Copyright Year 2022
ISBN 9780367547073
August 20, 2021 Forthcoming by Chapman and Hall/CRC
264 Pages 15 B/W Illustrations
The core content of even the most intricate intellectual edifices is often a simple fact or idea. So is it with quantum mechanics; the entire mathematical fabric of the formal description of quantum mechanics stems essentially from the fact that quantum probabilities interfere (i.e., from the superposition principle). This book is dedicated to substantiating this claim. In the process, the book tries to demonstrate how the factual content of quantum mechanics can be transcribed in the formal language of vector spaces and linear transformations by disentangling the empirical content from the usual formal description. More importantly, it tries to bring out what this transcription achieves.
The book uses a pedagogic strategy which reverse engineers the postulates of quantum mechanics to device a schematic outline of the empirical content of quantum mechanics from which the postulates are then reconstructed step by step. This strategy is adopted to avoid the disconcerting details of actual experiments (however simplified) to spare the beginner of issues that lurk in the fragile foundations of the subject.
In the Copenhagen interpretation of quantum mechanics, the key idea is measurement. But "measurement" carries an entirely different meaning from the connotation that the term carries elsewhere in physics. This book strives to underline this as strongly as possible.
The book is intended as an undergraduate text for a first course in quantum mechanics. Since the book is self contained, it may also be used by enthusiastic outsiders interested to get a glimpse of the core content of the subject.
Demonstrates why linear algebra is the appropriate mathematical language for quantum mechanics.
Uses a reconstructive approach to motivate the postulates of quantum mechanics.
Builds the vocabulary of quantum mechanics by showing how the entire body of its conceptual ingredients can be constructed from the single notion of quantum measurement.
Preface. Prologue. Theoretical Framework - A Working Definition. What is a theory. Formal Description of a Theory.Abstraction and Generalization. Philosophy and Fundamental Theorem. Theory vs Theoretical Framework. The Empirical Basis of QM. Professor Funnyman’s Ghosts. An experiment with Bullets. Elementary Concepts in QM. Notation. The Laws of QM. The Quantum State Redefined. States as Vectors. Vectors in Cn. Towards a Formal Description of QM. Vector Spaces and Inner Product Spaces. The Postulates of QM ? Version. Observables as Operators. Linear Operators. Describing Observables by Linear Operators. The Postulates of QM ? Version. Quantization. Expectation Values. Imprecise Measurements and Degeneracy. Precise and Imprecise Measurements. Postulates of QM - Version 3. Complete and Incomplete Measurements. Commuting Operators. Compatibility and Commutativity. Time Evolution of Quantum Systems. Unitary Operator. Time Evolution of Quantum States. Postulates of QM - Version 4. The Programme in QM. Solving Schrodinger Equation. Continuous Spectra. Description using Function Spaces. Modified Postulates. Quantization of Systems with Classical Analogues. Three Classic Eigenvalue Problems. Harmonic Oscillator. Angular Momentum. Hydrogen Atom. QM of Composite Systems. The Meaning of a Composite System. Tensor Product Spaces. Description of Composite Systems. Interactions between Subsystems. Measurement on a Subsystem. Examples of Composite Systems. Identical Particles. A Probability. Preliminary Background. Probability in the Frequentist Interpretation. Alternative Interpretations. Formal Description. B Linear Algebra. Vector Space. Inner-product space. Linear Operators. Eigen Systems. Direct Sum of Subspaces. Tensor Product Spaces. Bibliography. Index.
Tilak Sinha is an Assistant Professor in the Department of Physics at Narasinha Dutt College, Howrah, India. He did his PhD on nonperturbative aspects of quantum field theory from Saha Institute of Nuclear Physics, Kolkata, and held a research position in the University of Wuppertal, Germany before joining Narasinha Dutt College in 2007. His interests include ontological and epistemological issues in the foundations of Quantum Mechanics, Quantum Field Theory, and Physics Educatio
Copyright Year 2022
ISBN 9781032044187
ISBN 9781032017235(Paperback)
September 9, 2021 Forthcoming by Chapman and Hall/CRC
200 Pages 1 B/W Illustrations
Elementary Number Theory, Gove Effinger and Gary Mullen,
This text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students (and instructors) to study, understand, and come to love this truly beautiful subject.
