Copyright 2025
Hardback
ISBN 9781032954820
448 Pages
March 12, 2025 by Chapman & Hall
Contemporary students of mathematics differ considerably from those of half a century ago. In spite of this, many textbooks written and now considered to be “classics” decades ago are still prescribed for students today. These texts are not suitable for today’s students. This text is meant for and written to today’s mathematics students.
Set theory is a pure mathematics endeavour in the sense that it seems to have no immediate applications; yet the knowledge and skills developed in such a course can easily branch out to various fields of both pure mathematics and applied mathematics.
Rather than transforming the reader into a practicing mathematician this book is more designed to initiate the reader to what may be called “mathematical thinking” while developing knowledge about foundations of modern mathematics. Without this insight, becoming a practicing mathematician is much more daunting.
The main objective is twofold. The students will develop some fundamental understanding of the foundations of mathematics and elements of set theory, in general. In the process, the student will develop skills in proving simple mathematical statements with “mathematical rigor”.
Carefully presented detailed proofs and rigorous chains of logical arguments will guide the students from the fundamental ZFC axioms and definitions to show why a basic mathematical statement must hold true. The student will recognize the role played by each fundamental axiom in development of modern mathematics. The student will learn to distinguish between a correct mathematical proof and an erroneous one. The subject matter is presented while by passing the complexities encountered when using formal logic.
1 Axioms and classes
2 Class operations
3 Relations
4 Functions
5 From sets to numbers
6 Infinite sets
7 Cardinal numbers
8 Ordinal numbers
9 More on axioms: Choice, regularity and Martin's axiom
10 Ordinal arithmetic
Copyright 2025
Paperback
Hardback
ISBN 9781032966168
480 Pages 197 B/W Illustrations
March 7, 2025 by Chapman & Hall
Discrete Mathematics: An Open Introduction, Fourth Edition aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math and computer science majors, especially those who intend to teach middle and high school mathematics. The book began as a set of notes for the Discrete Mathematics course at the University of Northern Colorado. This course serves both as a survey of the topics in discrete math and as the “bridge” course for math majors.
Uses problem-oriented and inquiry-based methods to teach the concepts.
Suitable for undergraduates in mathematics and computer science.
Large scale restructuring.
Contains more than 750 exercises and examples.
New sections on probability, relations, and discrete structures and their proofs.
0. Introduction and Preliminaries. 0.1. What is Discrete Mathematics?. 0.2. Discrete Structures. 1. Logic and Proofs. 1.1. Mathematical Statements. 1.2. Implications. 1.3. Rules of Logic. 1.4. Proofs. 1.5. Proofs about Discrete Structures. 1.6. Chapter Summary. 2. Graph Theory. 2.1. Problems and Definitions. 2.2. Trees. 2.3. Planar Graphs. 2.4. Euler Trails and Circuits. 2.5. Coloring. 2.6. Relations and Graphs. 2.7. Matching in Bipartite Graphs. 2.8. Chapter Summary. 3. Counting. 3.1. Pascal’s Arithmetical Triangle. 3.2. Combining Outcomes. 3.3. Non-Disjoint Outcomes. 3.4. Combinations and Permutations. 3.5. Counting Multisets. 3.6. Combinatorial Proofs. 3.7. Applications to Probability. 3.8. Advanced Counting Using PIE. 3.9. Chapter Summary. 4. Sequences. 4.1. Describing Sequences. 4.2. Rate of Growth. 4.3. Polynomial Sequences. 4.4. Exponential Sequences. 4.5. Proof by Induction. 4.6. Strong Induction. 4.7. Chapter Summary. 5. Discrete Structures Revisited. 5.1. Sets. 5.2. Functions. 6. Additional Topics. 6.1. Generating Functions. 6.2. Introduction to Number Theory.
Copyright 2025
Paperback
Hardback
ISBN 9781032497174
243 Pages 6 B/W Illustrations
March 3, 2025 by Chapman & Hall
Statistics has developed as a field through seminal ideas and fascinating controversies. Seminal Ideas and Controversies in Statistics concerns a wide-ranging set of 15 important statistical topics, grouped into three general areas: philosophical approaches to statistical inference, important statistical methodology for applications, and topics on statistical design, focusing on the role of randomization. The key papers on each topic are discussed with commentaries to help explain them. The goal is to expand reader knowledge of the statistics literature and encourage a historical perspective.
