Format: Hardback, 223 pages, height x width: 235x155 mm, 14 Illustrations, color; 6 Illustrations, black and white; XV, 234 p. 29 illus., 1 Hardback
Series: Problem Books in Mathematics
Pub. Date: 18-Sep-2024
ISBN-13: 9783031627675
This book gathers problems based on over twenty years of the Indiana College Mathematics Competition, a regional problem-solving contest for teams of undergraduates. Its problems and solutions are accessible to students in a standard college curriculum, not necessarily with Olympiad-level training. Problem sets form the core of Part I, covering myriad aspects of algebra, calculus, number theory, probability, and geometry. Chapters are organized by year, and an index allows easy navigation through specific topics. In Part II, the reader finds detailed solutions to the exercises.
With revised solutions designed for a didactical approach, this book can be especially useful as a resource for problem-solving courses in college mathematics or as practice problems for graduate entrance exams. This volume is a sequel to Rick Gillman's "A Friendly Competition," which documented the first 35 years of the competition.
Historical Remarks and Acknowledgements.- Part I. Problems.- 2001
Problems.- 2002 Problems.- 2003 Problems.- 2004 Problems.- 2005 Problems.-
2006 Problems.- 2007 Problems.- 2008 Problems.- 2009 Problems.- 2010
Problems.- 2011 Problems.- 2012 Problems.- 2013 Problems.- 2014 Problems.-
2015 Problems.- 2016 Problems.- 2017 Problems.- 2018 Problems.- 2019
Problems.- 2020 Problems. 2021 Problems.- 2022 Problems.- 2023 Problems.-
Part II. Solutions.- 2001 Solutions.- 2002 Solutions.- 2003 Solutions.- 2004
Solutions.- 2005 Solutions.- 2006 Solutions.- 2007 Solutions.- 2008
Solutions.- 2009 Solutions.- 2010 Solutions.- 2011 Solutions.- 2012
Solutions.- 2013 Solutions.- 2014 Solutions.- 2015 Solutions.- 2016
Solutions.- 2017 Solutions.- 2018 Solutions.- 2019 Solutions.- 2020
Solutions.- 2021 Solutions.- 2022 Solutions.- 2023 Solutions.- Part III. More
History of the ICMC.- Top scoring teams.- Top scoring teams.- Updates to: A
Friendly Mathematics Competition.- Appendices.- References and photo
credits.- Index.
Format: Hardback, 150 pages, height x width: 235x155 mm, 5 Illustrations, color; 6 Illustrations, black and white; X, 150 p. 10 illus., 4 illus. in color.,
Series: Research Perspectives Ghent Analysis and PDE Center 7
Pub. Date: 14-Sep-2024
ISBN-13: 9783031628931
The aim of this volume is to present some new developments and ideas in partial differential equations and mathematical analysis, including spectral analysis and boundary value problems for PDE, harmonic analysis, inequalities, integral equations, and applications. This book is a collection of short summaries of reports from lectures delivered at Tbilisi Analysis & PDE seminars and workshops. In particular, it contains some applications and several open questions aimed at inspiring further research. The volume contains 21 research articles.
- Continuous inequalities: introduction, examples and related topics.-
Approximation by Vilenkin-Norlund Means in Lebesgue Spaces.- On Divergence of
Fejer Means with Respect to Walsh System on sets of Measure Zero.- Martingale
Hardy Spaces and Some Maximal Operators Associated with Walsh- Fejer Means.-
Generic Bessel potential spaces on Lie groups.- The finite Hilbert transform
acting in rearrangement invariant spaces on (1, 1).- The Banach Gelfand
triple and its role in classical Fourier analysis and operator theory.- A
note on a frictional unilateral contact problem in nonlinear elasticity.-
Maximal noncompactness of singular integral operators on Lp spaces with power
weights.- A remark on piecewise linear interpolation of continuous Fourier
multipliers.- Banach algebras of convolution type operators with PQC data.-
Integrability and convergence of trigonometric series and Fourier
transforms.- Commutators of CalderonZygmund Operators in Grand Variable
Exponent Morrey Spaces, and Applications to PDEs.- Symmetric SteinTomas, and
why do we care?.- On Solonnikov parabolicity of the evolution anisotropic
Stokes and Oseen PDE systems.- On Convergence and Divergence of Fourier
Series and Fejer Means with Applications to Lebesgue and Vilenkin-Lebesgue
Points.- On generalized sharpness of some Hardy-type inequalities.-
Interaction problems for n-dimensional Dirac operators with singular
potentials.- Convergence and summability in classical and martingale Hardy
spaces.- Modulus of Continuity and Convergence of Fejer Means of
Vilenkin-Fourier Series in the Variable Martingale Hardy Space Hp(・).- On
unconditional convergence of Fourier series with respect to general
orthonormal systems.
Format: Hardback, 107 pages, height x width: 235x155 mm, 4 Illustrations, color; 5 Illustrations, black and white; XII, 109 p., 1 Hardback
Pub. Date: 21-Sep-2024
ISBN-13: 9783031639210
This is a personal story about being involved in the study of nonlinear phenomena for more than half a century. The focus is on the development of ideas and the resulting knowledge. This is the visible part of research, but much is usually hidden. The author describes how the ideas were generated and how an invisible college of friends and colleagues has emerged. The presentation is spiced by thoughts about the beauty of science and philosophical considerations on the complex world, where nonlinear interactions play an important role.
The book is in some sense a biography but not so much about the personal life of the author it is about science and its actors. Based on the author's experience in many European research centres and science policy institutions, it reflects on the development of knowledge in nonlinear dynamics as well as science policy actions over the second half of the 20th century and the first quarter of the 21st century. Graduates and postgraduates interested in the progress of research will find the book particularly engaging.
