ISBN: 978-3-031-32954-8
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月17日
Series Title: Birkhauser Advanced Texts Basler Lehrbucher
This textbook offers a uniquely accessible introduction to flows on compact surfaces, filling a gap in the existing literature. The book can be used for a single semester course and/or for independent study. It demonstrates that covering spaces provide a suitable and modern setting for studying the structure of flows on compact surfaces. The thoughtful treatment of flows on surfaces uses topology (especially covering spaces), the classification of compact surfaces, and Euclidean and hyperbolic rigid motions to establish structural theorems that describe flows on surfaces generally. Several of the topics from dynamical systems that appear in this book (e.g., fixed points, invariant sets, orbits, almost periodic points) also appear in the many subareas of dynamical systems. The book successfully presents the reader with a self-contained introduction to dynamical systems or an expansion of one's existing knowledge of the field. Prerequisites include completion of a graduate-level topology course; a background in dynamical systems is not assumed.
Nelson G. Markley was a professor of mathematics at the University of Maryland for more than twenty-five years and also served as provost and senior vice president at Lehigh University. He authored numerous journal articles in the area of dynamical systems as well as textbooks on differential equations, topological groups, and probability. He received his PhD from Yale University.
?Mary Vanderschoot is a professor of mathematics at Wheaton College (IL). She holds a PhD in topological dynamical systems from the University of Maryland. Nelson Markley was her PhD advisor.
ISBN: 978-981-99-2294-9
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月4日
Series Title: Behaviormetrics: Quantitative Approaches to Human Behavior
The purpose of this book is to thoroughly prepare diverse areas of researchers in quantification theory. As is well known, quantification theory has attracted the attention of a countless number of researchers, some mathematically oriented and others not, but all of them are experts in their own disciplines. Quantifying non-quantitative (qualitative) data requires a variety of mathematical and statistical strategies, some of which are quite complicated. Unlike many books on quantification theory, the current book places more emphasis on preliminary requisites of mathematical tools than on details of quantification theory. As such, the book is primarily intended for readers whose specialty is outside mathematical sciences. The book was designed to offer non-mathematicians a variety of mathematical tools used in quantification theory in simple terms. Once all the preliminaries are fully discussed, quantification theory is then introduced in the last section as a simple application of those mathematical procedures fully discussed so far. The book opens up further frontiers of quantification theory as simple applications of basic mathematics.
ISBN: 978-3-031-33389-7
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月28日
Series Title: Statistics and Computing
This textbook provides an accessible overview of statistical learning methods and techniques, and includes case studies using the statistical software Stata. After introductory material on statistical learning concepts and practical aspects, each further chapter is devoted to a statistical learning algorithm or a group of related techniques. In particular, the book presents logistic regression, regularized linear models such as the Lasso, nearest neighbors, the Naive Bayes classifier, classification trees, random forests, boosting, support vector machines, feature engineering, neural networks, and stacking. It also explains how to construct n-gram variables from text data. Examples, conceptual exercises and exercises using software are featured throughout, together with case studies in Stata, mostly from the social sciences; true to the book’s goal to facilitate the use of modern methods of data science in the field. Although mainly intended for upper undergraduate and graduate students in the social sciences, given its applied nature, the book will equally appeal to readers from other disciplines, including the health sciences, statistics, engineering and computer science.
Matthias Schonlau is a Professor in the Department of Statistics and Actuarial Science at the University of Waterloo, Canada. Prior to his academic career, he spent 14 years at the RAND Corporation, USA, the Max Planck Institute for Human Development in Berlin, Germany, the German Institute for Economic Analysis (DIW), the National Institute of Statistical Sciences, USA, and AT&T Labs Research, USA. He won the Humboldt Prize and was elected Fellow of the American Statistical Association. He has published more than 80 peer-reviewed articles and is also the lead author of the book Conducting Research Surveys via E-Mail and the Web (RAND Corporation).
ISBN: 978-981-99-2737-1
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月20日
This textbook provides a comprehensive course in metric spaces. Presenting a smooth takeoff from basic real analysis to metric spaces, every chapter of the book presents a single concept, which is further unfolded and elaborated through related sections and subsections. Apart from a unique new presentation and being a comprehensive textbook on metric spaces, it contains some special concepts and new proofs of old results, which are not available in any other book on metric spaces. It has individual chapters on homeomorphisms and the Cantor set. This book is almost self-contained and has an abundance of examples, exercises, references and remarks about the history of basic notions and results. Every chapter of this book includes brief hints and solutions to selected exercises. It is targeted to serve as a textbook for advanced undergraduate and beginning graduate students of mathematics.
Surinder Pal Singh Kainth is Assistant Professor at the Department of Mathematics, Panjab University, Chandigarh, India. He has a Ph.D. degree in integration theory from the Indian Institute of Technology Bombay and is working in generalized integrals and graph theory. He has made some significant progress on the sphere-of-influence graph (SIG) dimension conjecture.
ISBN: 978-981-99-2950-4
Subject: Mathematics and Statistics
Planned Publication Date: 2023年8月9日
Series Title: Springer Undergraduate Texts in Mathematics and Technology
This textbook is for those who want to learn linear algebra from the basics. After a brief mathematical introduction, it provides the standard curriculum of linear algebra based on an abstract linear space. It covers, among other aspects: linear mappings and their matrix representations, basis, and dimension; matrix invariants, inner products, and norms; eigenvalues and eigenvectors; and Jordan normal forms. Detailed and self-contained proofs as well as descriptions are given for all theorems, formulas, and algorithms.
A unified overview of linear structures is presented by developing linear algebra from the perspective of functional analysis. Advanced topics such as function space are taken up, along with Fourier analysis, the Perron?Frobenius theorem, linear differential equations, the state transition matrix and the generalized inverse matrix, singular value decomposition, tensor products, and linear regression models. These all provide a bridge to more specialized theories based on linear algebra in mathematics, physics, engineering, economics, and social sciences.
Python is used throughout the book to explain linear algebra. Learning with Python interactively, readers will naturally become accustomed to Python coding. By using Python’s libraries NumPy, Matplotlib, VPython, and SymPy, readers can easily perform large-scale matrix calculations, visualization of calculation results, and symbolic computations. All the codes in this book can be executed on both Windows and macOS and also on Raspberry Pi.
Makoto Tsukada has been studied in the field of functional analysis. He has been teaching linear algebra, analysis, and probability theory for many years. Also, he has taught programming language courses using Pascal, Prolog, C, Python, etc. Yuji Kobayashi, Hiroshi Kaneko, Sin-Ei Takahasi, Kiyoshi Shirayanagi, and Masato Noguchi are specialists in algebra, analysis, statistics, and computers.