Discusses a number of important ideas in the history of statistics, including the likelihood principle, Bayes vs. frequentist approaches to inference, alternative approaches to least squares regression, shrinkage estimation, hypothesis testing, and multiple comparisons
Provides a deeper understanding and appreciation of the history of statistics
Discusses disagreements in the literature, which make for interesting reading
Gives guidance on various aspects of statistics research by reading good examples in the literature
Promotes the use of good English style in the presentation of statistical ideas, by learning from well-written papers
Includes an appendix of style tips on writing statistical papers
This book is aimed at researchers and graduate students in statistics and biostatistics, who are interested in the history of statistics and would like to deepen their understanding of seminal ideas and controversies. It could be used to teach a special topics course or useful for any researchers keen to understand the subject better and improve their statistical presentation skills.
1. Maximum likelihood
2. To C or not to C-- that is the question
3. Frequentist flaps: significance testing, hypothesis testing, or something else?
4. Fiducial inference and the Behrens-Fisher problem
5. Do you like the likelihood principle?
6. A Bayesian/frequentist compromise: Calibrated Bayes
7. Baseball averages, foreign cars, and shrinkage estimation
8. Alternatives to least squares in regression
9. Multiple perspectives on multiple comparisons
10.Generalized Estimating Equations
11.The Bootstrap and Bayesian Monte-Carlo methods
12.Exploratory data analysis and data science
13.Randomization in survey sampling
14.Randomized clinical trials and the Neyman/Rubin causal model
15.Propensity score methods
Copyright 2025
Paperback
Hardback
ISBN 9781032686196
170 Pages 23 B/W Illustrations
April 14, 2025 by Chapman & Hall
A Beginner’s Guide to Mathematical Proof prepares mathematics majors for the transition to abstract mathematics, as well as introducing a wider readership of quantitative science students, such as engineers, to the mathematical structures underlying more applied topics.
The text is designed to be easily utilized by both instructor and student, with an accessible, step-by-step approach requiring minimal mathematical prerequisites. The book builds towards more complex ideas as it progresses but never makes assumptions of the reader beyond the material already covered.
? No mathematical prerequisites beyond high school mathematics
? Suitable for an Introduction to Proofs course for mathematics majors and other students of quantitative sciences, such as engineering
? Replete with exercises and examples.
Mark DeBonis received his PhD in Mathematics from the University of California, Irvine, USA. He began his career as a theoretical mathematician in the field of group theory and model theory, but in later years switched to applied mathematics, in particular to machine learning. He spent some time working for the US Department of Energy at Los Alamos National Lab as well as the US Department of Defense at the Defense Intelligence Agency as an applied mathematician of machine learning. He is at present working for the US Department of Energy at Sandia National Lab. His research interests include machine learning, statistics, and computational algebra.
Preface, Chapter 1 Mathematical Logic, Chapter 2 Methods of Proof, Chapter 3 Special Proof Types, Chapter 4 Foundational Mathematical Topics, References, Index
In the series De Gruyter Textbook
This book delves into dynamic systems modeling, probability theory, stochastic processes, estimation theory, Kalman filters, and game theory. While many excellent books offer insights into these topics, our proposed book takes a distinctive approach, integrating these diverse subjects to address uncertainties and demonstrate their practical applications.
The author aims to cater to a broad spectrum of readers. The book features approximately 150 meticulously explained solved examples and numerous simulation programs, each with detailed explanations.
"Modelling Stochastic Uncertainties" provides a comprehensive understanding of uncertainties and their implications across various domains. Here is a brief exploration of the chapters:
Chapter 1: Introduces the book's philosophy and the manifestation of uncertainties.
Chapter 2: Lays the mathematical foundation, focusing on probability theory and stochastic processes, covering random variables, probability distributions, expectations, characteristic functions, and limits, along with various stochastic processes and their properties.
Chapter 3: Discusses managing uncertainty through deterministic and stochastic dynamic modeling techniques.
Chapter 4: Explores parameter estimation amid uncertainty, presenting key concepts of estimation theory.
Chapter 5: Focuses on Kalman filters for state estimation amid uncertain measurements and Gaussian additive noise.
Chapter 6: Examines how uncertainty influences decision-making in strategic interactions and conflict management.
Overall, the book provides a thorough understanding of uncertainties, from theoretical foundations to practical applications in dynamic systems modeling, estimation, and game theory.
Covers probability theory, stochastic processes, dynamic systems modeling, estimation theory, Kalman filters, and game theory.
Over 150 solved examples and numerous simulation codes
Uses open-source programming packages