Coauthor with Imre Csiszár of a tutorial connecting information theory with statistics. It develops information measures as tools for statistical modeling and inference.^[ref]

Author of notes on measure theory, asymptotic analysis and singular perturbations. The perturbation notes distinguish regular expansions from problems requiring inner scales and matching.^[ref]

Sheldon Axler authored texts on real analysis and linear algebra. The cited measure-and-integration text develops a framework in which limits and integrals can be compared through explicit convergence hypotheses, rather than relying on formal manipulation alone.^[ref]

Stephen Boyd coauthored a text on convex optimization with Lieven Vandenberghe. Convexity connects local optimality with global conclusions, while duality supplies bounds and certificates useful for understanding numerical answers.^[ref]

Imre Csiszár developed information-theoretic methods for probability and statistics. His method-of-types exposition organizes sequences by empirical distributions, turning many probabilistic estimates into finite counting and divergence calculations.^[ref]

Homepage: www.renyi.hu/~csiszar/

Publications: www.renyi.hu/~csiszar/publist2012.pdf

Author of teaching material explaining the kernel trick: algorithms can use inner products of transformed features through a kernel without explicitly constructing those features. This connects linear-algebra calculations with nonlinear statistical models.^[ref]

Coauthor with Carl Edward Rasmussen of a textbook on Gaussian processes for machine learning, developing covariance-based regression and the corresponding predictive uncertainty.^[ref]

Coauthor with Christopher K. I. Williams of a textbook on Gaussian processes for machine learning. It treats regression through probability distributions over functions, linking covariance choices with predictive means and uncertainties.^[ref]

Coauthor with David I. Ketcheson and Randall J. LeVeque of an interactive book on Riemann problems. Its computational examples connect analytic wave structure with approximate solvers for hyperbolic equations.^[ref]

Coauthor with David I. Ketcheson and Mauricio J. del Razo of a book connecting Riemann problems, hyperbolic partial differential equations and executable numerical examples.^[ref]

Coauthor with Randall J. LeVeque and Mauricio J. del Razo of an interactive book on Riemann problems and approximate solvers for hyperbolic partial differential equations. Computational notebooks let readers vary initial states and compare wave patterns.^[ref]

Coauthor with Dan Margalit (mathematician) of an interactive linear algebra textbook, connecting algebraic procedures with geometric explanations and worked examples.^[ref]

Developed asymptotic-efficiency methods for hypothesis tests based on sums of observations. The exponential-moment technique associated with Chernoff bounds turns a tail event into an optimization of a moment bound.^[ref]

The credited author of Chapter 24, Bernoulli and Euler Polynomials, in the NIST Digital Library of Mathematical Functions. The chapter collects their generating functions, recurrences and applications.^[ref]

Author of an introduction to point processes and their applications. The subject models random spatial configurations and distinguishes local point density from dependence between nearby points.^[ref]

The LAPACK project develops numerical software for linear algebra, including solving linear systems, least-squares problems, eigenvalue problems and singular value decomposition. Its routines combine mathematical factorizations with implementation choices intended to exploit reliable high-performance basic operations.

For example, DGETRS solves a system using a previously computed LU factorization, while DLARTG constructs a scaled Givens rotation. Distinguishing a factorization from the later solve permits reuse for several right-hand sides. The routine documentation specifies storage conventions and exceptional inputs; these details are part of using a numerical algorithm correctly.^[ref]

Coauthor of a textbook on Markov chains and mixing times, studying convergence to equilibrium and quantitative bounds on the time required.^[ref]

Yuval Peres coauthored a treatment of Markov chains and mixing times. Coupling, spectral methods and probabilistic estimates quantify how quickly a chain approaches equilibrium, connecting a limiting distribution with the time needed to approximate it.^[ref]

Coauthor of a textbook on Markov chains and mixing times. The subject asks how repeated random transitions approach a stationary distribution and how rapidly initial-state information is lost.^[ref]

Author of an open textbook on probability theory, statistics and stochastic processes. It develops probabilistic models from random experiments through standard distributions and stochastic-process examples.^[ref]