Includes bibliographical references and index.

Zbigniew Oziewicz's biographical notes -- Einstein's composition of velocities as a non-associative algebraic structure and the underlying geometry of symmetric spaces of E. Cartan -- Didactic experiences with the moodle for critical and creative thinking -- A construction for Clifford algebras - Exponential of endomorphism with minimal polynomial -- Mathematics and physical meaning in relativistic quantum mechanics -- Composition of relativistic velocities: algebraic loop deformation and geometry -- Evolution equations of relativistic dynamics along geodesic lines of hyperbolic and elliptic spaces -- Relative binary and ternary four-dimensional velocities in the special relativity in terms of manifestly covariant Lorentz transformation -- The space-time theories exploratorium -- Classical relativity and quantum relativity versus special relativity: meditations on the trails of Zbigniew Oziewicz -- Quantum calculi: differential forms and vector fields in non-commutative geometry -- Zbigniew Oziewicz's differential calculus with a classical thermodynamics point of view -- Binary Lie algebras with identities -- Kepler problem, Lorentz transformation, and Jordan algebra -- On the Leavitt path algebras of a class of random graphs -- Homology of small categories and Khovanov homology -- The golden ratio, variational principles, cyclic and wave phenomena and quanta -- Some categories of Alexandroff spaces -- Parametric Hopf adjunctions and monads -- Visible and invisible states: an algebraic and philosophical investigation on the relation between states and observables -- SU(n) and quantum SU(n) symmetries in physical systems -- Projective view on motion groups II: a quest for rational geometries -- Spheroidal quaternions and symmetries -- Special affine quaternion domain Fourier transform -- Vortices, knots, Chebyshev polynomials, Frobenius algebras, topological quantum field theories -- On negative-energy 4-spinors and masses in the dirac equation -- Yang-Mills-scalar-matter fields in the two-point space -- Representation of the anomalous magnetic moment of the Muons via the novel Einstein-Podolsky-Rosen entanglement -- The standard model of elementary particle physics -- Superdense coding and multiparty communication protocols using quantum systems of several levels -- Computable isomorphism problem -- Generating function for quantum hyperbolic planes -- Weak gravitational fields in the geometric algebra approach.

"Dedicated to the memory of the late Professor Zbigniew Oziewicz from Universidad Nacional Autónoma de México, the book consists of papers on a wide variety of topics related to the work of Professor Oziewicz, which were presented at the special conference on Graph-Operads-Logic (GOL 2021), selected through peer review to promote his scientific legacy. Professor Oziewicz was a great enthusiast and supporter of category theory and its applications in physics, as well as in various areas of mathematics (topology, noncommutative geometry, etc.). In particular, he made significant contributions to the theory of Frobenius algebras, which now are becoming more important due to their connection with topological quantum field theories that are used in mathematical physics and in quantum topology. Professor Oziewicz was a great and very generous teacher, who immersed his students in the beautiful ideas of category theory as well as mathematical physics and computation. It was his idea to start a series of conferences under the title Graphs-Operads-Logic, most of them held in Mexico, with some of them in the USA, which were a great platform to discuss various ideas connected with category theory and its various applications, and to make friends with other scientists. Despite his passing, the GOL 2021 conference is included in this series to pay tribute to his many contributions to diverse areas of science. The book is laid out in twelve main topics where we can find relevant works from distinguished experts"-- Publisher's website.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.