1 Nonlinearity.- 2 Starting the journey.- 3 Institute of Cybernetics.-
Centre for Nonlinear Studies - CENS, 1999-2015.- 5 Research goes on after
CENS.- 6 Science policy.- 7 Invisible college.- 8 Beauty of
nonlinearities.- 9 Epilogue.
Format: Paperback / softback, 613 pages, height x width: 235x155 mm, 141 Illustrations, color; 62 Illustrations, black and white; XX, 560 p. 201 illus., 139 illus. in color.,
Pub. Date: 16-Sep-2024
ISBN-13: 9783031638329
Now in its sixth edition, this textbook presents the tools and concepts used in multivariate data analysis in a style accessible for non-mathematicians and practitioners. Each chapter features hands-on exercises that showcase applications across various fields of multivariate data analysis. These exercises utilize high-dimensional to ultra-high-dimensional data, reflecting real-world challenges in big data analysis.
For this new edition, the book has been updated and revised and now includes new chapters on modern machine learning techniques for dimension reduction and data visualization, namely locally linear embedding, t-distributed stochastic neighborhood embedding, and uniform manifold approximation and projection, which overcome the shortcomings of traditional visualization and dimension reduction techniques.
Solutions to the books exercises are supplemented by R and MATLAB or SAS computer code and are available online on the Quantlet and Quantinar platforms. Practical exercises from this book and their solutions can also be found in the accompanying Springer book by W.K. Hardle and Z. Hl?vka: Multivariate Statistics - Exercises and Solutions.
Part I Descriptive Techniques.- 1 Comparison of Batches.- Part II
Multivariate Random Variables.- 2 A Short Excursion into Matrix Algebra.- 3
Moving to Higher Dimensions.- 4 Multivariate Distributions.- 5 Theory of the
Multinormal.- 6 Theory of Estimation.- 7 Hypothesis Testing.- Part III
Multivariate Techniques.- 8 Regression Models.- 9 Variable Selection.-10
Decomposition of Data Matrices by Factors.- 11 Principal Components
Analysis.- 12 Factor Analysis.- 13 Cluster Analysis.- 14 Discriminant
Analysis.- 15 Correspondence Analysis.- 16 Canonical Correlation Analysis.-
17 Multidimensional Scaling.- 18 Conjoint Measurement Analysis.- 19
Applications in Finance.- 20 Computationally Intensive Techniques.- 21
Locally Linear Embedding.- 22 Stochastic Neighborhood Embedding.- 23 Uniform
Manifold Approximation and Projection.- Part IV Appendix.- A Symbols and
Notations.- B Data.- Index.
Format: Paperback / softback, 333 pages, height x width: 235x155 mm, 85 Illustrations, black and white; X, 330 p. 12 illus.,
Series: Mathematics Study Resources 13
Pub. Date: 27-Aug-2024
ISBN-13: 9783662694114
This textbook is intended to be accessible to any second-year undergraduate in mathematics who has attended courses on basic real analysis and linear algebra. It is meant to help students to appreciate the diverse specialized mathematics courses offered at their universities. Special emphasis is on similarities between mathematical fields and ways to compare them. The organizing principle is the concept of a mathematical structure which plays an important role in all areas of mathematics.
The mathematical content used to explain the structural ideas covers in particular material that is typically taught in algebra and geometry courses. The discussion of ways to compare mathematical fields also provides introductions to categories and sheaves, whose ever-increasing role in modern mathematics suggests a more prominent role in teaching.
The book is the English translation of the second edition of Mathematische Strukturen (Springer, 2024) written in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
I Algebraic Structures.- 1 Rings.- 2 Modules.- 3 Multilinear Algebra.- 4
Pattern Recognition.- II Local Structures.- 5 Sheaves.- 6 Manifolds.- 7
Algebraic Varieties.- III Outlook.- 8 Transfer of Arguments and Structures.-
9 Specialization, Generalization and Unification of Structures.
Format: Hardback, 624 pages, height x width: 235x155 mm, 14 Illustrations, color; 56 Illustrations, black and white; XX, 664 p. 10 illus.,
Series: Systems & Control: Foundations & Applications
Pub. Date: 12-Sep-2024
ISBN-13: 9783031641237
This text explores the state-of-the-art in the rapidly developing theory of impulse control and introduces the theory of singular space-time transformations, a new method for studying shock mechanical systems. Two approaches in the theory of impulse control are presented: The first, more traditional approach defines the impulsive action as a discontinuity of phase coordinates depending on the current time, the state preceding the action, and its magnitude. The second requires the use of modern methods for describing dynamical systems - differential equations with measures. The impulse is treated as an idealization of a very short action of high magnitude, which produces an almost abrupt change of phase coordinates. The relation between these two approaches is also discussed, and several applications, both traditional and emerging, are considered.
This text is intended for graduate students and researchers in control engineering and optimal control theory for dynamical systems. Readers are assumed to be familiar with the theory of ODEs, optimal control, and functional analysis, though an appendix is included that covers many of the necessary mathematical concepts.
Preface.- Introduction.- Discrete-continuous systems with impulse
control.- Optimal impulse control problem with restricted number of
impulses.- Generalized solutions of nonlinear differential equations.-
Optimal generalized solutions in control problems.- The maximum principle in
problems of generalized optimal control.- Observations control in
discrete-continuous stochastic systems.- Impulsive control in shock
mechanics.- Appendix. Differential equations with measures.- Index.-
Bibliography.