Mathematical Puzzles and Curiosities (1版)

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【簡介】 This book is the result of a collaboration between three passionate puzzlers, inviting readers to challenge themselves with a diverse collection of puzzles and brainteasers from across the mathematical landscape. While the solutions are accessible to younger puzzlers, solving them independently can still pose an enjoyable challenge for adults. Beyond puzzles and solutions, the authors aim to teach problem-solving methods, interspersed with fascinating mathematical anecdotes that provide refreshing insights and breaks for dedicated solvers. Featuring a blend of never-before-seen puzzles and classic favorites with new twists, this unique collection offers challenges and curiosities to satisfy puzzlers, enrich mathematicians, and welcome novices eager to explore the beauty of mathematical thinking. Covering topics from logic and probability to geometry and number theory, this book has something for everyone who loves a good puzzle. Whether you seek puzzles for the pure joy of solving or wish to sharpen your logic skills while uncovering surprising mathematical insights, this book is a must-have addition to your collection.

Mathematical Foundations and Aspects of Discrete Mathematics (1版)

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【簡介】 This book is an introduction to discrete mathematics with a strong emphasis on formal reasoning. Beginning with the fundamentals of propositional and predicate logic, it develops proof techniques through deduction trees, truth tables, and formal semantics. The first chapter is devoted entirely to logical reasoning, providing a foundation for the rest of the text, which covers standard topics such as sets, functions, relations, induction, and recursion, as well as more advanced material like number theory, graph theory, and discrete probability. Highlights of this book include an initial chapter that provides a gentle introduction to basic logic, including proof trees and templates, written from the perspective of a master logician. For the more advanced audience, another chapter provides a deeper look into basic logic by providing details on Gentzen-style deduction trees, first-order theories, the simply-typed λ-calculus, and Kripke models for intuitionistic logic. Other highlights include the inclusion–exclusion principle, the Möbius inversion formula, the RSA cryptosystem, and a thorough discussion on network flow problems, including the Max-Flow Min-Cut theorem and the Ford and Fulkerson algorithm. Each chapter concludes with a detailed summary and a comprehensive set of problems, making the book especially suitable for undergraduate students in mathematics and theoretical computer science. 【目錄】

Mathematical Methods for Physics (1版)

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本書所包的內容十分豐富，幾乎包含應用數學所有的重要課題，如Complex Variables, Partial Differential Equations, Special Functions, Fourier Transforms, Laplace Transforms etc。就如同作者在序中所言，本書適合研究生或優秀大學部學生研習，本書有些難度。作者寫書的方式是在每章每節開始時，先討論一個課題的基本概念及方法，而後舉出很多各式各樣不同的例子，其中有許多是來自古典力學、流体力學、量子力學、電磁學的重要例子，如果讀者能將本書全部念完並消化之，將受益不淺 目次 Chapter 1.COMPLEX VARIABLES. Chapter 2.CONFORMAL MAPPINGS. Chapter 3.ELLIPTICAL FUNCTIONS. Chapter 4.TENSOR CALCULUS. Chapter 5.Sturm-Liouville Theory. Chapter 6.GAMMA FUNCTION. Chapter 7.BESSEL FUNCTION. Chapter 8.LEGENDRE FUNCTIONS. Chapter 9.OTHER SPECIAL FUNCTIONS Chapter 10.Fourier SeriesLAPLACE TRANSFORM. Chapter 11.LAPLACE TRANSFORM. Chapter 12.MELLIN AND HANKEL TRANSFORM.I Chapter 14.NTEGRAL EQUATIONS.