Field Theory by
"Springer has just released the second edition of Steven Roman's Field Theory, and it continues to be one of the best graduate-level introductions to the subject out there....Every section of the book has a number of good exercises that would make this book excellent to use either as a textbook or to learn the material on your own. All in all...a well-written expository account of a very exciting area in mathematics." --THE MAA MATHEMATICAL SCIENCES DIGITAL LIBRARY
History of Information Graphics by
In the age of big data and digital distribution, when news travel ever further and faster and media outlets compete for a fleeting slice of online attention, information graphics have swept center stage. At once nuanced and neat, they distill abstract ideas, complex statistics, and cutting-edge discoveries into succinct, compelling, and masterful designs. Cartographers, programmers, statisticians, designers, scientists, and journalists have developed a new field of expertise in visualizing knowledge. This XL-sized compendium explores the history of data graphics from the Middle Ages right through to the digital era. Curated by Sandra Rendgen, some 400 milestones span astronomy, cartography, zoology, technology, and beyond. Across medieval manuscripts and parchment rolls, elaborate maps, splendid popular atlasses, and early computer-based information design, we systematically break down each work's historical context, including such highlights as Martin Waldseemüller's famous world map, the meticulous nature studies of Ernst Haeckel, and many unknown treasures. Hot on the heels of the best-selling Information Graphics and Understanding the World, this third volume fills the gap as an unprecedented reference book for data freaks, designers, historians, and anyone thirsty for knowledge. An enthralling exploration into the teachings, research, and lives of generations past.
An Introduction to Laplace Transforms and Fourier Series by
In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems.
Group-Based Cryptography by
This book is about relations between three di'erent areas of mathematics and theoreticalcomputer science: combinatorialgroup theory, cryptography, and c- plexity theory. We explorehownon-commutative(in'nite) groups, which arety- callystudiedincombinatorialgrouptheory, canbeusedinpublickeycryptography. We also show that there is a remarkable feedback from cryptography to com- natorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research - enues within group theory. Then, we employ complexity theory, notably generic case complexity of algorithms, for cryptanalysisof various cryptographicprotocols based on in'nite groups. We also use the ideas and machinery from the theory of generic case complexity to study asymptotically dominant properties of some in'nite groups that have been used in public key cryptography so far. It turns out that for a relevant cryptographic scheme to be secure, it is essential that keys are selected from a "very small" (relative to the whole group, say) subset rather than from the whole group. Detecting these subsets ("black holes") for a part- ular cryptographic scheme is usually a very challenging problem, but it holds the keyto creatingsecurecryptographicprimitives basedonin'nite non-commutative groups. The book isbased onlecture notesfor the Advanced Courseon Group-Based CryptographyheldattheCRM, BarcelonainMay2007. Itisagreatpleasureforus to thank Manuel Castellet, the HonoraryDirector of the CRM, for supporting the idea of this Advanced Course. We are also grateful to the current CRM Director, JoaquimBruna, and to the friendly CRM sta?, especially Mrs. N. PortetandMrs. N. Hern andez, for their help in running the Advanced Course and in preparing the lecture notes.
Language and the Rise of the Algorithm by
A wide-ranging history of the intellectual developments that produced the modern idea of the algorithm. Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians long before the computer age. How do you draw the line between computational rules and the complexities of making systems comprehensible to people? Here Jeffrey M. Binder offers a compelling tour of four visions of universal computation that addressed this issue in very different ways: G. W. Leibniz's calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole's nineteenth-century logic system; and the early programming language ALGOL, whose name is short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. To what extent can meaning be controlled by individuals, like the values of a and b in algebra, and to what extent is meaning inevitably social? By attending to this long-neglected question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day. Machine learning, in its increasing dependence on words, now places this boundary in jeopardy, making its stakes all the more urgent to understand. The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction.
Secret Key Cryptography by
Explore the fascinating and rich world of Secret Key cryptography! This book provides practical methods for encrypting messages, an interesting and entertaining historical perspective, and an incredible collection of ciphers and codes--including 30 unbreakable methods. In Secret Key Cryptography: Ciphers, from simple to unbreakable you will: Measure the strength of your ciphers and learn how to guarantee their security Construct and incorporate data-compression codes Generate true random numbers in bulk Construct huge primes and safe primes Add an undetectable backdoor to a cipher Defeat hypothetical ultracomputers that could be developed decades from now Construct 30 unbreakable ciphers Secret Key Cryptography gives you a toolbox of cryptographic techniques and Secret Key methods. The book''s simple, non-technical language is easy to understand and accessible for any reader, even without the advanced mathematics normally required for cryptography. You''ll learn how to create and solve ciphers, as well as how to measure their strength. As you go, you''ll explore both historic ciphers and groundbreaking new approaches--including a never-before-seen way to implement the uncrackable One-Time Pad algorithm. about the technology Secret Key cryptography is the backbone of all modern computing infrastructure. Secret Key ciphers use the same key to encrypt and decrypt messages. Properly designed, these algorithms are efficient and practical. Some Secret Key approaches are uncrackable, even under attacks backed by supercomputers or quantum technology! about the book Secret Key Cryptography teaches anyone how to create a wide range of ciphers--even if you have no background in math or creating codes. You''ll combine Secret Key techniques to achieve ciphers that are effectively uncrackable and avoid common pitfalls that result in strong-looking but weak ciphers. The book reveals scores of different cipher methods, including both historic examples and current innovations in the field. RETAIL SELLING POINTS * Measure the strength of your ciphers and learn how to guarantee their security * Construct and incorporate data-compression codes * Generate true random numbers in bulk * Construct huge primes and safe primes * Add an undetectable backdoor to a cipher * Defeat hypothetical ultra computers that could be developed decades from now * Construct 30 unbreakable ciphers
A Primer for Undergraduate Research by
This highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading. The content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations research), yet have few enough prerequisites that the interested student can start exploring them under the guidance of a faculty member. Whether trying to start an undergraduate thesis, embarking on a summer REU, or preparing for graduate school, this book is appropriate for a variety of students and the faculty who guide them.
The Story of Proof by
How the concept of proof has enabled the creation of mathematical knowledge The Story of Proof investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as "infinitesimal algebra," and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field's power and progress.
A History of Non-Euclidean Geometry by
The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.
