Maths (specialist)

Open Courseware and Resources (specialist)

- Mathematics: body of knowledge centered on such concepts as quantity, structure, space and change and also the academic discipline that studies them (Wikipedia).

Multivariable Calculus

Java applets (Graphing along the x or y-axis, Intoduction to Integration, Riemann Sums, Simpson's Rule, Integration, The Chain Rule, Visualizing Vector Fields for First Order Differential Equations, Graphing Parametric Curves, Graphing Polar Curves, Matrix Utility, Polynomial Interpolation, Divided Differences), calculus problems & solutions

The Mathematics of Computation

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)

Probabilistic Systems Analysis and Applied Probability

formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference: Readings, Recitations, Tools, Related Resources

Mathematical Foundations of Computer Science

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

Game Theory

game theory and strategic thinking, dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, signaling, examples drawn from economics, politics & movies
 

Geometry and Quantum Field Theory

designed for mathematicians is rigorous introduction to perturbative quantum field theory using language of functional integrals, basics of classical field theory, free quantum theories & Feynman diagrams, goal to discuss using mathematical language basic notions and results of QFT necessary to for QFT and String Theory

Stochastic Evolution Equations

Random variables in Banach spaces, Stochastic integration in Banach spaces, Stochastic evolution equations, basic techniques of probability theory in infinite-dimensional spaces and their applications to stochastic partial differential equations, model a stochastic partial differential equation as an abstract stochastic evolution equation on a suitably chosen infinite-dimensional state space and solve this equation using fixed point techniques and stochastic integration in infinite dimensions

Calculus with Theory

Single Variable Calculus, rigorous level, careful reasoning and understanding of proofs, assumes knowledge of elementary calculus

A Problem Course in Mathematical Logic

definitions, statements of results, and problems, along with some explanations, examples, and hints

Calculus with Applications

differential calculus in one and several dimensions: readings, study materials

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