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Measure, Integration & Real Analysis
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations …
Ergodic Dynamics
This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable …
Introduction to Real Analysis
Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes …
Binomial Ideals
This textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of …
Mathematical Logic
This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical …
Lectures on Convex Geometry
This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an …
Random Walk, Brownian Motion, and Martingales
This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. …
Essentials of Integration Theory for Analysis
When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhäuser title by the same author, A Concise Introduction to …
Introduction to Riemannian Manifolds
?This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second …
Lessons in Enumerative Combinatorics
This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the …
An Invitation to Unbounded Representations of *-Algebras on Hilbert Space
This textbook provides an introduction to representations of general *-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has …
Quaternion Algebras
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of …