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Open Courseware and Resources (general)- Mathematics: body of knowledge centered on such concepts as quantity, structure, space and change and also the academic discipline that studies them (Wikipedia).
Mathematics - Open Courseware (OCW)
aims to explain interesting mathematics to a broad audience, to introduce exciting new research directions for geometry, and to fix some of the logical weaknesses of modern pure mathematics; Rational Trigonometry (much simpler, more powerful), Linear Algebra, Algebraic Topology, History of Mathematics, Universal Hyperbolic Geometry, Foundations of Mathematics
Java simulations: nonEuclid (Interactive Java software for creating ruler & compass constructions), paper-folding-fractals (Java software & HTML documentation), DFIELD & PPLANE (interactive tools for differential equations), CrystalLab (exploring interaction of light, crystals, & water droplets)
Elementary Mathematics, First Year Calculus, Discrete Mathematics, Linear Algebra, Miscellaneous Topics in First Year Mathematics, Multivariable and Vector Analysis, Introduction to Complex Analysis, Fundamentals of Analysis, Linear Functional Analysis, Introduction to Lebesgue Integration, Elementary Number Theory, Distribution of Prime Numbers, Lectures on Irregularities of Point Distribution
explores two revolutions in perception of the universe, Galileo (realization that what we see in the heavens—the moon, the planets, the sun and stars—are physical objects), Einstein (space and time are not as straightforward as they first appear, but related to each other in a simple but unexpected way)
A Tom Lehrer classic but as the uploader of this video comments - "btw don't take it seriously! Lobachevsky was a great mathematician ..."
theory of computability, Gödel's theorem, applications, Church's theorem, Tarski's theorem, Gödel's second incompleteness theorem
fundamentals of game theory and mechanism design, Motivations drawn from engineered/networked systems, emphasizes theoretical foundations, mathematical tools, modeling, and equilibrium notions in different environments
pass integrals to 'Mathematica' for instant evaluation: history of integration, inside the integrator, FAQ
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