Format: Hardback, 210 pages, height x width: 235x155 mm, 48 Tables, color; 54 Illustrations, color;
23 Illustrations, black and white; X, 210 p. 77 illus., 54 illus. in color.
Series: Springer Proceedings in Mathematics & Statistics 430
Pub. Date: 01-Nov-2023
ISBN-13: 9783031398636
This volume covers the latest results on novel methods in Risk Analysis and assessment, with applications in Biostatistics (which is providing food for thought since the first ICRAs, covering traditional areas of RA, until now), Engineering Reliability, the Environmental Sciences and Economics. The contributions, based on lectures given at the 9th International Conference on Risk Analysis (ICRA 9), at Perugia, Italy, May 2022, detail a wide variety of daily risks, building on ideas presented at previous ICRA conferences. Working within a strong theoretical framework, supporting applications, the material describes a modern extension of the traditional research of the 1980s. This book is intended for graduate students in Mathematics, Statistics, Biology, Toxicology, Medicine, Management, and Economics, as well as quantitative researchers in Risk Analysis.
Examining the network effects in bank risk: evidence from liquidity
creation in mutual banks.- Teaching Note-Data Science Training for Finance
and Risk Analysis: A Pedagogical Approach with Integrating Online Platforms.-
Analysing Misclassifications in Confusion Matrices.- Management excellence
model use - Brazilian electricity distributors case.- A statistical boost to
assess water quality.- Time series procedures to improve extreme quantile
estimation.- Factors associated with Powerful Hurricanes in the Atlantic.-
Reliable Alternative Ways to Manage the Risk of Extreme Events.- Risk
Analysis in Practice and Theory.- On some consequences of COVID-19 in EUR/USD
exchange rates and economy.- Natural risk assessment of Italian
municipalities for residential insurance.- Variable selection in binary
logistic regression for modelling bankruptcy risk.- Operations with
iso-structured models with commutative orthogonal block structure: an
introductory approach.- Long and Short-run dynamics in Realized Covariance
Matrices: a Robust MIDAS Approach.- Taxonomy-based Risk Analysis with a
Digital Twin.- Advanced Lattice Rules for Multidimensional Sensitivity
Analysis in Air Pollution Modelling.- On pitfalls in statistical analysis for
risk assessment of COVID-19.
Format: Paperback / softback, height x width: 235x155 mm, Approx. 260 p.; Approx. 260 p.
Series: Universitext
Pub. Date: 25-Dec-2023
ISBN-13: 9783031428982
This textbook provides a first introduction to category theory, a powerful framework and tool for understanding mathematical structures. Designed for students with no previous knowledge of the subject, this book offers a gentle approach to mastering its fundamental principles. Unlike traditional category theory books, which can often be overwhelming for beginners, this book has been carefully crafted to offer a clear and concise introduction to the subject. It covers all the essential topics, including categories, functors, natural transformations, duality, equivalence, (co)limits, and adjunctions. Abundant fully-worked examples guide readers in understanding the core concepts, while complete proofs and instructive exercises reinforce comprehension and promote self-study. The author also provides background material and references, making the book suitable for those with a basic understanding of groups, rings, modules, topological spaces, and set theory. Based on the author's course at the Vrije Universiteit Brussel, the book is perfectly suited for classroom use in a first introductory course in category theory. Its clear and concise style, coupled with its detailed coverage of key concepts, makes it equally suited for self-study.
1 Categories and Functors.- 2.- Limits and Colimits.- 3 Adjoint
Functors.- 4 Solutions to Selected Exercises.
Series on Knots and Everything: Volume 74
Pages: 172
ISBN: 978-981-127-512-8 (hardcover)
According to string theory, our universe exists in a 10- or 11-dimensional space. However, the idea the space beyond 3 dimensions seems hard to grasp for beginners. This book presents a way to understand four-dimensional space and beyond: with knots! Beginners can see high dimensional space although they have not seen it.
With visual illustrations, we present the manipulation of figures in high dimensional space, examples of which are high dimensional knots and n-spheres embedded in the (n+2)-sphere, and generalize results on relations between local moves and knot invariants into high dimensional space.
Local moves on knots, circles embedded in the 3-space, are very important to research in knot theory. It is well known that crossing changes are connected with the Alexander polynomial, the Jones polynomial, HOMFLYPT polynomial, Khovanov homology, Floer homology, Khovanov homotopy type, etc. We show several results on relations between local moves on high dimensional knots and their invariants.
The following related topics are also introduced: projections of knots, knot products, slice knots and slice links, an open question: can the Jones polynomial be defined for links in all 3-manifolds? and Khovanov-Lipshitz-Sarkar stable homotopy type. Slice knots exist in the 3-space but are much related to the 4-dimensional space. The slice problem is connected with many exciting topics: Khovanov homology, Khovanv?Lipshits?Sarkar stable homotopy type, gauge theory, Floer homology, etc. Among them, the Khovanov?Lipshitz?Sarkar stable homotopy type is one of the exciting new areas; it is defined for links in the 3-sphere, but it is a high dimensional CW complex in general.
Much of the book will be accessible to freshmen and sophomores with some basic knowledge of topology.
About the Author
Acknowledgment
Introduction
Local Moves On Knots: For Beginners
Four-Dimensional Space ?4
Local Moves in Higher-Dimensional Space: For Beginners
Knotted-Objects in 4-Space and Beyond
Local Moves on High-Dimensional Knots and Related Invariants
The Alexander and Jones Polynomials of One-Dimensional Links in ?3
Local Moves and Knot Polynomials in Higher Dimensions
Important Topics in Knot Theory
References
Index
Freshmen and sophomores of science and people with similar mathematical background; general public interested in science, sci-fiction, and high-dimensional space; novice researchers in knot theory.
