April 1, 2026
Language: English
Paperback ISBN: 9780443273902
Measure and Integration: Examples, Concepts, and Applications offers a comprehensive introduction to the fundamental principles and methods of real analysis, providing readers with a solid foundation through clear explanations, rigorous proofs, and an abundance of thoughtfully constructed exercises. From the very first chapter, students are encouraged to engage actively with concepts, applying them to a range of practical examples that reinforce both understanding and analytical skills. The book’s structured approach ensures that readers not only grasp key theorems and core techniques, but also develop the problem-solving abilities essential for higher-level mathematics and related applications.
The text also delves into advanced areas such as integration on product spaces, Radon functionals, functions of bounded variation, Lebesgue-Stieltjes measures, convolutions, probability, and differential equations. Each chapter concludes with advanced exercises, clearly marked for difficulty, allowing both students and instructors to tailor their study or coursework. An appendix with complete solutions supports independent learning, making the book a valuable resource for both classroom use and self-study.
1. Abstract Integration
2. Measures
3. Integration on Product Spaces
4. The Lebesgue-Radon-Nikodym Theorem
5. Radon Functionals on Locally Compact Hausdorff Spaces
6. Differentiation
7. Functions of Bounded Variation and Lebesgue-Stieltjes Measures
8. Convolutions
9. Probability
10. Differential Equations with measure coefficients
11. Appendices
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Published: March 2026
Format: Hardback
ISBN: 9781009490641
'High-Dimensional Probability,' winner of the 2019 PROSE Award in Mathematics, offers an accessible and friendly introduction to key probabilistic methods for mathematical data scientists.
Streamlined and updated, this second edition integrates theory, core tools, and modern applications. Concentration inequalities are central, including classical results like Hoeffding's and Chernoff's inequalities, and modern ones like the matrix Bernstein inequality. The book also develops methods based on stochastic processes – Slepian's, Sudakov's, and Dudley's inequalities, generic chaining, and VC-based bounds. Applications include covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, and machine learning. New to this edition are 200 additional exercises, alongside extra hints to assist with self-study. Material on analysis, probability, and linear algebra has been reworked and expanded to help bridge the gap from a typical undergraduate background to a second course in probability.
The most accessible book on the subject, designed so that students who finish basic undergraduate courses can jump right to this material
Updated with 200 new exercises to assist with course design, and extra hints added to help with self-study
Selects the core ideas and methods and presents them systematically with modern motivating applications to bring readers quickly up to speed
Foreword Sara van de Geer
Preface
Appetizer. Using probability to cover a set
1. A quick refresher on analysis and probability
2. Concentration of sums of independent random variables
3. Random vectors in high dimensions
4. Random matrices
5. Concentration without independence
6. Quadratic forms, symmetrization, and contraction
7. Random processes
8. Chaining
9. Deviations of random matrices on sets
Hints for the exercises
References
Index.
Series: Cambridge Studies in Advanced Mathematics
Published: March 2026
Format: Hardback
ISBN: 9781009641845
Addressing the active and challenging field of spectral theory, this book develops the general theory of spectra of discrete structures, on graphs, simplicial complexes, and hypergraphs. In fact, hypergraphs have long been neglected in mathematical research, but due to the discovery of Laplace operators that can probe their structure, and their manifold applications from chemical reaction networks to social interactions, they now constitute one of the hottest topics of interdisciplinary research. The authors' analysis of spectra of discrete structures embeds intuitive and easily visualized examples, which are often quite subtle, within a general mathematical framework. They highlight novel research on Cheeger type inequalities which connect spectral estimates with the geometry, more precisely the cohesion, of the underlying structure. Establishing mathematical foundations and demonstrating applications, this book will be of interest to graduate students and researchers in mathematics working on the spectral theory of operators on discrete structures.
