Technical Books

This note covers the following topics, Basic structures of topology and metrics, Basic tools of Functional Analysis, Theory of Distributions, Fourier Analysis, Analysis on Hilbert spaces.

This note covers preliminaries, Measure and measurable sets, Measurable functions, Lebesgue integral, Signed measures and differentiations, Lp spaces and probability theory.

This book contains below topics, Title Page, Real Numbers, Sequences and Series, Continuous Functions, The Derivative, The Riemann Integral, Sequences of Functions, Metric Spaces, List of Notation.

This book covers the following topics, Basic Concepts of Probability Theory, Random Variables, Multiple Random Variables, Vector Random Variables, Sums of Random Variables and LongTerm Averages, Random Processes, Analysis and Processing of Random Signals, Markov Chains, Introduction to Queueing Theory and Elements of a Queueing System.

These notes are intended to give a solid introduction to Probability Theory with a reasonable level of mathematical rigor. Topics covered includes, Elementary probability, Discretetime finite state Markov chains, Existence of Markov Chains, Discretetime Markov chains with countable state space, Probability triples, Limit Theorems for stochastic sequences, Moment Generating Function, The Central Limit Theorem, Measure Theory and Applications.

This book explains the following topics, Probability spaces, Random variables, Independence, Expectation, Convergence of sequences of random variables.

The contents include, Combinatorics, Axioms of Probability, Conditional Probability and Independence, Discrete Random Variables, Continuous Random Variables, Joint Distributions and Independence, More on Expectation and Limit Theorems, Convergence in probability, Moment generating functions, Computing probabilities and expectations by conditioning, Markov Chains, Introduction, Markov Chains, Classification of States, Branching processes, Markov Chains, Limiting Probabilities, Markov Chains, Reversibility, Three Application, Poisson Process.

The contents include, Combinatorics, Axioms of Probability, Independence, Conditional Probability and Independence, Random Variables, Some Discrete Distributions, Continuous Random Variable, Normal Distributions, Normal approximations to the binomial, Some continuous distributions, Multivariate distributions, Expectations, Moment generating functions, Limit Laws.

This note explains the following topics, events and probabilities, Combining events, Conditional probabilities, independence and bayes rule, Random variables and discrete distributions, Expectation and variance, Continuous random variables.

This note covers measure theory, Laws of large numbers, Central limit theorem, Martingales, Markov chains, Ergodic theorems, Brownian motion, Applications to random walk, Multidimensional Brownian motion.

These notes treat quantum theory as a nonclassical probability calculus. They come from a short course on generalized probability theories. The idea goes back to von Neumann and to the later literature on quantum logics.

to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. This note contains below topics, Very Short Introduction into Subject and History, The Notion of Freeness Definition Example and Basic Properties, Emergence of the Combinatorics of Free Probability Theory Free Central Limit Theorem, The Combinatorics of Free Probability Theory Free Cumulants, Free Convolution of Compactly Supported Probability Measures and the RTransform, Free Convolution of Arbitrary Probability Measures and the Subordination Function, Gaussian Random Matrices and Asymptotic Freeness, Unitary Random Matrices and Asymptotic Freeness and a Remark on Wigner Matrices, Von Neumann Algebras The Free Group Factors and Relation to Freeness, Circular and RDiagonal Operators, Applications of Freeness to von Neumann Algebras Compression of Free Group Factors, Some More Operator Algebraic Applications of Free Probability.

This note contains below topics, Noncommutative probability spaces and distributions, Free Cumulants, Additive free convolution and limit theorems, Asymptotic Freeness, Stransform, Subordination, Operatorvalued noncommutative random variables, Rdiagonal variables, Distributions of SelfAdjoint Variables and Their Transforms, Scaling Properties.

This note covers the following topics, Numerical Solution of Algebraic Equations, Gauss Elimination Method, LU Decomposition Method, Iterative Methods, Successive OverRelaxation SOR Method.

This note explains the following topics, IEEE Arithmetic, Root Finding, Systems of equations, Leastsquares approximation, Interpolation, Integration and Ordinary differential equations.