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Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference
This book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and …
Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics
This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such …
Fundamental Mathematical Analysis
This textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the …
Fundamental Mathematical Structures of Quantum Theory
This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months …
Introduction to Discrete Mathematics via Logic and Proof
This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with …
An Invitation to Abstract Mathematics
This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to …
Introduction to Infinity-Categories
This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects of modern pure mathematics. It treats the basics of the theory and supplies all …
Category Theory in Physics, Mathematics, and Philosophy
The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category …
Numerical Methods for Elliptic and Parabolic Partial Differential Equations
This graduate-level text provides an application oriented introduction to the numerical methods for elliptic and parabolic partial differential equations. It covers finite …
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 …
Essential Mathematics for Undergraduates
This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas. It guides …
The Essence of Numbers
This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects …