Format: Hardback, 138 pages, height x width: 235x155 mm, 35 Illustrations, color; 1 Illustrations, black and white; X, 138 p. 36 illus., 35 illus. in color
Series: Readings in Mathematics
Pub. Date: 22-Oct-2023
ISBN-13: 9783031375569
This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series-and infinite series in general-are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural.
Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor's guide with solutions to all the problems is available.
The book is intended as a supplementary textbook for calculus courses; lecturers and instructors will find innovative and engaging ways to teach this topic. The informal and conversational tone make the book useful to any student seeking to understand this essential aspect of analysis.
- To the reader.- Getting close with lines.- Getting closer with polynomials.- Going all the way: Convergence.- Power series.- Distant mountains.- Appendix A: SageMath: A (very) short introduction.- Appendix B: Why I do it this way.- Bibliography.
Format: Paperback / softback, height x width: 235x155 mm, Approx. 280 p.,
Series: Mathematics Study Resources 7
Pub. Date: 30-Oct-2023
ISBN-13: 9783662679739
This book contains the basics of abstract algebra.
In addition to elementary algebraic structures such as groups, rings and solids, Galois theory in particular is developed together with its applications to the cyclotomic fields, finite fields or the question of the resolution of polynomial equations.
Special attention is paid to the natural development of the contents. Numerous intermediate explanations support this basic idea, show connections and help to better penetrate the underlying concepts.
The book is therefore particularly suitable for learning algebra in self-study or accompanying online lectures.
1 Motivation and prerequisites1.1 Goals1.2 Prerequisites2 Field
extensions and algebraic elements2.1 Field extensions2.2 Intermediate Field
and algebraic elementsTasks3 Groups3.1 General Definition and Consequences3.2
Subgroups and group homorphismsTasks4 Group quotients and normal divisors4.1
Equivalence relations4.2 Group quotients4.3 Lagrange's theorem4.4 Normal
Divisors and Factor Groups4.5 The Homomorphism Theorem for Groups4.6 Finite
cyclic groupsTasks5 Rings and Ideals5.1 Commutative rings with one5.2 Ring
homomorphisms5.3 Units and zero divisors5.4 Ideals, factor rings and the
homomorphism theorem5.5 Primideals and maximal ideals5.6 The Chinese
Remainder Theorem5.7 Examples of rings in square number fieldsTasks6
Euclidean rings, principal ideal rings, Noether's rings6.1 Euclidean rings6.2
The Euclidean algorithm6.3 Noether's ringsTasks7 Factorial Rings7.1 Prime
elements and irreducible elements, factorial rings7.2 PropertiesTasks8
Quotient Fields for Integrity RangesTasks9 Irreducible polynomials in
factorial rings9.1 Content of polynomials9.2 Reduction modulo Primelement9.3
The Gauss Lemma9.4 Application of the reduction mod ? and Gauss' theoremTasks
10 Galois Theory (I) - Theorem A and its Variant A'10.1 The miraculous Field
creation10.2 The decomposition Field 10.3 Theorem A and A'10.4 Application in
the Field tower 10.5 The Galois groupTasks
11 Intermezzo - explicit example
Tasks12 Normal Field extensions12.1 Algebraic closure12.2 Continuation of
Field homorphisms12.3 Normal extensionsTasks13 Separability 13.1 Motivation
and Definition13.2 Formal derivation13.3 Characteristics of a Field and
separability13.4 The degree of separability13.5 The theorem of the primitive
elementTasks14 Galois Theory (II) - The Main Theorem14.1 The Main Theorem -
Statement14.2 Prospect of an application - midnight formula for all
degrees?14.3 Proof of the Main Theorem14.4 Proof of the additionTasks15
Cyclotomic fields 15.1 Unit roots15.2 Circle divisors and polynomialsTasks 16