Pages: 420
ISBN: 978-981-126-697-3 (hardcover)
This introductory book contains a rich collection of exercises and worked examples in Metric Spaces. Other than questions in the traditional setting, plenty of True-or-False type questions and open-ended questions are included. With detailed solutions, these are highly effective in helping students gain a bird's eye view and master the subject and pitfalls better. The presentation is clear in nurturing the mathematical insights and mathematical maturity of the readers.
In this book, the pictorialization or visualization of abstract situations into simple pictures is very often crucially conducive to the understanding of the materials. This serves to give an insightful view of the intricate problems, as well as a clue or a direction to formulate rigorous arguments.
The learning outcomes include:
Demonstrate knowledge and understanding of the basic features of mathematical analysis and point set topology (e.g., able to identify objects that are topological equivalent);
Apply knowledge and skills acquired in mathematical analysis to analyze and handle novel situations in a critical way (e.g., able to determine whether a specific function is uniformly continuous);
Think creatively and laterally to generate innovative examples and solutions to non-standard problems (e.g., able to construct counterexamples to inaccurate mathematical statements).
Acquire sufficient background for further studies in Functional Analysis, Real Analysis, Differential Geometry, Complex Analysis, Algebraic Geometry, Probability Theory, Mathematical Physics, Economics, and others.
Request Inspection Copy
Metric Spaces
Limits and Continuity
Connectedness
Uniform Continuity
Uniform Convergence
Advanced undergraduate students and fresh graduate students in mathematics, physics, engineering, economics and finance. Suitable for an introductory course in Topology and Mathematical Analysis.
Mathematical Olympiad Series: Volume 21
Pages: 200
This book not only introduces important methods and strategies for solving problems in mathematics competition, but also discusses the basic principles behind them and the mathematical way of thinking.
It may be used as a valuable textbook for a mathematics competition course or a mathematics education course at undergraduate and graduate level. It can also serve as a reference book for students and teachers in primary and secondary schools.
The materials of this book come from a book series of Mathematical Olympiad Competition. It is a collection of problems and solutions of the major mathematical competitions in China. The translation is done by Yongming Liu.
The authors are mathematical competition teachers and researchers, many China's national team coaches and national team leaders. Many techniques and approaches in the book come directly from their own research results.
Reduction
Proof by Contradiction
Induction
The drawer Principle
Inclusion-Exclusion Principle
Extreme Principle
Parity
Area Methods
Thinking Globally
Proper Representations
Combine Numbers and Figures
Correspondence and Pairing
Recurrence
Colouring
Assignment Methods
Calculate in Two Ways
Stepwise Adjustments
Constructive Proof
Invariants and Monovariants
Graph Theory
Solution for Exercises
Senior high school students and math teachers, undergraduate in mathematics, amateurs interested in mathematics.
Pages: 270
ISBN: 978-981-127-821-1 (hardcover)
This book presents an introduction to the key topics in Real Analysis and makes the subject easily understood by the learners. The book is primarily useful for students of mathematics and engineering studying the subject of Real Analysis. It includes many examples and exercises at the end of chapters. This book is very authentic for students, instructors, as well as those doing research in areas demanding a basic knowledge of Real Analysis. It describes several useful topics in Real Analysis such as sets and functions, completeness, ordered and field, neighborhoods, limit points of a set, open sets, closed sets, countable and uncountable sets, sequences of real numbers, limit, continuity and differentiability of real functions, uniform continuity, point-wise and uniform convergence of sequences and series of real functions, Riemann integration, improper integrals and metric spaces.
Sets and Functions
Real Number System
Basics of the Real Analysis
Sequences of Real Numbers
Limit and Continuity
Uniform Continuity of Real Functions
Differentiability of Real Functions
Uniform Convergence of Sequences and Series of Functions
Functions of Several Variables
Riemann Integration
Improper Integrals
Metric Spaces
Undergraduate and postgraduate students in Real Analysis.
Pages: 200
ISBN: 978-981-127-815-0 (hardcover)
ISBN: 978-981-127-874-7 (softcover)
Why is 2 times 3 equal to 3 times 2? One may think this is an axiom, but it has a proof, and a beautiful one at that. Elementary mathematics is as deep and as beautiful as higher mathematics. It includes some of the most important mathematical discoveries ever, for example the concept of the number, and the place-value method of representing numbers. We are so accustomed to this method , that we forget how clever and beautiful it is ? resulting in its incredible efficacy.
All this was a surprise for the author, a university professor of mathematics, when he went to teach in elementary school. He realized that good teaching of elementary mathematics requires understanding its fine points and conveying their beauty to the students. Sensing the beauty and understanding go hand in hand.
The book outlines the material from kindergarten to grade 6 (with an excursion into algebra as well). It also discusses teaching principles, and their close relatives ? thinking principles. Teachers and parents who imbue these principles are likely to convey the love of mathematics to the child.
What is Mathematics?
How Do Mathematicians Think?
Three Stages ? Concrete, Pictorial, Abstract
Words ? The Cement of Thought
Asking Why
Reversal
There is No Such Thing as "Too Simple"
The Most Misleading Term in Mathematical Education
"3 Times 4 Equals 4 Times 3" is Not an Axiom
In The Country of One-Fingered Creatures
The New Math
What is a Fraction?
Education, for children aged from 6 to 12 years. Parents, teachers, math enthusiasts.