- Table View
- List View
Performing Math: A History of Communication and Anxiety in the American Mathematics Classroom
by Andrew FissPerforming Math tells the history of expectations for math communication—and the conversations about math hatred and math anxiety that occurred in response. Focusing on nineteenth-century American colleges, this book analyzes foundational tools and techniques of math communication: the textbooks that supported reading aloud, the burnings that mimicked pedagogical speech, the blackboards that accompanied oral presentations, the plays that proclaimed performers’ identities as math students, and the written tests that redefined “student performance.” Math communication and math anxiety went hand in hand as new rules for oral communication at the blackboard inspired student revolt and as frameworks for testing student performance inspired performance anxiety. With unusual primary sources from over a dozen educational archives, Performing Math argues for a new, performance-oriented history of American math education, one that can explain contemporary math attitudes and provide a way forward to reframing the problem of math anxiety.
Peri-Urban Dynamics: Geospatial Linkages of Population, Development and Land in Gujarat, India (SpringerBriefs in Geography)
by Ankit Sikarwar Aparajita ChattopadhyayUrban expansion beyond the city’s administrative boundaries has altered villages to a great extent. These peri-urban villages are experiencing unforeseen changes in demographic, economic, land-use, and environmental characteristics. The concept of peri-urbanization is grabbing the attention of urban planners and policymakers globally. To understand the dynamics of the peri-urban region it is crucial to examine multiple rural and urban characteristics. This book studies major changes in population, land and development with the integration of remotely sensed data and census data for 615 peri-urban villages surrounding Ahmedabad city of India. The chapters of the book are designed to cover key aspects of peri-urban change with geospatial methods. This book offers a comprehensive understanding and importance of analyzing peri-urban dynamics at the smallest spatial unit. It provides a detailed conceptual and methodological framework for the students and researchers to study peri-urbanization as well as for the policymakers to redefine the urban policies.
Peridynamics and Its Applications Using Ansys
by Yanan Zhang Erdogan Madenci Sundaram Vinod AnicodeThis book introduces a unified implementation of bond- and state-based peridynamic theory (PD) within a commercial finite element framework, Ansys, utilizing its native elements. It details the implementation of the PD theory and its integration with traditional finite elements. The primary objective is to equip students, researchers, and practicing engineers with both theoretical and practical knowledge of the PD theory, along with the skills necessary for analyzing engineering problems using Ansys. The book demonstrates that, unlike the conventional finite element method (FEM), the PD theory is highly suitable for progressive failure analysis, the multi-scale analysis of materials involving fracture and failure, and multi-physics analysis, including electromigration, corrosion, and electrodeposition. Additionally, it provides a step-by-step illustration of the specific procedures in the pre-processing, solution, and post-processing phases of the analysis through the Graphical User Interface (GUI) for various applications. The book is designed to be introductory and self-contained, minimizing the need for additional reference material.
Perilous Problems for Puzzle Lovers: Math, Logic And Word Puzzles To Challenge Your Brain (Alex Bellos Puzzle Books #0)
by Alex BellosPut your wits—and survival instincts—to the test! Publisher’s Note: Perilous Problems for Puzzle Lovers was previously published in the UK under the title So You Think You’ve Got Problems? In Perilous Problems for Puzzle Lovers, Alex Bellos collects 125 of the world’s greatest stumpers—many dangerous to your person, and all dangerous to your pride. Brace yourself to wrestle with wordplay, grapple with geometry, and scramble for survival. For example . . . Ten lions and a sheep are in a pen. Any lion who eats the sheep will fall asleep. A sleeping lion will be eaten by another lion, who falls asleep in turn. If the lions are all perfect logicians, what happens? Bellos pairs his fiendish brainteasers with fascinating history, so you’ll meet Alcuin, Sam Loyd, and other puzzle masters of yore—in between deranged despots and wily jailers with an unaccountable taste for riddles. Will you make it out alive? And what about the sheep?
Perimeter, Area, and Volume: A Monster Book of Dimensions
by David A. AdlerGrab your jumbo popcorn—you're invited to the premiere of a 3-D movie, all about those three dimensions!Trusted math picture book duo David A. Adler and Ed Miller tackle the differences between two- and three-dimensional objects in their signature bright and kid-friendly way. Explaining length, width, and height-- and all the different ways we represent those figures-- Adler shows how changing the dimensions of an object affects its size. . . . with some help from a cast of funny, friendly movie monsters. Explaining key vocabulary in simple text and offering numerous concrete examples and sample math problems with included solutions, Perimeter, Area, and Volume is a perfect introduction to two- and three-dimensional geometry. The star-studded cast of monsters will help you calculate the perimeter of the set, the area of the movie screen, and the volume of your box of popcorn.Learning about dimensions has never been so entertaining!
