This is a highly informative and richly illustrated nonfiction book that conveys scientific content in a clear and understandable way. Drawing on numerous examples, it explains topics from geometry, physics, and biology and points out commonalities between the disciplines. The book contains approx. 300 links to video animations and is accompanied by a freely accessible interactive software that allows readers to delve even deeper into the content covered in the book.
The content, videos, and software were developed by the Department of Geometry at the University of Applied Arts Vienna. Georg Glaeser’s research focuses particularly on interdisciplinary mathematical and biological issues, and he worked for many years with Franz Gruber, who was highly adept at visualizing complex issues.
Includes links to around 300 video animations, accessible via QR codes
Compact, informative, and easy-to-understand explanations of scientific issues in the disciplines of geometry, physics, and biology
With numerous images and illustrations
Frontmatter 1
Preface
Publicly Available 8
Kinematics: Motions in Nature and Technology 11
Gearwheels: Precise and Robust 31
Patterns and Fractals: Simulation of Nature 41
Strange Angles: Spirals? 61
Projections: Necessary and Practical 69
Polyhedra: Building Blocks! 79
Simple-Curved: Developable! 93
Double-Curved: The Norm 107
Minimal Surfaces: Elegant and Practical 127
Wave Models: Strange Phenomena 137
Photography: Surprises? 149
Air and Water: Fluids! 169
Distributions: Attraction and Repulsion 193
Our Solar System: Free Play of Forces 207
Illusions: Fake or Real? 223
Simulations: Close to Reality? 235
Index 242
Acknowledgements and Homepage
Volume 4 in the series De Gruyter Series in Probability and Stochastics
Fractional calculus has emerged as a powerful and effective mathematical tool in the study of several phenomena in science and engineering. This text addressed to researchers, graduate students, and practitioners combines deterministic fractional calculus with the analysis of the fractional Brownian motion and its associated fractional stochastic calculus and includes examples, exercises, and problems that focus on computational aspects.
This text provides an overview of the elements of fractional analysis and processes, and includes a wide variety of hands-on applications and exercises that help the reader master the technique of calculations associated with fractional operators.
Frontmatter I
Introduction V
Contents IX
List of notations and abbreviations XIII
1 Fractional integrals and derivatives 1
2 Integral and differential equations involving fractional operators 120
3 Fractional Brownian motion and its environment 191
4 Stochastic processes and fractional differential equations 259
5 Numerical methods and simulation 338
A Basics in complex analysis and integral transforms 399
B Special functions 411
C Stochastic processes 417
Bibliography 429
Index
In the series De Gruyter Textbook
This book treats the elements of discrete mathematics that have important applications in computer science, thus providing the necessary tools for the reader to come to a competent mathematical judgement of modern developments in the age of information. Almost all assertions are shown with full proofs. Exercises are provided, with solutions presented in full detail.
A modern approach to complex analysis of one and multiple variables.
Well suited for introductory and advanced courses on complex analysis.
Contains a large number of problems with selected solutions
Frontmatter I
Preface V
Acknowledgment IX
Notation XI
Contents XV
1 Algebraic structures 1
2 Elementary number theory 15
3 Some useful growth estimates 42
4 Discrete probability 56
5 Combinatorics 65
6 Generating functions 108
7 Group actions and special families of groups 126
8 Graph theory 144
9 Order structures and lattices 185
10 Boolean functions and circuits 212
Solutions 221
Bibliography 251
Index
In the series De Gruyter Textbook
The subject of applied complex variables is so fundamental that most of the other topics in advanced engineering mathematics (AEM) depend on it. The present book contains complete coverage of the subject, summarizing the more elementary aspects that you find in most AEM textbooks and delving into the more specialized topics that are less commonplace. The book represents a one-stop reference for complex variables in engineering. The applications of conformal mapping in this book are significantly more extensive than in other AEM textbooks. The treatments of complex integral transforms enable a much larger class of functions that can be transformed, resulting in an expanded use of complex-transform techniques in engineering analysis. The inclusion of the asymptotics of complex integrals enables the analysis of models with irregular singular points. The book, which has more than 300 illustrations, is generous with realistic example problems.