Finite Fields16.1 Prime fields, finite field and Frobenius16.2 Finite
FieldsTasks17 More Group Theory - Group Operations and Sylow17.1 Group
operations17.2 The Sylow Theorems17.3 Applications of the Sylow Theorems and
Common Tricks17.4 Proof of the Sylow TheoremsTasks18 Solvability of
polynomial equations18.1 Solvable groups18.2 Solving polynomial equations by
radicals18.3 The general equation n-th degreeTasksA Proof of the existence of
an algebraic closure B Tricks and methods to classify groups of a given
orderB.1 Standard arguments and examplesB.2 Explicit examples
Format: Hardback, 255 pages, height x width: 235x155 mm, 36 Illustrations, color;
23 Illustrations, black and white; X, 255 p. 59 illus., 36 illus. in color
Pub. Date: 31-Oct-2023
ISBN-13: 9783031397905
This book focuses on the statistical modeling of geophysical and environmental data using Bayesian latent Gaussian models. The structure of these models is described in a thorough introductory chapter, which explains how to construct prior densities for the model parameters, how to infer the parameters using Bayesian computation, and how to use the models to make predictions. The remaining six chapters focus on the application of Bayesian latent Gaussian models to real examples in glaciology, hydrology, engineering seismology, seismology, meteorology and climatology. These examples include: spatial predictions of surface mass balance; the estimation of Antarctica’s contribution to sea-level rise; the estimation of rating curves for the projection of water level to discharge; ground motion models for strong motion; spatial modeling of earthquake magnitudes; weather forecasting based on numerical model forecasts; and extreme value analysis of precipitation on a high-dimensional grid. The book is aimed at graduate students and experts in statistics, geophysics, environmental sciences, engineering, and related fields.
Preface.
Chapter
1. Birgir Hrafnkelsson and Haakon Bakka: Bayesian
latent Gaussian models.
Chapter
2. Giri Gopalan, Andrew Zammit-Mangion, and
Felicity McCormack: A review of Bayesian modelling in glaciology.
Chapter
3.
Birgir Hrafnkelsson, Rafael Daniel Vias, Solvi Rognvaldsson, Axel Orn
Jansson, and Sigurdur M. Gardarsson: Bayesian discharge rating curves based
on the generalized power law.
Chapter
4. Sahar Rahpeyma, Milad Kowsari, Tim
Sonnemann, Benedikt Halldorsson, and Birgir Hrafnkelsson: Bayesian modeling
in engineering seismology: Ground-motion models.
Chapter
5. Atefe Darzi,
Birgir Hrafnkelsson, and Benedikt Halldorsson: Bayesian modelling in
engineering seismology: Spatial earthquake magnitude model.
Chapter
6.
Joshua Lovegrove and Stefan Siegert: Improving numerical weather forecasts by
Bayesian hierarchical modelling.
Chapter
7. Arnab Hazra, Raphael Huser, and
Arni V. Johannesson: Bayesian latent Gaussian models for high-dimensional
spatial extremes.
Format: Hardback, 580 pages, height x width: 235x155 mm, 350 Tables, color; 350 Illustrations,
color; 100 Illustrations, black and white; XX, 580 p. 450 illus., 350 illus. in color.
Series: Trends in Mathematics
Pub. Date: 12-Nov-2023
ISBN-13: 9783031414190
This volume collects the proceedings of the International Conference on Recent Developments in Mathematics (ICRDM), held at Canadian University Dubai, UAE, in August 2022. This is the second of two volumes, with this volume focusing on more applied topics, particularly mathematical modeling and scientific computing, and the first covering recent advances in algebra and analysis. Each chapter identifies existing research problems, the techniques needed to solve them, and a thorough analysis of the obtained results. Advances in Mathematical Modeling and Scientific Computing will appeal to a range of postgraduate students, researchers, and industry professionals interested in exploring recent advancements in applied mathematics.