Period Mappings and Period Domains (Cambridge Studies in Advanced Mathematics)
by Stefan Müller-Stach James Carlson Chris PetersThis up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Khler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford-Tate groups and their associated domains, the Mumford-Tate varieties and generalizations of Shimura varieties.
Period Mappings with Applications to Symplectic Complex Spaces
by Tim KirschnerExtending Griffiths' classical theory of period mappings for compact Kähler manifolds, this book develops and applies a theory of period mappings of "Hodge-de Rham type" for families of open complex manifolds. The text consists of three parts. The first part develops the theory. The second part investigates the degeneration behavior of the relative Frölicher spectral sequence associated to a submersive morphism of complex manifolds. The third part applies the preceding material to the study of irreducible symplectic complex spaces. The latter notion generalizes the idea of an irreducible symplectic manifold, dubbed an irreducible hyperkähler manifold in differential geometry, to possibly singular spaces. The three parts of the work are of independent interest, but intertwine nicely.
Periodic Character and Patterns of Recursive Sequences
by Michael A. RadinThis textbook on periodic character and patterns of recursive sequences focuses on discrete periodic patterns of first order, second order and higher order difference equations. Aimed toward advanced undergraduate students and graduate students who have taken a basic course in Calculus I and Discrete Mathematics, this book serves as a core text for a course in Difference Equations and Discrete Dynamical Systems. The text contains over 200 exercises to provide readers with a hands-on experience working with the material; the exercises include computations of specific examples and proofs of general results. Readers will receive a first-hand introduction to patterns of periodic cycles and patterns of transient terms with exercises for most sections of the text, preparing them for significant research work in the area.
Periodic Feedback Stabilization for Linear Periodic Evolution Equations
by Gengsheng Wang Yashan XuThis book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.
Periodic Monopoles and Difference Modules (Lecture Notes in Mathematics #2300)
by Takuro MochizukiThis book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis–Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi–Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity.The theory of periodic monopoles of GCK type has applications to Yang–Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson.This work will be of interest to graduate students and researchers in differential and algebraic geometry, as well as in mathematical physics.
Periodic Review Inventory Systems
by Thomas WensingThe focus of the work is twofold. First, it provides an introduction into fundamental structural and behavioral aspects of periodic review inventory systems. Second, it includes a comprehensive study on analytical and optimization aspects of a specific class of those systems. For the latter purpose, general solution methods for problems of inventory management in discrete time are described and developed along with highly specialized methods to solve very specific problems related to the model variants examined. The work is thus addressed to students and practitioners who seek a deeper understanding of managing inventories in discrete time as well as to software developers who require implementation aids on specific problems of inventory management.
Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics
by Seshadev Padhi John R. Graef P D N SrinivasuThis book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, and the environment.
Periodicities in Nonlinear Difference Equations
by G. Ladas E.A. GroveSharkovsky's Theorem, Li and Yorke's "period three implies chaos" result, and the (3x+1) conjecture are beautiful and deep results that demonstrate the rich periodic character of first-order, nonlinear difference equations. To date, however, we still know surprisingly little about higher-order nonlinear difference equations. During the last
Periods and Nori Motives
by Annette Huber Stefan Müller-StachThis book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives. It develops Nori's approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori's unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.
Periods in Quantum Field Theory and Arithmetic: ICMAT, Madrid, Spain, September 15 – December 19, 2014 (Springer Proceedings in Mathematics & Statistics #314)
by Kurusch Ebrahimi-Fard José Ignacio Burgos Gil Herbert GanglThis book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory'' at the ICMAT (Instituto de Ciencias Matemáticas, Madrid) in 2014. The activity was aimed at understanding and deepening recent developments where Feynman and string amplitudes on the one hand, and periods and multiple zeta values on the other, have been at the heart of lively and fruitful interactions between theoretical physics and number theory over the past few decades. In this book, the reader will find research papers as well as survey articles, including open problems, on the interface between number theory, quantum field theory and string theory, written by leading experts in the respective fields. Topics include, among others, elliptic periods viewed from both a mathematical and a physical standpoint; further relations between periods and high energy physics, including cluster algebras and renormalisation theory; multiple Eisenstein series and q-analogues of multiple zeta values (also in connection with renormalisation); double shuffle and duality relations; alternative presentations of multiple zeta values using Ecalle's theory of moulds and arborification; a distribution formula for generalised complex and l-adic polylogarithms; Galois action on knots. Given its scope, the book offers a valuable resource for researchers and graduate students interested in topics related to both quantum field theory, in particular, scattering amplitudes, and number theory.