Develops discrete spectral theory from elementary examples to the most recent research
Particular emphasis on hypergraphs, demonstrating to readers their applications in a wide range of fields
Presents novel and general results about Cheeger type inequalities for eigenvalues of discrete operators
This title is also available as open access on Cambridge Core
Preface
Acknowledgments
Organization of the book
Part I. Basics: Foundational Material, Elementary Aspects, Examples:
1. Introduction
2. The abstract setting
3. The classical case
4. First properties of the spectrum
5. Floer theory
Part II. Eigenvalues and Eigenfunctions on Simplicial Complexes and Hypergraphs:
6. Lovász extensions
7. Discrete p-Laplacians
8. Cheeger inequalities
9. Nodal domains
Part III. Additional topics: Interlacing, Tensors, Non-backtracking Laplacians, and Applications:
10. Interlacing and spectral classes
11. Spectral theory of hypergraphs via tensors
12. The non-backtracking Laplacian
13. Applications
Bibliography
Index.
Copyright 2025
Hardback
ISBN 9781041003717
208 Pages 83 Color & 4 B/W Illustrations
December 29, 2025 by Chapman & Hall
This book provides fundamental concepts and algorithms of the Hidden Markov Model (HMM) and its applications in finance, such as stock price predictions, and other areas such as speech recognition. Their wide range uses make HMMs very attractive to researchers in both academia and industry. Only a basic knowledge of probability, statistics, and programming is necessary, and readers will learn the concepts and algorithms of the HMM through definitions, real-life examples, and R code.
Key Features:
• A comprehensive introduction to the concepts and algorithms of Hidden Markov Models (HMMs).
• Real-world examples that can be worked through using a calculator or R.
• Applications across disciplines, including finance, bioinformatics, and speech recognition.
• Fully annotated R code for hands-on learning and practical implementation.
Preface Author 1 Introduction 2 Three Main Problems of The HMM and Its Algorithms 3 Model Selections 4 Applications of HMM in Finance 5 Applications of HMM in other disciplines Bibliography Index
Copyright 2026
Hardback
ISBN 9781041126843
322 Pages
January 27, 2026 by Chapman & Hall
The modern theory of functional spaces and operators, built on powerful analytical methods, continues to evolve in the search for more precise, universal, and effective tools. Classical inequalities such as Hardy’s inequality, Remez’s inequality, the Bernstein-Nikolsky inequality, the Hardy-Littlewood-Sobolev inequality for the Riesz transform, the Hardy-Littlewood inequality for Fourier transforms, O’Neil’s inequality for the convolution operator, and others play a fundamental role in analysis, and their influence is hard to overestimate. With the development of new interpolation methods, new functional spaces, and novel problem formulations for functions of many variables, these inequalities have undergone significant advancements.
Inequalities and Integral Operators in Function Spaces focuses primarily on new approaches to the interpolation of spaces, which significantly extend the classical framework of the methods developed by Lions and Peetre. The book demonstrates how the use of net spaces and modern interpolation techniques not only provides a deeper understanding of the structure of functional spaces but also leads to stronger results that cannot be achieved within the traditional framework.
• Can be used for specialized courses in harmonic analysis focusing on interpolation
• Suitable for both researchers in the field of real analysis and mathematicians interested in applying these methods to related areas
• Contains new and interesting results, previously unpublished.
Foreword Preface 1 Inequalities related to permutations of functions 2 Multiparameter interpolation method 3 Interpolation method for spaces with mixed metric 4 Interpolation theorems for integral operators 5 Nikolsky’s inequalities 6 Remez inequalities 7 Hardy-Littlewood inequalities for trigonometric series 8 Stein inequalities for the Fourier transform 9 Net spaces and Nursultanov inequalities 10 Weighted norm inequalities for Fourier transforms 11 O’Neil inequalities 12 Weighted norm inequalities for convolution and Riesz potential13 O’Neil inequalities on Morrey spaces14 Interpolation theorems for nonlinear integral operators Bibliography Index
Copyright 2026
Hardback
ISBN 9781041045632
612 Pages 94 B/W Illustrations
March 10, 2026 by Chapman & Hall
Now in its second edition, this book provides a rigorous treatment of the foundations of differential and integral calculus. It proceeds gradually from an axiomatic characterization of the real number system to the study of differentiation and integration on m-dimensional surfaces. Proofs of theorems are given in detail, and many examples are provided to illustrate the concepts expressed in the theorems.