PART 1 - Differential Equations: High-Precision Algorithms For Fredholm
Integral Equations (Awawdeh).- A new decay estimate for a weakly dissipative
viscoelastic suspension bridge (Al-Gharablic).- Existence and uniqueness of
Renormalized solution to non-coercive elliptic problem with measure data
(Ouedraogo).- Fixed-Point Theorems Based Evaluation of Analytical Solution in
Fractional Diffusion Equations (Malathi).- Control and Synchronization of a
Modified Chaotic Finance System with Integer and Non-Integer Orders
(Moaddy).- Dutch Book Methods for difference and differential equations
(Gandolfi).- Fourier modes in fluid flow and energy cascade (Afanasyeva).-
Approximate solutions of third order time fractional dispersive equations
with singular and non singular kernel derivatives (Raghavendar).- Choosing
between vaccine efficacy and vaccine price: mathematical model for COVID19
(Al-arydah).- Classification of Cosmological Wormhole Solutions in the
Framework of General Relativity (Al-Ali).- Use of Technology and Software in
Mathematics Education (Jain).- Modified VIM for the Solutions of Gas Dynamics
(Fatima).- PART 2 - Mechanics: Nanofluid containing motile gyrotactic
microorganisms squeezed between parallel disks (Umavathi).- Linear model for
two layer porous bed suspended with nano sized particles (Umavathi).- Effect
of Variable Viscosity on Magnetohydrodynamics Mixed Convection Flow from a
Vertical Flat Plate (Ajaykumar).- Line effects in the Darcy-Benard
instability in a rotating anisotropic porous layer saturated with a fluid of
variable viscosity (Suthar).- Soret and Dufour Effects on Radiative MHD
Thermosolutal Viscoplastic Nanofluid Mixed convective Flow Past a
Bidirectional Stretching Sheet (Venkatadri).- Influence of Slip Velocity on
an Infinite Cylinder and Rough Flat Plate lubricated with couple stress fluid
(Sreekala).- Simulation of MHD Quadratic Natural Convection Flow of Nanofluid
Inside a Square Enclosure with Thermal Radiation Effect (Venkatadri).-
Combined Effects of Magnetic Field and Heat Source on Double Diffusive
Marangoni Convection in Fluid-Porous Structure (Manjunatha).- Peristalsis and
Taylor Dispersion of Solute in the Flow of Casson Fluid (Nagarani).- An
Aligned Magnetic field effect on Unsteady Heat and Mass Transfer Flow of
non-Newtonian Fluid through Porous Medium (Maheshbabu).- Effect of viscosity
variation and slip velocity on the squeeze film characteristics between a
cylinder and a plane plate with couple stress fluid (Salma).- Turbulence
Generators and Turbulence Structure (Selvam).- Conjugate buoyant convection
of nanoliquids in a porous saturated annulus (Arokiaraj).- The characteristic
of squeeze film due to Impact of couple stress and MHD on curved annular
circular plates (Nair).- An Exact Analytical Solution Marangoni Boundary
Layer Flow with Heat and Mass Transfer (Hatami).- Hybrid Nanofluid Flow and
Thermal Transport Analysis in a Linearly Heated Cylindrical Annulus
(Sankar).- Influence of non-similar heating on nanofluid buoyant convection
of nanofluid in a tilted porous parallelogrammic geometry (Sankar).- Buoyant
Convection of Nanofluid in an annular domain with linearly heating (Girish).-
Thermal and entropy management of nanoliquid in a discretely heated inclined
square geometry (Kumara Swamy).- Linear and Non-linear Analysis of
Unicellular Rayleigh-Benard Magneto Convection in a Micropolar Fluid
Occupying Enclosures (Jestine).- Study uf Rayleigh - Benard - Marangoni
Convention in a Microfliud with Corirlos Force (Baby).- Performance of
magnetic dipole contribution on ferromagnetic heat and mass transfer flow
with the influence of non-linear radiative heat flux (Venkatadri).-
Thermogravitational Convective Flow inside a Cavity with a Heated Circular
Cylinder: A Finite Difference Analysis via Vorticity Stream Function Approach
(Venkatadri).- An Unsteady Flow of Fluid Velocity, Temperature and Heat
Emission on Mhd Free Convection Flow of Some Nanofuids (Ramesh Babu)Finite
Element Analysis of Unsteady Dispersion in Casson Fluid Flow (Nagarani).-
Thermosolutal Convection in a Tilted Porous Parallelogrammic Enclosure with
Discrete Heating and Salting (Sankar).- An application of generalized Fourier
and Fick's law over a different non Newtonian fluid (Padmavathi).- Micropolar
