Received During the 2023-2024
Academic School Year:
Plato's Ghost by Jeremy GrayPlato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
Call Number: QA26 .G73 2022
ISBN: 9780691242040
Publication Date: 2022-12-13
Paradoxes and Inconsistent Mathematics by Zach WeberLogical paradoxes - like the Liar, Russell's, and the Sorites - are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses "dialetheic paraconsistency" - a formal framework where some contradictions can be true without absurdity - as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
Call Number: QA9 .W43 2021
ISBN: 9781108834414
Publication Date: 2021-10-21
Understanding Cryptography by Christof Paar; Jan Pelzl; Bart Preneel (Foreword by)Cryptography is now ubiquitous - moving beyond the traditional environments, such as government communications and banking systems, we see cryptographic techniques realized in Web browsers, e-mail programs, cell phones, manufacturing systems, embedded software, smart buildings, cars, and even medical implants. Today's designers need a comprehensive understanding of applied cryptography. After an introduction to cryptography and data security, the authors explain the main techniques in modern cryptography, with chapters addressing stream ciphers, the Data Encryption Standard (DES) and 3DES, the Advanced Encryption Standard (AES), block ciphers, the RSA cryptosystem, public-key cryptosystems based on the discrete logarithm problem, elliptic-curve cryptography (ECC), digital signatures, hash functions, Message Authentication Codes (MACs), and methods for key establishment, including certificates and public-key infrastructure (PKI). Throughout the book, the authors focus on communicating the essentials and keeping the mathematics to a minimum, and they move quickly from explaining the foundations to describing practical implementations, including recent topics such as lightweight ciphers for RFIDs and mobile devices, and current key-length recommendations. The authors have considerable experience teaching applied cryptography to engineering and computer science students and to professionals, and they make extensive use of examples, problems, and chapter reviews, while the book's website offers slides, projects and links to further resources. This is a suitable textbook for graduate and advanced undergraduate courses and also for self-study by engineers.
Call Number: Z104 .P33 2010
ISBN: 9783642041006
Publication Date: 2011-10-19
Why Does Math Work ... If It's Not Real? by Dragan RadulovicAccording to G. H. Hardy, the 'real' mathematics of the greats like Fermat and Euler is 'useless,' and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this 'useless' mathematics. Mobile phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth's orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is like some magic hand had guided the ancient mathematicians so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck's discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.
Call Number: QA36 .R338 2023
ISBN: 9781009054812
Publication Date: 2023-06-08
Classical and Modern Cryptography for Beginners by Rajkumar Banoth; Rekha RegarThis textbook offers the knowledge and the mathematical background or techniques that are required to implement encryption/decryption algorithms or security techniques. It also provides the information on the cryptography and a cryptosystem used by organizations and applications to protect their data and users can explore classical and modern cryptography. The first two chapters are dedicated to the basics of cryptography and emphasize on modern cryptography concepts and algorithms. Cryptography terminologies such as encryption, decryption, cryptology, cryptanalysis and keys and key types included at the beginning of this textbook . The subsequent chapters cover basic phenomenon of symmetric and asymmetric cryptography with examples including the function of symmetric key encryption of websites and asymmetric key use cases. This would include security measures for websites, emails, and other types of encryptions that demand key exchange over a public network. Cryptography algorithms (Caesar cipher, Hill cipher, Playfair cipher, Vigenere cipher, DES, AES, IDEA, TEA, CAST, etc.) which are varies on algorithmic criteria like- scalability, flexibility, architecture, security, limitations in terms of attacks of adversary. They are the core consideration on which all algorithms differs and applicable as per application environment. The modern cryptography starts from invent of RSA (Rivest-Shamir-Adleman) which is an asymmetric key algorithm based on prime numbers. Nowadays it is enabled with email and digital transaction over the Internet. This textbook covers Chinese remainder theorem, Legendre, Jacobi symbol, Rabin cryptosystem, generalized ElGamal public key cryptosystem, key management, digital signatures, message authentication, differential cryptanalysis, linear cryptanalysis, time-memory trade-off attack, network security, cloud security, blockchain, bitcoin, etc. as well as accepted phenomenon under modern cryptograph. Advanced level students will find this textbook essential for course work and independent study. Computer scientists and engineers and researchers working within these related fields will also find this textbook useful.