Perl Testing: A Developer's Notebook
by Ian Langworth ChromaticIs there any sexier topic in software development than software testing? That is, besides game programming, 3D graphics, audio, high-performance clustering, cool websites, et cetera? Okay, so software testing is low on the list. And that's unfortunate, because good software testing can increase your productivity, improve your designs, raise your quality, ease your maintenance burdens, and help to satisfy your customers, coworkers, and managers.Perl has a strong history of automated tests. A very early release of Perl 1.0 included a comprehensive test suite, and it's only improved from there. Learning how Perl's test tools work and how to put them together to solve all sorts of previously intractable problems can make you a better programmer in general. Besides, it's easy to use the Perl tools described to handle all sorts of testing problems that you may encounter, even in other languages.Like all titles in O'Reilly's Developer's Notebook series, this "all lab, no lecture" book skips the boring prose and focuses instead on a series of exercises that speak to you instead of at you. Perl Testing: A Developer's Notebook will help you dive right in and:Write basic Perl tests with ease and interpret the resultsApply special techniques and modules to improve your testsBundle test suites along with projectsTest databases and their dataTest websites and web projectsUse the "Test Anything Protocol" which tests projects written in languages other than PerlWith today's increased workloads and short development cycles, unit tests are more vital to building robust, high-quality software than ever before. Once mastered, these lessons will help you ensure low-level code correctness, reduce software development cycle time, and ease maintenance burdens. You don't have to be a die-hard free and open source software developer who lives, breathes, and dreams Perl to use this book. You just have to want to do your job a little bit better.
Perl Testing: A Developer's Notebook
by Ian LangworthIs there any sexier topic in software development than software testing? That is, besides game programming, 3D graphics, audio, high-performance clustering, cool websites, et cetera? Okay, so software testing is low on the list. And that's unfortunate, because good software testing can increase your productivity, improve your designs, raise your quality, ease your maintenance burdens, and help to satisfy your customers, coworkers, and managers. Perl has a strong history of automated tests. A very early release of Perl 1.0 included a comprehensive test suite, and it's only improved from there. Learning how Perl's test tools work and how to put them together to solve all sorts of previously intractable problems can make you a better programmer in general. Besides, it's easy to use the Perl tools described to handle all sorts of testing problems that you may encounter, even in other languages. Like all titles in O'Reilly's Developer's Notebook series, this "all lab, no lecture" book skips the boring prose and focuses instead on a series of exercises that speak to you instead of at you. Perl Testing: A Developer's Notebook will help you dive right in and: Write basic Perl tests with ease and interpret the results Apply special techniques and modules to improve your tests Bundle test suites along with projects Test databases and their data Test websites and web projects Use the "Test Anything Protocol" which tests projects written in languages other than Perl With today's increased workloads and short development cycles, unit tests are more vital to building robust, high-quality software than ever before. Once mastered, these lessons will help you ensure low-level code correctness, reduce software development cycle time, and ease maintenance burdens. You don't have to be a die-hard free and open source software developer who lives, breathes, and dreams Perl to use this book. You just have to want to do your job a little bit better.