nanofluid enfolded with viscous fluid: Three layer flow Operation Research
Production inventory model for three levels of production with defective
items, shortages including multi delivery policy (Karthikeyan).-
Accomplishment Expedients Of Batch Arrival Queuing Model by Fuzzy Ordering
approach (Ramesh).- Analysis of a M[ x]/G/1 retrial queue with Secondary
optional Service subject to Bernoulli Vacation, Server Breakdown and Customer
Baulking (Indhira).- Solving Neutrosophic Bi-objective Assignment Problem
using Different Approaches (Anuradha).- Analysis of Attainment Estimates of
Loss System Queue (Seenivasan).- Performance scrutinity of an M/G/1 Retrial
Queue with Two-Phase Service and Preemptive Resume under Working Vacations
and Working Breakdowns (Indhira).- Models of Goal Programming & R Programming
to Earmark Acreage (Shalini).- Neutral- Bipolar Fuzzy Sets and its
Applications (Rosline).- Critical path in an intuitionistic triangular fuzzy
number for Time Cost Trade Off in project network by the modified traditional
method (Deepa).- Operations on Alternate Quadra - Submerging Polar (AQSP)
Fuzzy Graphs and its Applications (Rosline).- Optimal Solution for
Transportation Problems using Trapezoidal Fuzzy Numbers (Boobalan).-
Heterogeneous Queueing Model with Intermittently Obtainable Server with
Feedback (Indhira).- An Economic order quantity inventory model for the food
supply chain with waste minimization based on a circular economy
(Karthikeyan).- Achievement Estimations of Priority Queue System in Fuzzy
Environment (Seenivasan).- Poisson jumps and state-dependent delay in a
sequential approximation of stochastic neutral partial integro-differential
systems (Pradeepa).- A hybrid genetic algorithm based linear programming
model to optimize feed cost for Indian Ruminants: With Stochastic Model in
Comparison (Kuntal).- PART 3 - Statistics: Outlier Detection using the Range
Distribution Dania Dallah and Hana Sulieman (Dallah).- Presenting a flexible
class of INAR(p) models to analyze the COVID-19 series in Mauritius
(Youssef).- Prediction of Social Status on Depression by using Logistic
Regression (Karthikeyan).- Single Working Vacation Queue, Server Failure With
Appearance of Backup Server (Seenivasan).- Exploring ARIMA models with
interacted lagged variables for forecasting (Dhandra).- A Novel Hybrid Model
for Time Series Forecasting Using Artificial Neural Networks and
Autoregressive Integrated Moving Average Models (Baskaran).- PART 4 - Graph
Theory Sigma chromatic number of Mycielski transformation of graphs
(Balamurugan).- Bipartite Decomposition of Graphs using Chromatic Number
(Karthika).- Degree-Based Topological Indices and QSPR Analysis of Some Drugs
Used in the Treatment of Dengue (Balamurugan).- Orientation Number of Two
Complete Bipartite Graphs with Linkages (Rajasekaran).- Packing Chromatic
Number of Windmill related Graphs (Santiago).- Complementary triple connected
total domination number of a graph (Mahadevan).- Pebbling Number and
2-Pebbling property for the Middle Graphs of the graph obtained from fan
graph by deleting f independent Edges (Dhivviyanandam).- The De Brunn Graoh
Ofsequential Repetition of Patterns in DNA Strings (Fong).- Independent
Domination Number of Cyclic and Acyclic Graphs (Balamurugan).- Computation of
Complete Partite- Zumkeller Graphs (Balamurugan).- Characterizations of
(gamma(i), gamma(DDS), gamma(DSNS)) - Trees (Yamuna).- Mobius Cordial
Labeling of Graphs (Balamurugan).- Selfipendant and Extremal Pendant Graphs
(Kottarathil).- PART 5 - Mathematical Education : Computing the CD-number of
Strong product of graphs (Mahadevan).- Detection of TCC-Domination number for
some product related graphs (Mahadevan).- Learners' Mental Constructions in
Learning Circle Geometry (Brijlall).- N - Separation Axioms in Topological
Spaces (Alsalem).- Investigating how the Activity, Classroom Discussion, and
Exercise (ACE)Teaching Cycle influences Learners' Problem-Solving and
achievement in Circle Geometry (Brijlal).- Exploring possible teacher and
learner support structures to improve learner Mathematics performance
(Brijlal).- A study of Mathematical Epidemiology Model of Dengue Spread with
fractional Properties (Jain).
