Self-love, Egoism and the Selfish Hypothesis - Key Debates from Eighteenth-Century British Moral Philosophy
pdf | 1.67 MB | English | Isbn:‎ 978-1474477970 | Author: Maurer, Christian; | Year: 2020

Christian Maurer, "Self-love, Egoism and the Selfish Hypothesis: Key Debates from Eighteenth-Century British Moral Philosophy"
English | ISBN: 1474477976 | 2020 | 240 pages | PDF | 2 MB

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English | 2021 | ISBN: 1536194220 | 232 pages | True PDF | 13.21 MB
This book is an introductory and comprehensive presentation of the Riemann Hypothesis, one of the most important open questions in math today. It is introductory because it is written in an accessible and detailed format that makes it easy to read and understand. And it is comprehensive because it explains and proves all the mathematical ideas surrounding and leading to the formulation of the hypothesis. Chapter 1 begins by defining the zeta function and exploring some of its properties when the argument is a real number. It proceeds to identify the series' domain of convergence and proves Euler's product formula. Chapter 2 introduces complex numbers and the complex analytic tools necessary to understand the zeta function in complex plane. Chapter 3 extends the domain of the zeta function for the first time by introducing the eta function. Presenting proofs by Sondow, it is shown that zeta can be defined for any complex number whose real part is positive. Next, the functional equation of the zeta function is derived in Chapter 4. This provides a method to extend the definition of zeta to the entirety of the complex plane. Chapter 5 is where the Riemann Hypothesis is properly introduced for the first time. It relates the zeros of the zeta and eta functions which leads to a simple formulation of the hypothesis. Chapters 6 and 7 connect the topics of zeta's zeros and the distribution of prime numbers. Chapter 6 introduces Riemann explicit formula and explains the use of Mobius transform to rewrite the prime counting function in terms of the Riemann prime counting one and it provides a detailed numerical example on how to use the Riemann's formula. Chapter 7 derives the von Mangoldt formula via the residue theorem and elucidates some of its important properties. Certain necessary mathematical tools, such as Fourier analysis and theta and gamma functional equations, are included in the appendices to make the chapters more concise and focused.

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Defense of the Scientific Hypothesis: From Reproducibility Crisis to Big Data by Bradley E. Alger
English | October 15, 2019 | ISBN: 0190881488 | EPUB | 488 pages | 1.76 MB
Defense of Scientific Hypothesis: From Reproducibility Crisis to Big Data sets out to explain and defend the scientific hypothesis. Alger's mission is to counteract the misinformation and misunderstanding about the hypothesis that even seasoned scientists have concerning its nature and place in modern science. Most biological scientists receive little or no formal training in scientific thinking. Further, the hypothesis is under attack by critics who claim that it is irrelevant to science. In order to appreciate and evaluate scientific controversies like global climate change, vaccine safety, etc., the public first needs to understand the hypothesis.