Copyright 2024
Paperback
SBN 9781032483191
Hardback
ISBN 9781032499987
296 Pages 240 Color Illustrations
June 27, 2024 by A K Peters/CRC Press
Parabola is a mathematics magazine published by UNSW, Sydney. Among other things, each issue of Parabola has contained a collection of puzzles/problems, on various mathematical topics and at a suitable level for younger (but mathematically sophisticated) readers.
Parabolic Problems: 60 Years of Mathematical Puzzles in Parabola collects the very best of almost 1800 problems and puzzles into a single volume. Many of the problems have been re-mastered, and new illustrations have been added. Topics covered range across geometry, number theory, combinatorics, logic, and algebra. Solutions are provided to all problems, and a chapter has been included detailing some frequently useful problem-solving techniques, making this a fabulous resource for education and, most importantly, fun!
Hundreds of diverting and mathematically interesting problems and puzzles.
Accessible for anyone with a high school-level mathematics education.
Wonderful resource for teachers and students of mathematics from high school to undergraduate level, and beyond.
1. Problems. 2. Solutions. 3. Some Useful Problem-solving Techniques. 3.1. Greatest Common Divisor. 3.2. Solving Linear Diophantine Equations. 3.3. Modular Arithmetic. 3.4. Graph Theory. 3.5. Basic Combinatorics. 3.6. The Binomial Theorem. 3.7. Some Trigonometric Formulae. 3.8. Proof by Mathematical Induction. 3.9. Pickfs Theorem. 3.10. Roots and Coefficients of Polynomials. 3.11. Inequalities.
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Not yet published - available from April 2024
FORMAT: Paperback ISBN: 9781108995009
Logical paradoxes ? like the Liar, Russell's, and the Sorites ? are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses gdialetheic paraconsistencyh ? a formal framework where some contradictions can be true without absurdity ? as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
Part I. What are the Paradoxes?: Introduction to an inconsistent world
1. Paradoxes
or, 'here in the presence of an absurdity'
Part II. How to Face the Paradoxes?:
2. In search of a uniform solution
3. Metatheory and naive theory
4. Prolegomena to any future inconsistent mathematics. Part III. Where are the Paradoxes?:
5. Set theory
6. Arithmetic
7. Algebra
8. Real analysis
9. Topology. Part IV. Why Are there Paradoxes?:
10. Ordinary paradox
Part of London Mathematical Society Lecture Note Series
Not yet published - available from May 2024
FORMAT: Paperback ISBN: 9781009465953
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Provides an in-depth look at four important mathematical topics emphasizing their common roots in linear algebra
Features numerous exercises in each chapter rounding out the theory
All chapters can be read independently but contain many cross-references and commonalities
1. Topics in representation theory of finite groups Tullio Ceccherini-Silberstein, Fabio Scarabotti and Filippo Tolli
2. Quantum probability approach to spectral analysis of growing graphs Nobuaki Obata
3. Laplacian eigenvalues and optimality R. A. Bailey and Peter J. Cameron
4. Symbolic dynamics and the stable algebra of matrices Mike Boyle and Scott Schmieding
Author index
Subject index.
Not yet published - available from August 2024
FORMAT: Paperback ISBN: 9781009338394
Play of Chance and Purpose emphasizes learning probability, statistics, and stochasticity by developing intuition and fostering imagination as a pedagogical approach. This book is meant for undergraduate and graduate students of basic sciences, applied sciences, engineering, and social sciences as an introduction to fundamental as well as advanced topics. The text has evolved out of the author's experience of teaching courses on probability, statistics, and stochastic processes at both undergraduate and graduate levels in India and the United States. Readers will get an opportunity to work on several examples from real-life applications and pursue projects and case-study analyses as capstone exercises in each chapter. Many projects involve the development of visual simulations of complex stochastic processes. This will augment the learners' comprehension of the subject and consequently train them to apply their learnings to solve hitherto unseen problems in science and engineering.
Coverage ranges from foundational concepts like conditional probability to advanced ones like Markov chains, M/M/n queues, and principal component analysis
Margin notes and illustrations for visualizations of theoretical constructs and concepts
Computer-aided projects and case studies based on real-life scenarios
Instructors' resources include solution manual and Python compendium
List of Tables
List of Figures
Preface
Acknowledgements
Chapter 1. Thinking in Probability
Chapter 2. Probability Distributions
Chapter 3. Discrete Time Markov Chains
Chapter 4. Continuous Time Markov Chains and Queues
Chapter 5. Statistical Experiments
Chapter 6. Prediction and Time Series Modelling
Chapter 7. Glimpses of multivariate statistics
Appendix: A Brief Tour of Matrices
Appendix: A Breeze through MATLAB
Index.
Copyright 2024
Hardback
ISBN 9781032594705
396 Pages
May 7, 2024 by Chapman & Hall
This book offers an introduction to some combinatorial (also, set-theoretical) approaches and methods in geometry of the Euclidean space Rm. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry.
The authorfs primary intention is to discuss those themes of Euclidean geometry which might be of interest to a sufficiently wide audience of potential readers. Accordingly, the material is explained in a simple and elementary form completely accessible to the college and university students. At the same time, the author reveals profound interactions between various facts and statements from different areas of mathematics: the theory of convex sets, finite and infinite combinatorics, graph theory, measure theory, classical number theory, etc.
All chapters (and also the five Appendices) end with a number of exercises. These provide the reader with some additional information about topics considered in the main text of this book. Naturally, the exercises vary in their difficulty. Among them there are almost trivial, standard, nontrivial, rather difficult, and difficult. As a rule, more difficult exercises are marked by asterisks and are provided with necessary hints.
The material presented is based on the lecture course given by the author. The choice of material serves to demonstrate the unity of mathematics and variety of unexpected interrelations between distinct mathematical branches.
1. The index of an isometric embedding
2. Maximal ot-subsets of the Euclidean plane
3. The cardinalities of at-sets in a real Hilbert space
4. Isosceles triangles and it-sets in Euclidean space
5. Some geometric consequences of Ramseyfs combinatorial theorem
6. Convexly independent subsets of infinite sets of points
7. Homogeneous coverings of the Euclidean plane
8. Three-colorings of the Euclidean plane and associated triangles of a prescribed type
9. Chromatic numbers of graphs associated with point systems in Euclidean space
10. The Szemeredi?Trotter theorem
11. Minkowskifs theorem, number theory, and nonmeasurable sets
12. Tarskifs plank problem
13. Borsukfs conjecture
14. Piecewise affine approximations of continuous functions of several variables and Caratheodory?Gale polyhedral
15. Dissecting a square into triangles of equal areas
16. Geometric realizations of finite and infinite families of sets
17. A geometric form of the Axiom of Choice