A credited contributor to Chapters 1 and 18 of the NIST Digital Library of Mathematical Functions, treating algebraic and analytic methods and orthogonal polynomials. These credits refer to the named chapters, rather than the whole reference.^[ref]

A credited contributor to chapters of the NIST Digital Library of Mathematical Functions on algebraic and analytic methods and orthogonal polynomials. These chapters connect differential equations, asymptotic methods and special-function formulas.^[ref]

A credited contributor to Chapter 1 of the NIST Digital Library of Mathematical Functions, covering algebraic and analytic methods. His chapter contribution connects elementary identities with the methods used to study special functions.^[ref]

Frank W. J. Olver worked on special functions, asymptotic analysis of differential equations and reliable numerical methods. His research relates limiting descriptions of solutions to the computation of functions such as Bessel functions and hypergeometric functions. He authored the integer-order Bessel chapter in the original NIST handbook and helped develop the modern NIST Digital Library of Mathematical Functions.^[ref]

Homepage: dlmf.nist.gov/about/bio/FWJOlver

A credited Chapter 1 contributor to the NIST Digital Library of Mathematical Functions. That chapter develops algebraic and analytic methods, including complex analysis, integral transforms and differential equations. Chapter authorship is distinct from authorship of the entire reference.^[ref]

Author of MIT teaching notes in complex analysis, including the argument principle and its use in counting zeros and poles by a contour integral.^[ref]

Coauthor with Gavin C. Cawley of research on overfitting during model selection, distinguishing selection of a fitted model from an unbiased evaluation of its predictive performance.^[ref]

Coauthor with Nicola L. C. Talbot of research on overfitting during model selection. Their analysis explains how repeatedly optimizing a validation criterion can bias the final performance estimate.^[ref]

Author of teaching material on ridge regression, cross-validation and statistical model selection. These topics connect penalized fitting with the separate task of estimating predictive performance.^[ref]

Author of teaching material in topology, including the quotient topology and the criterion for continuous maps out of a quotient. These constructions explain how identifying points produces a new topological space.^[ref]

Coauthor with John A. Beachy of an abstract algebra textbook. Its subject includes the structural viewpoint that connects familiar arithmetic with more general algebraic systems.^[ref]

Coauthor with William D. Blair of an abstract algebra textbook treating algebraic structures through definitions, examples and proofs.^[ref]

Author of an elementary number theory text whose treatment of Chebyshev functions connects weighted prime counts with questions in analytic number theory.^[ref]

Terence Tao works in harmonic analysis, partial differential equations, analytic number theory, arithmetic combinatorics and related areas.^[ref] His Nonlinear dispersive equations: local and global analysis by Terence Tao studies the existence and evolution of nonlinear waves, while 254A: Topics in Ergodic Theory by Terence Tao develops mathematical tools for long-time averages and recurrence. These works connect estimates for functions and operators with qualitative questions about dynamical evolution.

Homepage: www.math.ucla.edu/~tao/

Author of a 1918 study of products of absolutely convergent and Cesàro-summable series. The paper places multiplication results within the developing theory of Cesàro summation. Initials are retained as printed on the inspected source, without expanding an unverified identity.^[ref]

Author of mathematics tutorials including a treatment of Cesàro summation. His examples compare ordinary partial sums with their arithmetic averages, including Grandi's series.^[ref]

Developed a normality-test correction for the Kolmogorov-Smirnov test when the normal mean and variance are estimated from the same sample. Fitting those parameters changes the null distribution, so known-parameter critical values cannot simply be reused.^[ref]

Keith Conrad is a mathematician working in number theory.^[ref] His expository notes develop topics across algebra and number theory; for example, Bilinear Forms by Keith Conrad treats forms on vector spaces, while The p-adic expansion of rational numbers by Keith Conrad explains representations of rational numbers in P-adic numbers.

Christian Clason authored an introduction to finite-element methods. The approach replaces a differential equation with a weak formulation and a finite-dimensional approximation space, connecting functional analysis with a computable matrix problem.^[ref]

Claude Shannon established a mathematical framework for communication using probabilistic sources and channels. Entropy measures source uncertainty, while coding theorems relate channel noise to the rate at which information can be transmitted reliably. His framework separates communication reliability from the semantic interpretation of a message.^[ref]