Perlen der Mathematik: 20 geometrische Figuren als Ausgangspunkte für mathematische Erkundungsreisen
by Claudi Alsina Roger B. NelsenDieses Buch handelt von 20 geometrischen Figuren (Icons), die eine wichtige Rolle bei der Veranschaulichung mathematischer Beweise spielen. Alsina und Nelsen untersuchen die Mathematik, die hinter diesen Figuren steckt und die sich aus ihnen ableiten lässt.Jedem in diesem Buch behandelten Icons ist ein eigenes Kapitel gewidmet, in dem sein Alltagsbezug, seine wesentlichen mathematischen Eigenschaften sowie seine Bedeutung für visuelle Beweise vieler mathematischer Sätze betont werden. Diese Sätze umfassen unter anderem auch klassische Ergebnisse aus der ebenen Geometrie, Eigenschaften der natürlichen Zahlen, Mittelwerte und Ungleichungen, Beziehungen zwischen Winkelfunktionen, Sätze aus der Differenzial- und Integralrechnung sowie Rätsel aus dem Bereich der Unterhaltungsmathematik. Darüber hinaus enthält jedes Kapitel eine Auswahl an Aufgaben, anhand derer die Leser weitere Eigenschaften und Anwendungen der Diagramme erkunden können.Das Buch ist für alle geschrieben, die Freude an der Mathematik haben; Lehrkräfte und Dozenten der Mathematik werden in diesem Buch sehr nützliche Beispiele für Problemlösungen sowie umfangreiches Unterrichts- und Seminarmaterial zu Beweisen und mathematischer Argumentation finden.
Permittivity and Permeability Tensors for Cloaking Applications
by Rakesh Mohan Jha Balamati Choudhury Pavani Vijay ReddyThis book is focused on derivations of analytical expressions for stealth and cloaking applications. An optimal version of electromagnetic (EM) stealth is the design of invisibility cloak of arbitrary shapes in which the EM waves can be controlled within the cloaking shell by introducing a prescribed spatial variation in the constitutive parameters. The promising challenge in design of invisibility cloaks lies in the determination of permittivity and permeability tensors for all the layers. This book provides the detailed derivation of analytical expressions of the permittivity and permeability tensors for various quadric surfaces within the eleven Eisenhart co-ordinate systems. These include the cylinders and the surfaces of revolutions. The analytical modeling and spatial metric for each of these surfaces are provided along with their tensors. This mathematical formulation will help the EM designers to analyze and design of various quadratics and their hybrids, which can eventually lead to design of cloaking shells of arbitrary shapes.
Permutation Groups (Dover Books on Mathematics)
by Donald S. PassmanThis volume by a prominent authority on permutation groups consists of lecture notes that provide a self-contained account of distinct classification theorems. A ready source of frequently quoted but usually inaccessible theorems, it is ideally suited for professional group theorists as well as students with a solid background in modern algebra.The three-part treatment begins with an introductory chapter and advances to an economical development of the tools of basic group theory, including group extensions, transfer theorems, and group representations and characters. The final chapter features thorough discussions of the work of Zassenhaus on Frobenius elements and sharply transitive groups in addition to an exploration of Huppert's findings on solvable doubly transitive groups.
Permutation Groups and Cartesian Decompositions (London Mathematical Society Lecture Note Ser. #449)
by Cheryl E. Praeger Csaba SchneiderPermutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nan–Scott theory are presented not only for primitive permutation groups but also for the larger families of quasiprimitive and innately transitive groups, including several classes of infinite permutation groups. Their precision is sharpened by the introduction of a cartesian decomposition concept. This facilitates reduction arguments for primitive groups analogous to those, using orbits and partitions, that reduce problems about general permutation groups to primitive groups. The results are particularly powerful for finite groups, where the finite simple group classification is invoked. Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures. Students and researchers with an interest in mathematical symmetry will find the book enjoyable and useful.
Permutation Statistical Methods
by Kenneth J. Berry Janis E. Johnston Paul W. MielkeThis researchmonograph provides a synthesis of a number of statistical tests and measures,which, at first consideration, appear disjoint and unrelated. Numerouscomparisons of permutation and classical statistical methods are presented, andthe two methods are compared via probability values and, where appropriate,measures of effect size. Permutationstatistical methods, compared to classical statistical methods, do not rely ontheoretical distributions, avoid the usual assumptions of normality andhomogeneity of variance, and depend only on the data at hand. This text takes aunique approach to explaining statistics by integrating a large variety ofstatistical methods, and establishing the rigor of a topic that to many mayseem to be a nascent field in statistics. This topic is new in that it tookmodern computing power to make permutation methods available to people working inthe mainstream of research.