The book consists of three parts. Part I treats the calculus of functions of one variable. Traditional topics such as sequences, continuity, differentiability, Riemann integrability, numerical series, and the convergence of sequences and series of functions are covered. Optional sections on Stirling’s formula, Riemann–Stieltjes integration, and other topics are also included.
The second part focuses on functions of several variables. It introduces the topological ideas (such as compact and connected sets) needed to describe analytical properties of multivariable functions. This part also discusses differentiability and integrability of multivariable functions, and it develops the theory of differential forms on surfaces in Rn.
Many proofs and explanations in the first edition have been revised, and details have been added to clarify the exposition. Part III contains appendices on set theory and linear algebra as well as solutions to some of the exercises are offered, whilst a full solutions manual contains complete solutions to all exercises for qualifying instructors.
Preface
Part I: Functions of One Variable
1. The Real Number System
1.1 Algebraic Properties of R
1.2 Order Properties of R
1.3 Completeness Property of R
1.4 Mathematical Induction
1.5 Euclidean Space
2. Numerical Sequences
2.1 Limits of Sequences
2.2 Monotone Sequences
2.3 Subsequences and Cauchy Sequences
2.4 Limits Inferior and Superior
3. Limits and Continuity on R
3.1 Limit of a Function
3.2 Limits Inferior and Superior
3.3 Continuous Functions
3.4 Properties of Continuous Functions
3.5 Uniform Continuity
4. Differentiation on R
4.1 Definition of Derivative and Examples
4.2 The Mean Value Theorem
4.3 Convex Functions
4.4 Inverse Functions
4.5 L’Hospital’s Rule
4.6 Taylor’s Theorem on R
4.7 Newton’s Method
5. Riemann Integration on R
5.1 The Riemann–Darboux Integral
5.2 Properties of the Integral
5.3 Evaluation of the Integral
5.4 Stirling’s Formula
5.5 Integral Mean Value Theorems
5.6 Estimation of the Integral
5.7 Improper Integrals
5.8 A Deeper Look at Riemann Integrability
5.9 Functions of Bounded Variation
5.10 The Riemann–Stieltjes Integral
6. Numerical Infinite Series
6.1 Definition and Examples
6.2 Series with Nonnegative Terms
6.3 More Refined Convergence Tests
6.4 Absolute and Conditional Convergence
6.5 Double Sequences and Series
7. Sequences and Series of Functions
7.1 Convergence of Sequences of Functions
7.2 Properties of the Limit Function
7.3 Convergence of Series of Functions
7.4 Power Series
Part II: Functions of Several Variables
8. Metric Spaces
8.1 Definitions and Examples
8.2 Open and Closed Sets
8.3 Closure, Interior, and Boundary
8.4 Limits and Continuity
8.5 Compact Sets
