Books as Coauthor/(Co-)Editor
Proof and Computation II
Proof and Computation II
From Proof Theory and Univalent Mathematics to Program Extraction and Verification
Editors: Klaus Mainzer, Peter Schuster, Helmut Schwichtenberg
World Scientific Singapore 2022
ISBN 9789811236471
This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Verantwortung in Unternehmen und Institutionen für eine nachhaltige Technikentwicklung
Verantwortung in Unternehmen und Institutionen für eine nachhaltige Technikentwicklung
acatech POSITION
Klaus J. Beckmann, Klaus Kornwachs, Klaus Mainzer, Marc-Denis Weitze
Verlag: acatech - Deutsche Akademie der Technikwissenschaten, 2021
ISBN 3968340132, 9783968340135
Proof and Computation
Proof and Computation
Digitization in Mathematics, Computer Science, and Philosophy
Editors: Klaus Mainzer, Peter Schuster, Helmut Schwichtenberg
World Scientific Publishing Company
2018
ISBN 978-981-3270-95-4
This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
The Concept of Law in Science
The Concept of Law in Science, European Review European Review (Cambridge University Press) Vol 22, supplement no.1 (2014)
ISSN 1062-7987
Proceedings of an International Conference on Complexity of the Academia Europaea (The Academy of Europe) supported by the Klaus Tschira Stiftung.
The conference topic was dedicated to the concept of law in science. In the classical tradition, natural laws were considered as eternal truths of the world. Galileo and Newton even proclaimed them as "thoughts of God" represented by mathematical equations. In the Kantian tradition, they became categories of the human mind. David Hume criticized their ontological status and demanded their reduction to habituations of sentiments and statistical correlations of observations.
Numbers (English)
Numbers (English)
(with H.-D. Ebbinghaus, H. Hermes, F. Hirzebruch, M. Koecher, J. Neukirch, A. Prestel, R. Remmert), Springer: Berlin/Heidelberg/New York/Tokyo 1990,
391 pages, (German editions: 1983, 3rd edition 1992).
ISBN 0-387-97497-0
This is a book about numbers - all kinds of numbers, from integers to p-adics, from rationals to octonions, from reals to infinitesimals. This is the story about one of the major threads of mathematics over thousands of years. This is also a fundamental view of some major developments in the 20th century mathematics.
Japanese Translation of the German Edition 1983:
Japanese Translation of
the German Edition 1983:
Numbers 2 vols.
Springer: Tokyo 1992, 452 pages
ISBN 4-431-70602-X
French Translation of the 3rd German Edition 1992:
French Translation of the
3rd German Edition 1992:
Les Nombres
Vuibert 1998, 433 pages
ISBN 2-7117-8901-2
Philosophy and Physics of Space-Time (German)
Philosophy and Physics of Space-Time (German)
(Ed. with J. Audretsch), Series: Foundations of Mathematical Sciences vol. 7, B. I. Wissenschaftsverlag: Mannheim/Wien/Zürich 1988, 231 pages, 2nd edition 1994.
ISBN 3-411-17072-1
Physical foundations of space-time in special relativity with respect to philosophical and historical aspects.
Physical foundations of space-time in special relativity with respect to philosophical and historical aspects.
Contributions of K. Mainzer, J. Audretsch, P. Mittelstaedt, E. Scheibe, G. Ludwig, J. Schröter, J. Ehlers, P. Janich.
The Beginning of the Universe. Science - Philosophy - Religion - Myth (German)
The Beginning of the Universe.
Science - Philosophy - Religion - Myth (German)
(Ed. with J. Audretsch), C.H. Beck: München 1989, 2nd edition 1990, 288 pages.
ISBN 3-406-33925-5
Discussion of the relativistic standard models in modern cosmology with respect to philosophical and religious questions of the world view.
Discussion of the relativistic standard models in modern cosmology with respect to philosophical and religious questions of the world view. Contributions of K. Mainzer, J. Mittelstraß, J. Audretsch, G. A. Tammann, H. Dehnen, B. Kanitscheider, A. Deißler, K. Hübner.
How Many Lives has Schrödinger’s Cat? Physics and Philosophy of Quantum Mechanics (German)
How Many Lives has Schrödinger’s Cat?
Physics and Philosophy of Quantum Mechanics
(German)
(Ed. with J. Audretsch), B.I. Wissenschaftsverlag: Mannheim/Wien/Zürich 1990, 318 pages, 2nd edition: Spektrum-Verlag: Heidelberg/Berlin/Oxford 1996.
ISBN 3-411-14281-2
Introduction of quantum mechanical concepts and epistemic discussion of the measurement problem (‘Schrödinger’s Cat’).
Introduction of quantum mechanical concepts and epistemic discussion of the measurement problem (‘Schrödinger’s Cat’). Contributions of J.Audretsch, A. Zeilinger, H. Walther, P. Mittelstaedt, E. Scheibe, G. Ludwig, H. Primas, K. Mainzer.
The Question of Life (German)
The Question of Life (German)
(Ed. with E. P. Fischer), Piper-Verlag: Munich 1990, 264 pages.
ISBN 3-492-11119-X
Nearly fifty years after Schrödinger’s famous book ‘What is Life?’, physicists, chemists, biologists, mathematicians, and philosophers discuss the origin of life from a modern point of view.