Format: Hardback, 606 pages, height x width: 235x155 mm, 50 Illustrations, black and white; XVI, 606 p. 50 illus.
Series: Frontiers in Probability and the Statistical Sciences
Pub. Date: 09-Oct-2023
ISBN-13: 9783031370533
This book covers an extensive class of models involving inhomogeneous Poisson processes and deals with their identification, i.e. the solution of certain estimation or hypothesis testing problems based on the given dataset. These processes are mathematically easy-to-handle and appear in numerous disciplines, including astronomy, biology, ecology, geology, seismology, medicine, physics, statistical mechanics, economics, image processing, forestry, telecommunications, insurance and finance, reliability, queuing theory, wireless networks, and localisation of sources.
Beginning with the definitions and properties of some fundamental notions (stochastic integral, likelihood ratio, limit theorems, etc.), the book goes on to analyse a wide class of estimators for regular and singular statistical models. Special attention is paid to problems of change-point type, and in particular cusp-type change-point models, then the focus turns to the asymptotically efficient nonparametric estimation of the mean function, the intensity function, and of some functionals. Traditional hypothesis testing, including some goodness-of-fit tests, is also discussed. The theory is then applied to three classes of problems: misspecification in regularity (MiR),corresponding to situations where the chosen change-point model and that of the real data have different regularity; optical communication with phase and frequency modulation of periodic intensity functions; and localization of a radioactive (Poisson) source on the plane using K detectors.
Each chapter concludes with a series of problems, and state-of-the-art references are provided, making the book invaluable to researchers and students working in areas which actively use inhomogeneous Poisson processes.
Poisson Processes.- Parameter Estimation.- Non-parametric Estimation.- Hypothesis Testing.- Applications.- Likelihood ratio and properties of MLE and BE.
Format: Hardback, 311 pages, height x width: 235x155 mm, 76 Tables, color; 56 Illustrations,
color; 29 Illustrations, black and white; IV, 311 p. 85 illus., 56 illus. in color
Series: Contributions to Statistics
Pub. Date: 31-Oct-2023
ISBN-13: 9783031400544
This volume presents a selection of articles on statistical modeling and simulation, with a focus on different aspects of statistical estimation and testing problems, the design of experiments, reliability and queueing theory, inventory analysis, and the interplay between statistical inference, machine learning methods and related applications. The refereed contributions originate from the 10th International Workshop on Simulation and Statistics, SimStat 2019, which was held in Salzburg, Austria, September 2?6, 2019, and were either presented at the conference or developed afterwards, relating closely to the topics of the workshop. The book is intended for statisticians and Ph.D. students who seek current developments and applications in the field.
