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Unsolved Problems in Number Theory
Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.
Cryptography
This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication. Beginning with classical ciphers and their cryptanalysis, this book proceeds to focus on modern public key cryptosystems such as Diffie-Hellman, ElGamal, RSA, and elliptic curve cryptography with an analysis of vulnerabilities of these systems and underlying mathematical issues such as factorization algorithms. Specialized topics such as zero knowledge proofs, cryptographic voting, coding theory, and new research are covered in the final section of this book. Aimed at undergraduate students, this book contains a large selection of problems, ranging from straightforward to difficult, and can be used as a textbook for classes as well as self-study. Requiring only a solid grounding in basic mathematics, this book will also appeal to advanced high school students and amateur mathematicians interested in this fascinating and topical subject.
Singularities, Mirror Symmetry, and the Gauged Linear Sigma Model
This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model. Most of the expository works are based on introductory lecture series given at the workshop and provide an approachable introduction for graduate students to some fundamental topics in mirror symmetry and singularity theory, including quasimaps, localization, the gauged linear sigma model (GLSM), virtual classes, cosection localization, $p$-fields, and Saito's primitive forms. These articles help readers bridge the gap from the standard graduate curriculum in algebraic geometry to exciting cutting-edge research in the field. The volume also contains several research articles by leading researchers, showcasing new developments in the field.
Western Travellers to Constantinople
This volume provides a survey of the thousands and thousands of people from the West who travelled to Constantinople between 962 and 1204, and of the influence Byzantium exerted on them and on those who remained home. Crusaders were an important group, but other social groups played a key role as well in the exchange of ideas.
Applied Algebra and Number Theory
This book contains survey articles on modern topics related to the work of Harald Niederreiter, written by close colleagues and leading experts.
Algorithmic Number Theory
This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.
Western Travellers to Constantinople
This volume deals with relations between the West and Byzantium, from the accession of Otto I the Great in Germany in 962, until the Fourth Crusade when Constantinople was conquered by the Western crusading armies in 1204. The impact which these contacts and confrontations had on both sides is discussed in sections dealing with specific areas (such as the North, Britain, France, Germany, Italy and Spain) as well as in sections dealing with specific aspects of the process: the journey, the attractions of the East, and the idea of "autoritates" and "translationes" of various political and intellectual ideas. An extensive index will help readers to find specific topics. The book is illustrated with maps, and with a number of objects betraying Byzantine influence in the West, or Western presence in Byzantium.
Early Records of the City and County of Albany and Colony of Rensselaerswyck
Roughly half of the volume is devoted to detailed descriptions of places in Georgia of every conceivable size and shape--counties, towns, villages, post offices, rivers, streams, creeks, mountains, ridges, peninsulas, islands, missionary stations--many of which are no longer in use but are likely to crop up in a genealogical investigation. Preceding the gazetteer itself is an excellent overview of Georgia history and an account of the institutions and living conditions in evidence at the time of the book's original publication in 1837. Included are chapters on the founding of Georgia, the state's role in the American Revolution and thereafter, and lists of federal and state officials.
Arithmetic Geometry, Number Theory, and Computation
This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
Abelian Varieties and Number Theory
This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanoes, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfeld modular varieties, representations of etale fundamental groups and specialization of algebraic cycles, Deuring's theory of constant reductions, etc. The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.