Nearly fifty years after Schrödinger’s famous book ‘What is Life?’, physicists, chemists, biologists, mathematicians, and philosophers discuss the origin of life from a modern point of view. Contributions of K. Mainzer, E. P. Fischer, H. Primas, B.-O. Küppers, R. Knippers, H. Haken/A. Wunderlin, G. Adam, E. Florey, E. Bohl.
Natural Sciences and Humanities.
Natural Sciences and Humanities.
Perspectives and Experiences with Interdisciplinary Teaching (German) (Ed.), Springer: Berlin/Heidelberg/New York/London/Tokyo 1990, 124 pages.
ISBN 3-540-52377-4
The global problems arising with modern technology, economy, and society cannot be solved in the disciplinary framework of sciences.
The global problems arising with modern technology, economy, and society cannot be solved in the disciplinary framework of sciences.
The book discusses interdisciplinary models of teaching in several universities and institutions. Contributions of K. Mainzer, W. Wild, U. Müller-Herold, J. Brüning, W. Arber, J. Audretsch, J. Becker, C. Rückhardt, H. Mohr, W. Prinz, D. Groh, H. Gassert.
Economy and Ecology (German/French)
Economy and Ecology (German/French)
(Ed.), P. Haupt-Verlag: Bern/Stuttgart 1993.
ISBN 3-258-04692-1
German-Swiss conference
German-Swiss conference on ecological, economical, social, and political problems of modern society with contributions of R. Bürgenmeier, C. Raffestin, K. Mainzer, R. Blum, S. C. Schaltegger, A. J. Sturm, G. Gandard, J. Grinevald, U. Müller-Herold, R. Civelli, D. Wachter, R. Schmidt, M. Timmermann.
Quanta, Chaos, and Demons.
Quanta, Chaos, and Demons.
Epistemic Aspects of Modern Physics (German)
(Ed. with W. Schirmacher), B.I. Wissenschaftsverlag: Mannheim/Wien/Zürich 1994, 363 pages.
ISBN 3-411-16301-1
Epistemic discussion of chaos theory, quantum theory (‘quantum chaos’), and applications of complex dynamical systems in nature and society.
Epistemic discussion of chaos theory, quantum theory (‘quantum chaos’), and applications of complex dynamical systems in nature and society. Contributions of K. Mainzer, J. Audretsch, P. Mittelstaedt, P. Busch, W. Brenig, H. Thomas, T. Leiber, H. Friedrich, O. E. Rössler, H. Haken, A. Wunderlin, W. Weidlich, M. Markus, P. Kafka.
From Simplicity to Complexity. Part II Information-Interaction-Emergence
From Simplicity to Complexity. Part II
Information-Interaction-Emergence
(Ed. with A. Müller and W. G. Saltzer), Vieweg: Braunschweig/Wiesbaden 1998, 233 pages.
ISBN 3-528-06757-8
Physicists, chemists, biologists, and philosophers of science try to decode nature's pathways from simple to more complex systems.
Physicists, chemists, biologists, and philosophers of science try to decode nature's pathways from simple to more complex systems. Contributions of S. D. Bosanac, H.-P. Dürr, T. Görnitz, C. K. Jørgensen, T. Dorfmüller, A. Müller, M. T. Pope, C. L. Hill, X. Zhang, B. Hess, W. F. Gutmann, G. J. Klauer, K. Mainzer, P. L. Eisenhardt, D. Kurth, E. R. Scerri, R. E. Zimmermann, R. Löther, H. Hörz, W. G. Saltzer.
Complex Systems and Nonlinear Dynamics in Nature and Society.
Complex Systems and Nonlinear Dynamics in Nature and Society. Complexity Research in Germany towards the next Century (German) (Ed.) Springer: Berlin/Heidelberg /New York 1999, 484 pages.
ISBN 3 540 65329 5
Complex Systems are analyzed in different sciences like physics, chemistry, biology and medicine, but also in cognitive sciences and psychology, sociology and economics.
Complex Systems are analyzed in different sciences like physics, chemistry, biology and medicine, but also in cognitive sciences and psychology, sociology and economics.
The book is a comprehensive overview on current and future research on complex systems and nonlinear dynamics in nearly all disciplines of sciences. It dates back to the 1st congress of the German Society of Complex Systems and Nonlinear Dynamics and can be read in the internet. Contributions by K. Mainzer, H. Haken, S. Großmann, J. Kurths, H. Kantz, E. R. Nakamura, A. Müller, P. Schuster, H. Meinhard, C. von der Malsburg, M. A. Stadler, K.-H. Leist, Z. J. Kowalik, T. Leiber, U. an der Heiden, H. M. Emrich, K. G. Troitzsch, W. Weidlich, G. Küppers, H.-W. Lorentz, C. J. G. Evertsz, H.-O. Peitgen, F. J. Radermacher, W. Ebeling et al.
Complexity (Ed.)
Complexity (Ed.)
European Review (Cambridge University Press) Vol 17 (2009) 2, p. 219-452
ISSN 1062-7987
Proceedings of an International Conference on Complexity of the Academia Europaea (The Academy of Europe) supported by the Klaus Tschira Stiftung
The theory of nonlinear complex systems has become a proven problem-solving approach in the natural sciences from cosmic and quantum systems to cellular organisms and the brain. It is now recognized that many of our ecological, social, economic, and political problems are also of a global, complex, and nonlinear nature ... Cover/Content
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