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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).
art of guessing results and solving problems without doing a proof or exact calculation, techniques (extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, pictorial analysis), applications (mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, differential equations): readings, related resources
Estimation of Average Treatment Effects Under Unconfoundedness, Linear Panel Data Models, Regression, Discontinuity Designs, Nonlinear Panel Data Models, Instrumental Variables with Treatment Effect, Heterogeneity, Control Function and Related Methods, Bayesian Inference Cluster and Stratified Sampling, Partial Identification, Difference-in-Differences Estimation, Discrete Choice Models, Missing Data, Weak Instruments and Many Instruments, Quantile Methods, Generalized Method of Moments and Empirical Likelihood
includes java applets to explore mathematical concepts & topics: interactive exploring and tutorials in precalculus (equations in two variables, functions & graphs, inverse of a function and one to one functions, explore other functions, exponential and logarithmic functions, hyperbolic functions, trigonometry, systems of equations, polar coordinates & equations, polynomials, rational functions, matrix multiplication, geometry), online algebra & trigonometry tutorials, graphing, online problems & self tests with answers, calculus tutorials
mathematical concepts behind important modern applications: Cryptography, Error correction & compression, Probability & Statistics, Birth, Growth, Death & Chaos, Graph Theory, Voting & Social Choice
set of visual and computational tools designed to help students better visualize concepts of Calculus: Scientific calculator, tools (plotting, Numerical, Linear algebra, Differential equations), Content-specific applications, Other Calculus visualization tools, Tutorial-style help system
numerical linear algebra & methods for solving ordinary differential equations, linear systems of equations, least square, eigenvalue & singular value problems: tools
statistics tools for internet and classroom instruction (for business, social science, or liberal arts, important statistical & probabilistic concepts,subjective decisions, pitfalls in analyzing data & making inferences from numbers): notes, tools (binomial histogram, calculator, chi-square distribution, controlling for variables, confidence intervals, correlation & regression, histogram, law of large numbers, normal approximation to data, normal curve & probabilities, calculator, sampling distributions, scatterplots, Student's t distribution, Venn diagrams)
math, fractals, logic, paradoxes, infinities, art, language, computer science, physics, music, intelligence, consciousness, unified theories, based on Douglas Hofstadter's Pulitzer Prize winning book, higher dimensions of recursive thinking
numerical methods, initial-value problems, network flows and optimization: Readings, Projects, Study Materials
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