Covers advanced topics in applied complex variables to solve complex engineering problems in closed form
Relatively easy-to-follow presentation of an otherwise difficult subject
Contains a solution manual that fully solves all the exercise problems
This volume presents a collection of articles devoted to representations of algebras and related topics. Distinguished experts in this field presented their work at the International Conference on Representations of Algebras in 2020. The book reflects recent trends in the representation theory of algebras and its interactions with other central branches of mathematics, including combinatorics, commutative algebra, algebraic geometry, topology, data analysis, Lie algebras, quantum groups, homological algebra, and theoretical physics. There are thirteen independent articles, written by leading experts in the field. Most are expository survey papers, but some are also original research contributions. This collection is addressed to researchers and graduate students in algebra as well as to a broader mathematical audience. It contains open problems and new perspectives for research in the field.
The vast majority of statistics books delineate techniques used to analyze collected data. The Joy of Statistics is not one of these books. It consists of a series of 42 "short stories", each illustrating how statistical methods applied to data produce insight and solutions to the questions the data were collected to answer. Real-life and sometimes artificial data are used to demonstrate the often painless method and magic of statistics. In addition, the text contains brief histories of the evolution of statistical methods and a number of brief biographies of the most famous statisticians of the 20th century. Sprinkled throughout are statistical jokes, puzzles and traditional stories. The levels of statistical texts span a spectrum, from elementary to introductory to application to theoretical to advanced mathematical.
The Joy of Statistics explores a variety of statistical applications using graphs and plots, along with detailed and intuitive descriptions, and occasionally a bit of 10th grade mathematics. Examples of a few of the topics included among these "short stories" are pet ownership, gambling games such as roulette, blackjack and lotteries, as well as more serious subjects such as comparison of African-American and white infant mortality risk, infant birth weight and maternal age, estimation of coronary heart disease risk and racial differences in Hodgkin disease. The statistical descriptions of these topics are in many cases accompanied by easy to understand explanations labelled "How It Works."
1:Probabilities ? rules and review
2:Distributions of data ? four plots
3:Mean value ? estimation and a few properties
4:Boxplots ? construction and interpretation
5:The lady who tasted tea ? a bit of statistical history
6:Outlier/extreme values ? a difficult decision
7:The role of summary statistics ? brief description
8:Correlation and association ? interpretation
9:Proportional reduction in error ? a measure of association
10:Quick Tests ? four examples
11:Confounding ? African-American and white infant mortality
12:Odds ? a sometimes measure of likelihood
13:Odds ratio ? a measure of risk?
14:Odds ratio ? two properties rarely mentioned
15:Percent increase ? ratios?
16:Diagnostic tests ? assessing accuracy
17:Regression to the mean ? father/son data
18:Life table ? a summary of mortality experience
19:Coincidence ? a statistical description
20:Draft lottery numbers (1970)
21:Lotto ? How to get in .... How to win
22:Fatal coronary disease ? risk
23:Pictures
24:The Monty Hall problem
25:Eye-witness evidence ? Collins versus state of California
26:Probabilities and puzzles
27:Jokes and quotes
28:A true life puzzle
29:Rates ? definition and estimation
30:Geometry of an approximate average rate
31:Simpson’s paradox ? two examples and a bit more
32:Smoothing ? median values
33:Two by two table ? a missing observation
34:Survey data ? randomized response
35:Viral incidence estimation ? a shortcut
36:Two-way table ? a graphical analysis
37:Data ? too good to be true?
38:A binary variable ? twin pairs
39:Mr. Rich and Mr. Poor ? a give and take equilibrium
40:Log-normal distribution ? leukemia and pesticide exposure
41:Poem ? A Contribution to Statistics
APP:appendix: golden mean, Pythagorean theorem, chord theorem, pi
A sweeping cultural history of one of the most influential mathematical books ever written
Paperback
ISBN: 9780691235769
Published: Nov 14, 2023
Euclid’s Elements of Geometry is one of the fountainheads of mathematics?and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today.
In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid’s book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans’ studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space.
Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.