From Integers to the Big Bang: The Historical Development of Mathematical Physics (1版)

類似書籍推薦給您

【簡介】 This book offers a concise catalogue of the mathematical subjects underpinning modern theoretical physics. It traces the logical progression of ideas from the primitive beginnings of our earliest number systems to the calculation of the transcendental numbers e and π and their uses in complex analysis. What took the human race thousands of years to accomplish is here presented in a coherent, intuitive sequence. Along the way, the book introduces core topics in mathematical physics, including electromagnetism, statistical mechanics, thermodynamics, relativity, and nuclear fission and fusion, breakthroughs that have been foundational to the sophisticated scientific landscape in which we find ourselves.Topics that are often taught in isolation, at scattered intervals, are here woven into a unified narrative that prioritises the logical development of ideas, offering an approach grounded in intuitive reasoning. Whether encountering these subjects for the first time or seeking to consolidate earlier learning, readers will benefit from the book’s unique perspective on the underlying structure of mathematics and physics, and how these disciplines have guided humanity from its early agrarian roots to the intricate, technologically advanced world of today.

Modern Mathematical Concepts for Engineers

類似書籍推薦給您

This textbook provides a comprehensive exploration of mathematical modeling, emphasizing the limitations of pointwise analysis and highlighting the great potential of measure theory. Measure theory not only offers better representations of phenomena, such as distributions and continuous probabilities, but also facilitates the analysis of classical partial differential equation problems. Additionally, the book introduces new classes of problems that go beyond traditional pointwise and infinitesimal analysis, integrating random and deterministic aspects into a unified framework. The narrative follows Bernard Namier, a young engineering apprentice, and Laurent Corps, a retired mathematics expert who tutors Bernard to tackle a challenging project assigned at work. Through their interwoven dialogue and the fictitious texts they study, readers are immersed in mathematical modeling as applied to engineering problems, with insights that extend to broader applications. This unique structure bridges two educational traditions: the abstract, Bourbaki-style approach common in France and the progressive, example-based learning prevalent in the Anglosphere. As a result, readers will master core concepts through rigorous proofs and applied examples and gain confidence in handling complex systems.

Game Theory Explained: A Mathematical Introduction with Optimization (1版)

類似書籍推薦給您

【簡介】 This book provides an introduction to the mathematical theory of games using both classical methods and optimization theory. Employing a theorem-proof-example approach, the book emphasizes not only results in game theory, but also how to prove them.Part 1 of the book focuses on classical results in games, beginning with an introduction to probability theory by studying casino games and ending with Nash’s proof of the existence of mixed strategy equilibria in general sum games. On the way, utility theory, game trees and the minimax theorem are covered with several examples. Part 2 introduces optimization theory and the Karush-Kuhn-Tucker conditions and illustrates how games can be rephrased as optimization problems, thus allowing Nash equilibria to be computed. Part 3 focuses on cooperative games. In this unique presentation, Nash bargaining is recast as a multi-criteria optimization problem and the results from linear programming and duality are revived to prove the classic Bondareva-Shapley theorem. Two appendices covering prerequisite materials are provided, and a ＂bonus＂ appendix with an introduction to evolutionary games allows an instructor to swap out some classical material for a modern, self-contained discussion of the replicator dynamics, the author’s particular area of study.