The Axiomatic Method in Biology
Author:
Publisher: CUP Archive
Published:
Total Pages: 196
ISBN-13:
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Entropy and Diversity
Author: Tom Leinster
Publisher: Cambridge University Press
Published: 2021-04-22
Total Pages: 457
ISBN-13: 1108832709
DOWNLOAD EBOOKDiscover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.
Foundations of Biophilosophy
Author: Martin Mahner
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 456
ISBN-13: 3662033682
DOWNLOAD EBOOKOver the past three decades, the philosophy of biology has emerged from the shadow of the philosophy of physics to become a respectable and thriving philosophical subdiscipline. The authors take a fresh look at the life sciences and the philosophy of biology from a strictly realist and emergentist-naturalist perspective. They outline a unified and science-oriented philosophical framework that enables the clarification of many foundational and philosophical issues in biology. This book will be of interest both to life scientists and philosophers.
Systems Biology
Author: A.K. Konopka
Publisher: CRC Press
Published: 2006-11-20
Total Pages: 258
ISBN-13: 1420015125
DOWNLOAD EBOOKWith extraordinary clarity,the Systems Biology: Principles, Methods, and Concepts focuses on the technical practical aspects of modeling complex or organic general systems. It also provides in-depth coverage of modeling biochemical, thermodynamic, engineering, and ecological systems. Among other methods and concepts based in logic, computer
Teleology, First Principles, and Scientific Method in Aristotle's Biology
Author: Allan Gotthelf
Publisher: Oxford University Press
Published: 2012-02-23
Total Pages: 464
ISBN-13: 0191629162
DOWNLOAD EBOOKThis volume presents an interconnected set of sixteen essays, four of which are previously unpublished, by Allan Gotthelf—one of the leading experts in the study of Aristotle's biological writings. Gotthelf addresses three main topics across Aristotle's three main biological treatises. Starting with his own ground-breaking study of Aristotle's natural teleology and its illuminating relationship with the Generation of Animals, Gotthelf proceeds to the axiomatic structure of biological explanation (and the first principles such explanation proceeds from) in the Parts of Animals. After an exploration of the implications of these two treatises for our understanding of Aristotle's metaphysics, Gotthelf examines important aspects of the method by which Aristotle organizes his data in the History of Animals to make possible such a systematic, explanatory study of animals, offering a new view of the place of classification in that enterprise. In a concluding section on 'Aristotle as Theoretical Biologist', Gotthelf explores the basis of Charles Darwin's great praise of Aristotle and, in the first printing of a lecture delivered worldwide, provides an overview of Aristotle as a philosophically-oriented scientist, and 'a proper verdict' on his greatness as scientist.
Axiomatic Method and Category Theory
Author: Andrei Rodin
Publisher: Springer Science & Business Media
Published: 2013-10-14
Total Pages: 285
ISBN-13: 3319004042
DOWNLOAD EBOOKThis volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Geometry and Its Applications
Author: Walter A. Meyer
Publisher: Elsevier
Published: 2006-02-21
Total Pages: 560
ISBN-13: 0080478034
DOWNLOAD EBOOKMeyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. - Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns - Physics - Robotics - Computer vision - Computer graphics - Stability of architectural structures - Molecular biology - Medicine - Pattern recognition - Historical notes included in many chapters
Perspectives on Organisms
Author: Giuseppe Longo
Publisher: Springer Science & Business Media
Published: 2013-12-13
Total Pages: 293
ISBN-13: 3642359388
DOWNLOAD EBOOKThis authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in biology, in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould's analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field.
Thinking about Godel and Turing
Author: Gregory J. Chaitin
Publisher: World Scientific
Published: 2007
Total Pages: 368
ISBN-13: 9812708979
DOWNLOAD EBOOKDr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as GAdel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of GAdel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity."
Evolutionary Theory
Author: Sean H. Rice
Publisher: Sinauer Associates Incorporated
Published: 2004
Total Pages: 370
ISBN-13: 9780878937028
DOWNLOAD EBOOKEvolutionary Theory is for graduate students, researchers, and advanced undergraduates who want an understanding of the mathematical and biological reasoning that underlies evolutionary theory. The book covers all of the major theoretical approaches used to study the mechanics of evolution, including classical one- and two-locus models, diffusion theory, coalescent theory, quantitative genetics, and game theory. There are also chapters on theoretical approaches to the evolution of development and on multilevel selection theory. Each subject is illustrated by focusing on those results that have the greatest power to influence the way that we think about how evolution works. These major results are developed in detail, with many accompanying illustrations, showing exactly how they are derived and how the mathematics relates to the biological insights that they yield. In this way, the reader learns something of the actual machinery of different branches of theory while gaining a deeper understanding of the evolutionary process. Roughly half of the book focuses on gene-based models, the other half being concerned with general phenotype-based theory. Throughout, emphasis is placed on the fundamental relationships between the different branches of theory, illustrating how all of these branches are united by a few basic, universal, principles. The only mathematical background assumed is basic calculus. More advanced mathematical methods are explained, with the help of an extensive appendix, when they are needed.