8.6 The Arzelà–Ascoli Theorem
8.7 Connected Sets
8.8 The Stone–Weierstrass Theorem
8.9 Baire’s Theorem
9. Differentiation on Rn
9.1 Definition of the Derivative
9.2 Properties of the Differential
9.3 Further Properties of the Differential
9.4 Inverse Function Theorem
9.5 Implicit Function Theorem
9.6 Higher Order Partial Derivatives
9.7 Higher Order Differentials and Taylor’s Theorem
9.8 Optimization
10. Lebesgue Measure on Rn
10.1 General Measure Theory
10.2 Lebesgue Outer Measure
10.3 Lebesgue Measure
10.4 Borel Sets
10.5 Measurable Functions
11. Lebesgue Integration on Rn
11.1 Riemann Integration on Rn
11.2 The Lebesgue Integral
11.3 Convergence Theorems
11.4 Connections with Riemann Integration
11.5 Iterated Integrals
11.6 Change of Variables
12. Curves and Surfaces in Rn
12.1 Parameterized Curves
12.2 Integration on Curves
12.3 Parameterized Surfaces
12.4 m-Dimensional Surfaces
13. Integration on Surfaces
13.1 Differential Forms
13.2 Integrals on Parameterized Surfaces
13.3 Partitions of Unity
13.4 Integration on Compact m-Surfaces
13.5 The Fundamental Theorems of Calculus
13.6 Closed Forms in Rn
Part III: Appendices
A Set Theory
B Linear Algebra
C Solutions to Selected Problems
Language: English
Published/Copyright: 2026
Logic and Deduction differs from other titles and offers fresh viewpoints and suggestions for more effective and better utilization of logic in the sciences and mathematics, such as theoretical physics, number theory, sociology, and economics. Much of the title touches on scientific and mathematical topics, e.g., mathematical proof, Godel's incompleteness theorems, set theory, infinity, the work of well-known logicians such as Frege and Russell, calculus, relativity, quantum theory, chaos, unified field theory, speed of light, gravity, etc., including the soft sciences such as economics and sociology. The coverage is comprehensive, as logic applies not only to the hard sciences but also to the soft sciences. The book could be useful to scholars, researchers, students of the hard and soft sciences, intellectuals, professionals such as physicists working on unified field theory & mathematicians working on number theory, logicians, philosophers, lawyers arguing criminal law cases, writers, economists, sociologists, government bureaucrats & policy-makers, corporate executives, activists aiming for a better society, and anyone keen on increasing brainpower or mind-expansion. It could inspire and spur further thought on logic.
Provides a broad and wide variety of topics, e.g., relativity, unified field theory, Godel’s theorems, number theory, chaos, probability, etc.
It contains novel and original original ideas.
It inspires/stimulates further scientific thought.
