iBerry

distance, open sets, parametric surfaces & smooth functions, smooth manifolds & scalar fields, tangent vectors & space, contravariant & covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, geodesics & local inertial frames, Riemann curvature tensor, comoving frames & proper time, stress & stress-energy tensor, basic premises of general relativity, Einstein field equations, Schwarzschild metric & event horizons, white dwarfs, neutron stars, black holes

Gambling, Mathematical Modeling to Win
 

snapshot of some lectures, focus on presenting vector calculus in an applied and engineering context while maintaining mathematical rigour, emphasis on examples and proofs
 

mathematics for modeling and reasoning about problems in computer science, useful applications, proof methods to reason about recursive and iterative programs, data structures (graphs, trees, sets, functions and their asymptotic growth, combinatorics and probability, regular languages and finite automata)

Matrix multiplication, Inverting matrices, system of equations, vector combination problem), Singular Matrices, 3-variable linear equations, Equations with 3 Unknowns, Introduction to Vectors, Vector Examples, Parametric Representations of Lines, Combinations and Span, Linear Independence, Subspaces, Dot Product and Vector Length & Properties, Cauchy-Schwarz Inequality, Vector Triangle Inequality, Defining angle between vectors, Defining a plane in R3 with a point and normal vector, Cross Product, Relationship between cross product and sin of angle, dot and Cross Product, Reduced Row Echelon ..................................
 

formal mathematical concepts of computer science, elementary logic, set theory, relations, deduction, induction, algorithmic processes, graph theory, models of computation

differential calculus and applications, introduction to integration
 

basics, graphs, functions and their graphs, equations & inequalities, polynomial & rational functions, exponential & logarithmic functions, systems of equations, some discrete topics, the x-y files
 

The site provides access to a series of lectures and exercises on probability, statistics and econometrics at an intermediate level.