Permutation Statistical Methods for Criminology and Criminal Justice (Society, Environment and Statistics)
by Kenneth J. Berry Janis E. Johnston Michael J. Lynch Michael A. Long Paul StreteskyThis book takes a unique approach to explaining permutation statistical methods for advanced undergraduate students, graduate students, faculty, researchers, and other professionals interested in the areas of criminology or criminal justice. The book integrates permutation statistical methods with a wide range of classical statistical methods. It opens with a comparison of two models of statistical inference: the classical population model espoused by J. Neyman and E. Pearson and the permutation model first introduced by R.A. Fisher and E.J.G. Pitman. Numerous comparisons of permutation and classical statistical methods are illustrated with examples from criminology and criminal justice and supplemented with a variety of R scripts for ease of computation. The text follows the general outline of an introductory textbook in statistics with chapters on central tendency, variability, one-sample tests, two-sample tests, matched-pairs tests, completely-randomized analysis of variance, randomized-blocks analysis of variance, simple linear regression and correlation, and the analysis of goodness of fit and contingency. Unlike classical statistical methods, permutation statistical methods do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity, depend solely on the observed data, and do not require random sampling, making permutation statistical methods ideal for analyzing criminology and criminal justice databases. Permutation methods are relatively new in that it took modern computing power to make them available to those working in criminology and criminal justice research. The book contains detailed examples of permutation analyses. Each analysis is paired with a conventional analysis; for example, a permutation test of the difference between experimental and control groups is contrasted with Student's two-sample $t$ test. An added feature is the inclusion of multiple historical notes on the origin and development of both parametric and conventional tests and measures. Designed for an audience with a basic statistical background and a strong interest in parametric and non-parametric statistics, the book can easily serve as a textbook for undergraduate and graduate students in criminology, criminal justice, or sociology, as well as serving as a research source for faculty, researchers, and other professionals in the area of criminology. No statistical training beyond a first course in statistics is required, but some knowledge of, or interest in, criminology or criminal justice is assumed.
Permutation Testing for Isotonic Inference on Association Studies in Genetics
by Livio Corain Luigi Salmaso Rosa Arboretti Dario MazzaroThe purpose of this book is to illustrate a new statistical approach to test allelic association and genotype-specific effects in the genetic study of diseases. There are some parametric and non-parametric methods available for this purpose. We deal with population-based association studies, but comparisons with other methods will also be drawn, analysing the advantages and disadvantages of each one, particularly with regard to power properties with small sample sizes. In this framework we will work out some nonparametric statistical permutation tests and likelihood-based tests to perform case-control analyses to study allelic association between marker, disease-gene and environmental factors. Permutation tests, in particular, will be extended to multivariate and more complex studies, where we deal with several genes and several alleles together. Furthermore, we show simulations under different assumptions on the genetic model and analyse real data sets by simply studying one locus with the permutation test.
Permutation Tests for Complex Data: Theory, Applications and Software (Wiley Series in Probability and Statistics)
by Luigi Salmaso Fortunato PesarinTIMELY UPDATE OF A POPULAR EDITION ON PERMUTATION TESTING WITH NUMEROUS CASE STUDIES INCLUDED THROUGHOUT The newly revised and updated Second Edition of Permutation Tests for Complex Data describes permutation tests from the point of view of experimental design, with methodological details and illustrating the process of devising an appropriate permutation test through case studies. In addition to the text, this book includes two open source packages for permutation tests in Python and R which include a comprehensive code base to implement common permutation tests as well as code to implement each of the book’s case studies. The focus of this book is the permutation approach to a variety of univariate and multivariate problems of hypothesis testing in a typical nonparametric framework. The book examines the most up-to-date methodologies of univariate and multivariate permutation testing, includes real case studies from both experimental and observational studies, and presents and discusses solutions to the most important and frequently encountered real problems in multivariate analyses. Written by two highly qualified authors in the field of nonparametrics and applied statistics, Permutation Tests for Complex Data includes information on sample topics including: Theory of one-dimensional and multi-dimensional permutation tests, covering test statistics, arguments for selecting permutation tests, and examples of one-sample and multi-sample problems Multiplicity control and closed testing, covering raw and adjusted p-values, the MinP Bonferroni-Holm procedure, and weighted methods for controlling FWE and FDR Multivariate categorical variables, covering stochastic ordering, tests on moments for ordered variables, and heterogeneity comparisons NPC tests for survival analysis and shape analysis, covering analysis of PERC data and analysis with correlated landmarks Presenting a thorough overview of permutation testing with both formal description and proofs, Permutation Tests for Complex Data is an excellent introduction to permutation tests for graduate-level statistics or data science courses and will be ideal as a handbook for researchers hoping to use the open source code.