Frontmatter
Publicly Available VII
Author’s Message
Part One
1 Viewpoints on Logic
2 Introduction
3 Mind and Logic
4 More on Logic
5 Logic and Reality in Life
6 Godel’s Proof and Mathematical Logic
7 Some Ideas Relating to Godel’s Undecidable Theorem and Mathematical Logic
8 Mathematical Logic and Proof
9 The Philosophy and Principles of Logic
10 Is a New Kind of Logic or Reason Possible?
11 The Basis and Reality of Logic
12 Reason and Logic in Human Affairs
13 Humanity and Logic
14 More on Mathematical Logic and Proof
15 Are We Rational?
16 The Conduct of Rational Argument
17 The Logic of Moral Behavior
18 The Logic of Evil
19 The Logic of Cause and Effect or Causal Effect
20 The Theory and Logic of Numbers
21 The Logic of Mathematical Equations
22 Logical Deduction
23 The Author’s Encounters with Logic
24 Conclusion
25 Epilogue: A Constructive and Important Proposal for Logic
Part Two
1 What if Ideas, the Logic of Ideas, Are Such That … ? Further Thoughts …
2 Something to Ponder About
3 Some Interesting Bizarre Scenarios That Would Seriously Test the Power and Reliability of Logic
4 A Tongue-in-Cheek, Even Humorous, Slant on Human Logic
5 More on the Logic of Moral Behavior
6 The Logic of Good Versus Evil
7 More on the Logic of Evil
8 The Difficult Logic of Morals
9 The Logic of Human Relations
10 The Logic of Competition Versus Cooperation or Teamwork in Economics
11 The General Logic of Cooperation, Teamwork, Harmony, Peace, and Happiness
12 The Logic of Democratic Leadership
13 The Logic of Nature
14 The Paradoxical “Logic” of Time Travel in Theoretical Physics
15 The Logic of Space-Time in Theoretical Physics
16 The Logic of the Existence of God
17 The Logic of Religion and God
18 The Inscrutable Logic of Nature
19 The Logic of Planetary Movements
20 The Logic of Life, Nature, and the Supranatural in Our Universe: A No-Holds-Barred Analysis
21 The Possible Ultimate Logic Which Explains Everything in the Universe Including the Mysterious and the Unexplainable
22 The Logic of the Act of Thinking
23 The Logic of Probability or Luck
24 The Discrepancy in the Logic of Algebra
25 The Logic of Infinity
26 The Logic of Reality
27 Will the Laws or Logic of Physics Always Be Useful?
28 Practical Logic
29 Conflicts Arising from Logic and Their Solutions
30 The Serious Problem with Logic and Its Correction – Why Logic Goes Wrong and How to Prevent It from Going Wrong
31 The Simplification of Logic
32 Being Logical
33 A Short, Simple, and Effective Way of Dealing with Logical Problems and Disputes in Everyday Affairs
34 The Last Say on Logical Reasoning or the Use of Logic
35 The Future of Logic
36 Final Conclusion: What Logic Really Is After All
Appendices
Appendix 1: Is Our Physics the Only Reality?
Appendix 2: The Logic of Space-Time and Time Travel
Appendix 3: The Puzzling Logic of Gravity
Appendix 4: The Logic Behind a Scientific Discovery (Maxwell Equations)
Appendix 5: A Reply to the Editor of a Prestigious Mathematical Journal Raising Some Important Points
Appendix 6: Notes – Some Logical Concepts of Calculus (Mathematics)
Appendix 7: Notes – Some Logical Concepts of Quantum Theory (Physics)
Appendix 8: Economic Reasoning at Work (with Commentary)
Appendix 9: Scientific Reasoning at Work (with Commentary)
Appendix 10: Mathematical Reasoning at Work (with Commentary)
Appendix 11: Interesting Quotations on Logic and Thought – Something to Ponder About
Bibliography
Index
This volume presents a collection of articles devoted to representations of algebras and related topics. Distinguished experts in this field presented their work at the International Conference on Representations of Algebras which took place in Montevideo and Buenos Aires in 2022.
The book reflects recent trends in the representation theory of algebras and its interactions with other central branches of mathematics. There are fourteen expository survey papers, written by leading experts in the field.
This collection is addressed to researchers and graduate students in algebra as well as to a broader mathematical audience. Researchers of representation theory will find in this volume interesting and stimulating contributions to the development of the subject.
pp. i–iv
Front matter
pp. v–vii
Preface
pp. ix–xii
Contents
pp. 1–45
On infinite-dimensional Hopf algebras
Nicolás Andruskiewitsch
DOI 10.4171/ECR/21/1
pp. 47–83
Spaces of Bridgeland stability conditions in representation theory
Anna Barbieri
DOI 10.4171/ECR/21/2
pp. 85–119
Quasi-cluster algebras: An overview
Véronique Bazier-Matte
DOI 10.4171/ECR/21/3
pp. 121–160
Exact structures for persistence modules
Benjamin BlanchetteThomas BrüstleEric J. Hanson
DOI 10.4171/ECR/21/4
pp. 161–189
What is an exact dg category?
