Suggested Books of the Week 26, 2018

Check out these books below by Cambridge University Press and Ancient Origins.

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The Cambridge Monographs on Applied and Computational Mathematics publishes expositions on all aspects of applicable, numerical and computational mathematics. The series represents the growth in applications of mathematical and numerical techniques to problems from all areas of science. 

Multivariate Approximation

Multivariate Approximation

This self-contained, systematic treatment of multivariate approximation begins with classical linear approximation, and moves on to contemporary nonlinear approximation. It covers substantial new developments in the linear approximation theory of classes with mixed smoothness, and shows how it is directly related to deep problems in other areas of mathematics. For example, numerical integration of these classes is closely related to discrepancy theory and to nonlinear approximation with respect to special redundant dictionaries, and estimates of the entropy numbers of classes with mixed smoothness are closely related to (in some cases equivalent to) the Small Ball Problem from probability theory...
Researchers will find that the many open problems in the theory outlined in the book provide helpful directions and guidance for their own research in this exciting and active area.

• Introduces readers to the theoretical foundations of the subject, at a level suitable for teaching graduate courses
• Describes open questions in the area, providing ideas for further research
• Shows the links between the study of classes of mixed smoothness and other areas of mathematics, offering deeper insight into both

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Partial Differential Equation Methods for Image Inpainting 

Partial Differential Equation Methods
for Image Inpainting

This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task...
This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.

• Serves as an introduction to the use of partial differential equations (PDEs) for digital image restoration
• Provides insight into mathematical modelling, partial differential equations, functional analysis, variational calculus, optimisation, and numerical analysis
• Targeted at readers with a basic knowledge in functional analysis, partial differential equations, measure theory, and convex optimisation

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Multiscale Methods for Fredholm Integral Equations 

Multiscale Methods for  
Fredholm Integral Equations

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods...
The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

• Provides a wide selection of stable, fast and accurate algorithms for solving integral equations 
• New techniques may be applied to other integral equations used in applied mathematics and engineering 
• Opens up the history of the subject for those entering the field
  

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Forbidden Configurations in Discrete Geometry 

Forbidden Configurations in  
Discrete Geometry

This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view...
The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.

• Proposes a unified view of problems in discrete geometry, helping readers understand the connections and commonalities between problems in the area 
• Combines mathematical and computational views of the subject, and pseudocode for numerous algorithms, providing a readable introduction for computer science and mathematics students 
• The book is accessible and motivating, featuring both recreational puzzles along with recent breakthroughs and open problems  

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Statistical Inference for Engineers and Data Scientists 

Statistical Inference for
Engineers and Data Scientists

This book is a mathematically accessible and up-to-date introduction to the tools needed to address modern inference problems in engineering and data science, ideal for graduate students taking courses on statistical inference and detection and estimation, and an invaluable reference for researchers and professionals... 

The password-protected solutions manual and the image gallery from the book are available online.

• Presents the core principles of statistical inference in a unified manner which were previously only available piecemeal, particularly those involving large sample sizes 
• The book is mathematically accessible, and provides plenty of examples to illustrate the concepts explained and to connect the theory with practical applications 
• Contains a wealth of illustrations to emphasize the key features of the theory, the implications of the assumptions made, and the subtleties that arise when applying the theory
  

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The Sistine Secrets: Michelangelo's Forbidden Messages in the Heart of the Vatican 

The Sistine Secrets:  
Michelangelo's Forbidden Messages
in the Heart of the Vatican

Five hundred years ago Michelangelo began work on a painting that became one of the most famous pieces of art in the world—the Sistine Chapel ceiling. Every year millions of people come to see Michelangelo's Sistine ceiling, which is the largest fresco painting on earth in the holiest of Christianity's chapels; yet there is not one single Christian image in this vast, magnificent artwork.
The Sistine Secrets tells the fascinating story of how Michelangelo embedded messages of brotherhood, tolerance, and freethinking in his painting to encourage "fellow travelers" to challenge the repressive Roman Catholic Church of his time... 
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Blood of the Celts: The New Ancestral Story 

Blood of the Celts:
The New Ancestral Story

From prehistory to the present day, an unrivaled look deep into the contentious origins of the Celts.
Blood of the Celts brings together genetic, archaeological, and linguistic evidence to address the often-debated question: who were the Celts? What peoples or cultural identities should that term describe? And did they in fact inhabit the British Isles before the Romans arrived? Author Jean Manco challenges existing accounts of the origins of the Celts, providing a new analysis that draws on the latest discoveries as well as ancient history...
102 illustrations 
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The Maurya Empire: The History and Legacy of Ancient India’s Greatest Empire 

The Maurya Empire:  
The History and Legacy of
Ancient India’s Greatest Empire

During the last centuries of the first millennium BCE, most of the Mediterranean basin and the Near East were either directly or indirectly under the influence of Hellenism. The Greeks spread their ideas to Egypt, Mesopotamia, and Persia and attempted to unify all of the peoples of those regions under one government. Although some of the Hellenistic kingdoms proved to be powerful in their own rights – especially Ptolemaic Egypt and the Seleucid Empire, which encompassed all of Mesopotamia, most of the Levant, and much of Persia during its height – no single kingdom ever proved to be dominant. The Hellenic kingdoms battled each other for supremacy and even attempted to claim new lands, especially to the east, past the Indus River in lands that the Greeks referred to generally as India. But as the Hellenistic Greeks turned their eyes to the riches of India, a dynasty came to power that put most of the Indian subcontinent under the rule of one king.
The dynasty that came to power in the late fourth century BCE is known today as the Mauryan Dynasty, and although the ruling family was short-lived and their power was ephemeral, its influence resonated for several subsequent centuries and spread as far east as China and into the Hellenistic west.

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Enjoy your reading!   

Source: Cambridge University Press and Ancient Origins