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Equations and Inequalities
A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.
Counting and Configurations
This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.
The Problem of Catalan
In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In other words, 32 – 23 = 1 is the only solution of the equation xp – yq = 1 in integers x, y, p, q with xy ≠ 0 and p, q ≥ 2. In this book we give a complete and (almost) self-contained exposition of Mihăilescu’s work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume a very modest background:a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.
Advances in Cryptology – ASIACRYPT 2022
The four-volume proceedings LNCS 13791, 13792, 13793, and 13794 constitute the proceedings of the 28th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2022, held in Taipei, Taiwan, during December 5-9, 2022. The total of 98 full papers presented in these proceedings was carefully reviewed and selected from 364 submissions. The papers were organized in topical sections as follows: Part I: Award papers; functional and witness encryption; symmetric key cryptanalysis; multiparty computation; real world protocols; and blockchains and cryptocurrencies. Part II: Isogeny based cryptography; homomorphic encryption; NIZK and SNARKs; non interactive zero knowledge; and symmetric cryptography. Part III: Practical cryptography; advanced encryption; zero knowledge; quantum algorithms; lattice cryptoanalysis. Part IV: Signatures; commitments; theory; cryptoanalysis; and quantum cryptography.
Nagoya Mathematical Journal
Issue for Mar. 1970 dedicated to Professor Katuzi Ono on his 60th birthday with portrait, sketch of his life, and list of mathematical papers.
Acta arithmetica
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