Xiaofa Chen
DOI 10.4171/ECR/21/5
pp. 191–225
Differential graded enhancements of singularity categories
Xiao-Wu ChenZhengfang Wang
DOI 10.4171/ECR/21/6
pp. 227–259
Tame symmetric algebras: Hybrid algebras as a route to a classification
Karin Erdmann
DOI 10.4171/ECR/21/7
pp. 261–296
Wall-and-chamber structures for finite-dimensional algebras and τ-tilting theory
Maximilian KaipelHipolito Treffinger
DOI 10.4171/ECR/21/8
pp. 297–332
Towards bound quivers for exact categories
Julian Külshammer
DOI 10.4171/ECR/21/9
pp. 333–384
An introduction to monomorphism categories
Sondre Kvamme
DOI 10.4171/ECR/21/10
pp. 385–416
Bricks and mutation
Rosanna Laking
DOI 10.4171/ECR/21/11
pp. 417–440
Categories associated to punctured surfaces and surface braid twist group actions on triangulated categories
Sebastian Opper
DOI 10.4171/ECR/21/12
pp. 441–464
Mutations and derived equivalences for commutative Noetherian rings
Jorge Vitória
DOI 10.4171/ECR/21/13
pp. 465–493
Derived equivalences of Brauer graph algebras
Alexandra Zvonareva
DOI 10.4171/ECR/21/14
pp. 495–496
List of contributors
Published ahead of schedule, this book is part of the 2026 MEMS collection and may become open access under our Subscribe to Open programme in 2026.
We consider the stability of symmetric flows in a two-dimensional channel (including the Poiseuille flow). In 2015 Grenier, Guo, and Nguyen have established instability of these flows in a particular region of the parameter space, affirming formal asymptotics results from the 1940's. We prove that these flows are stable outside this region in parameter space. More precisely we show that the Orr--Sommerfeld operator
B=(−
dx
2
d
2
+iβ(U+iλ))(
dx
2
d
2
−α
2
)−iβU
′′
,
which is defined on
D(B)={u∈H
4
(0,1),u
′
(0)=u
(3)
(0)=0 and u(1)=u
′
(1)=0}.
is bounded on the half-plane ℜλ≥0 for α≫β
−1/10
or α≪β
−1/6
Frontmatter
Download pp. i–iv
Abstract
Download p. v
Contents
Download pp. vii–viii
1 Introduction
Download pp. 1–9
2 The inviscid operator
pp. 11–74
3 Neumann–Dirichlet Schrödinger operators
pp. 75–105
4 No-slip Schrödinger operators
pp. 107–133
5 The Orr–Sommerfeld operator
pp. 135–199
6 Proof of the main theorems
pp. 201–202
References
pp. 203–204
Published ahead of schedule, this book is part of the 2026 MEMS collection and may become open access under our Subscribe to Open programme in 2026.
The functional graph of a function g:X→X is the directed graph with vertex set X the edges of which are of the form x→g(x) for x∈X. Functional graphs are studied because they allow one to understand the behavior of g under iteration (i.e., to understand the discrete dynamical system (X,g)), which has various applications, especially when X is a finite field F
q
. This memoir is an extensive study of the functional graphs of so-called index d generalized cyclotomic mappings of F
q
, which are a natural and manageable generalization of monomial functions. We provide both theoretical results on the structure of their functional graphs and Las Vegas algorithms for solving fundamental problems, such as parametrizing the connected components of the functional graph by representative vertices, or describing the structure of a connected component given by a representative vertex. The complexity of these algorithms is analyzed in detail, and we make the point that for fixed index d and most prime powers q (in the sense of asymptotic density), suitable implementations of these algorithms have an expected runtime that is polynomial in logq on quantum computers, whereas their expected runtime is subexponential in logq on a classical computer. We also discuss four special cases in which one can devise Las Vegas algorithms with this kind of complexity behavior over most finite fields that solve the graph isomorphism problem for functional graphs of generalized cyclotomic mappings.
Frontmatter
Download pp. i–iv
Abstract
Download p. v
Contents
Download p. vii
1 Introduction
Download pp. 1–14
2 Preparations
pp. 15–43
3 Functional graphs of generalized cyclotomic mappings
pp. 45–61
4 Computations and examples
pp. 63–83
5 Algorithmic complexity analysis
pp. 85–217
6 Open problems
pp. 219–231
A Tabular overview of notation and terminology
pp. 233–255
References
pp. 257–262