Part I Invited Papers.- Likelihood Ratios in Forensics: What They Are and What They Are Not.- MANOVA for large number of treatments.- Pollutant Dispersion Simulation by means of a Stochastic Particle Model and a Dynamic Gaussian-Plume Model.- On an alternative trigonometric strategy for statistical modeling.- Part II Design of Experiments.- Incremental construction of nested designs based on two-level fractional factorial designs.- A study of L-optimal designs for the two-dimensional exponential model.- Testing for randomized block single-case designs by combined permutation tests with multivariate mixed data.- Adaptive design criteria motivated by a plug-in percentile estimator.- Part III Survival, Risk and Inventory Analysis.- On a parametric estimation for a convolution of exponential densities.- Statistical Estimation with a Known Quantile and Its Application in a Modified ABC-XYZ Analysis.- Symptom Analysis of Multidimensional Categorical Data with Application in Genetics.- Part IV Machine Learning and Applications.- A study of Design of Experiments and machine learning methods to improve fault detection algorithms.- A Brief Survey of AutoML and its use for Neural Architecture.- Microstructure Image Segmentation Using Patch-Based Clustering Approach.- Clustering and Symptom Analysis in Binary Data with Application.- Big Data for Credit Risk Analysis: Efficient Machine Learning Models Using PySpark
Format: Paperback / softback, 359 pages, height x width: 235x155 mm, 152 Illustrations, black and white; XIX, 359 p. 152 illus.,
Series: Universitext
Pub. Date: 31-Oct-2023
ISBN-13: 9783031400438
This text is based on lectures delivered by the first author on various, often nonstandard, parts of knot theory and related subjects. By exploring contemporary topics in knot theory including those that have become mainstream, such as skein modules, Khovanov homology and Gram determinants motivated by knots, this book offers an innovative extension to the existing literature. Each lecture begins with a historical overview of a topic and gives motivation for the development of that subject. Understanding of most of the material in the book requires only a basic knowledge of topology and abstract algebra. The intended audience is beginning and advanced graduate students, advanced undergraduate students, and researchers interested in knot theory and its relations with other disciplines within mathematics, physics, biology, and chemistry.
Inclusion of many exercises, open problems, and conjectures enables the reader to enhance their understanding of the subject. The use of this text for the classroom is versatile and depends on the course level and choices made by the instructor. Suggestions for variations in course coverage are included in the Preface. The lecture style and array of topical coverage are hoped to inspire independent research and applications of the methods described in the book to other disciplines of science. An introduction to the topology of 3-dimensional manifolds is included in Appendices A and B. Lastly, Appendix C includes a Table of Knots.
1. History of Knot Theory From Ancient Times to Gauss and His Student
Listing.-
2. History of Knot Theory From Gauss to Jones. -
3. FROM FOX
3-COLORING TO THE YANG-BAXTER OPERATOR. -
4. Lecture ?: Goeritz and Seifert
Matrices.-
5.
Chapter Heading.-
6. The HOMFLYPT and the 2-variable Kauffman
Polynomial.-
7. Lecture 8: The Temperley - Lieb Algebra and Braid Groups. -
8. Lecture 9: Symmetrizers of Finite Groups and Jones-Wenzl Idempotents. -
9.
Lecture 10: Plucking polynomial of rooted trees and its use in knot theory. -
10. Lecture 11: Basics of Skein Modules. -
11. Lecture 12: The Kauffman
Bracket Skein Module. -
12. Lecture 13: The Kauffman Bracket Skein Module
and Algebra of Surface I-bundles. -
13. Lecture 14: Multiplicative Structure
of the Kauffman Bracket Skein Algebra of the Thickened T-Shirt.-
14. Spin
Structure and the Framing Skein Module of Links in 3-Manifolds.-
15. Lecture
16: The Witten - Reshetikhin - Turaev Invariant of 3-manifolds. -
16.
Lecture 19: Type A Gram determinant.-
17. Lecture 18: Gram Determinants of
Type B and Type M b. -
18. Lecture 19: Khovanov homology: a categorification
of The Jones polynomial. -
19. Lecture 20: Long Exact Sequence of Khovanov
Homology and Torsion.-
20. Lecture 21: Categorification of Skein Modules of
Twisted I-bundles over surfaces. - Appendix A: Basics of 3-Dimensional
Topology. -Appendix B: Surgery on Links in the 3-Sphere and Kirby's Calculus.
-Glossary. - SOlutions
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