Explore linear transformations with Oxford mathematician Dr Tom Crawford, covering definitions, properties, and examples in R3, including matrix multiplication and differentiation.
The Story of Mathematical Proof - From Ancient Greece to Modern Logic
Explore the evolution of mathematical proof across number theory, geometry, topology, and logic, delving into the fascinating gap between natural and real numbers.
Integral Calculation with an Unexpected Twist
Explore an intriguing integral problem with an unexpected twist, enhancing problem-solving skills and mathematical intuition.
Integral Analysis - Lessons from a Complex Problem
Explore the rich insights and techniques hidden within a complex integral, uncovering multiple mathematical concepts and problem-solving strategies.
Archimedes' Area Formula for Archimedean de Casteljau Bezier Cubics - Lecture 8
Discover a new cubic version of Archimedes' Parabolic Area Formula for special de Casteljau Bezier curves. Explore the Archimedean condition and its fascinating geometric connections.
Chebyshev and Spread Polynumbers - Exploring the Goh Factorization
Explore polynomials in number theory, focusing on Chebyshev and spread polynomials. Learn about the Goh factorization and its implications for modern mathematics and computation.
Difficulties with Real Numbers as Infinite Decimals - Part 1
Explores challenges in defining real numbers as infinite decimals, examining advantages and drawbacks of the infinite choice approach, and discussing historical debates on arithmetic laws and mathematical foundations.
Newton's Method for Finding Zeros - Real Numbers and Limits
Explore Newton's method for finding zeros, focusing on quadratic functions and approximating square roots. Learn about tangent lines, recursion, and practical applications in mathematics.
Calculus on the Unit Circle - Arithmetic and Geometry Math Foundations 78
Explore algebraic calculus on unit circles, covering subderivatives, Taylor expansions, tangents, and 3D visualizations. Gain insights into foundational mathematics with a unique approach to this fundamental topic.
Lines and Parabolas - Quadratic Polynomials and Geometric Relations
Explore advanced parabola concepts: algebraic calculus, subderivatives, tangent lines, Taylor expansions, and geometric relations. Learn to analyze and graph parabolas using completing the square method.
Tangent Lines and Conics of Polynomials - Math Foundations 71
Explore tangent lines and conics of polynomials using polynumbers. Learn to define tangents, compute approximations, and understand Taylor expansions in this advanced mathematical exploration.
Calculus with Integral Polynumbers - Arithmetic and Geometry Math Foundations 70
Explore calculus with integral polynumbers, covering Pascal's Array, Taylor polynumbers, derivatives, and subderivatives. Learn alternative approaches to traditional calculus concepts and their applications.
Applications of Rational Spherical Trigonometry - Universal Hyperbolic Geometry Lecture 43
Exploring rational spherical trigonometry through a specific spherical triangle example, demonstrating its connection to hyperbolic geometry and three-dimensional space.
The Mostly Absent Theory of Real Numbers - Math Foundations 115
Explores flaws in standard treatments of real numbers in calculus and analysis textbooks, challenging conventional thinking and advocating for a more rigorous mathematical foundation.
Real Numbers and Cauchy Sequences of Rationals - Math Foundations 111
Explores Cauchy sequences of rational numbers as a foundation for real numbers, discussing limits, equivalence classes, and the logical challenges in this approach to constructing the real number system.
Limits to Infinity - Real Numbers and Limits
Exploring limits of sequences approaching infinity, focusing on rational polynomials and functions. Introduces a simplified definition for verifying limits as finite tasks.