Each chapter, after an introduction, develops a new topic clearly broken out in sections which include theoretical material together with numerous examples, each worked out in considerable detail. At the end of each chapter, after a summary of the topic, there are a number of solved problems, also worked out in detail, followed by a set of supplementary problems. These latter problems give students a chance to test their own understanding of the material; solutions to some but not all of them complete the chapter.
The first eight chapters discuss some standard material in elementary number theory. The remaining chapters discuss topics which might be considered a bit more advanced. The text closes with a chapter on Open Problems in Number Theory. Students (and of course instructors) are strongly encouraged to study this chapter carefully and fully realize that not all mathematical issues and problems have been resolved! There is still much to be learned and many questions to be answered in mathematics in general and in number theory in particular.
1. Divisibility in the Integers Z 2. Prime Numbers and Factorization 3. Congruences and the Sets Zn 4. Solving Congruences 5. The Theorems of Fermat and Euler 6. Applications in Modern Cryptography 7. Quadratic Residues and Quadratic Reciprocity 8. Some Fundamental Number Theory Functions 9. Diophantine Equations 10. Finite Fields 11. Some Open Problems in Number Theory Appendixes Index Bibliographies
Gove Effinger received his Ph.D. in Mathematics from the University of Massachusetts (Amherst) in 1981 and subsequently taught at Bates College for 5 years and then Skidmore College for 29 years. He is the author of three books: An Elementary Transition to Abstract Mathematics (with Gary L. Mullen, CRC Press), Additive Number Theory of Polynomials over a Finite Field (with David R. Hayes), and Common-Sense BASIC: Structured Programming with Microsoft Quick BASIC (with Alice M. Dean), as well as numerous research papers. His research focus has primarily been concerned with the similarities of polynomials over a finite fields and ordinary integers.
Gary L. Mullen is Professor of Mathematics at the Pennsylvania State University, University Park, PA. He has taught both undergraduate and graduate courses there for over 40 years. In addition, he has written more than 150 research papers and co-authored seven books, including both graduate as well as undergraduate textbooks. He also served as department head for seven years and has served as an editor on numerous editorial boards, including having served as Editor-in-Chief of the journal Finite Fields and Their Applications since its founding in 1995.
Copyright Year 2022
ISBN 9780367613129
September 6, 2021 Forthcoming by CRC Press
264 Pages 130 B/W Illustrations
This book provides advance research in the field of applications of Differential Equations in engineering and sciences and offers a theoretical sound background along with case studies.
It describes the advancement of Differential Equations in real life for engineers. Along with covering many advanced Differential Equations and explaining the utility of these equations, the book gives a broad knowledge of Differential Equations used to solve and analyze many real value problems such as calculating the movement or flow of electricity, the motion of an object to and fro like a pendulum, or explaining thermodynamics concepts by making use of various mathematical tools, techniques, strategy, and methods in engineering applications.
This book is written for researcher scholars, as well as undergraduate, and postgraduate students of engineering.
1. Differential, Integral and Integro-Differential Equations. 2. Ordinary and Partial Linear and Nonlinear Delay, Stochastic, and Random Differential Equations. 3. Dynamical Systems and Stability. 4. Control Non-Linear, Adaptive, Hierarchical, Optimal, Robust, and Stochastic Intelligence. 5. Modelling and Simulation of Dynamical Systems. 6. Complex Dynamical Systems. 7. Dynamical Systems in Robotics. 8. Information Technology and Computational Intelligence for Dynamical Systems. 9. Applications of Differential Equations in Systems Engineering. 10. Bifurcations and Chaos in Dynamical Systems, Asymptotic Methods in Nonlinear Dynamics.
Nupur Goyal received the Bachelor’s degree in Computer science in 2009 from Kurukshetra University, Kurukshetra, Haryana, India. She received the master’s degree in mathematics in 2011 from H.N.B. Garhwal University, Srinagar, Uttarakhand, India and Ph.D. degree from Graphic Era University, Dehradun, Uttarakhand, India in November 2016. Her research interests are in the area of reliability theory and operation research. She has been an Assistant Professor in the Mathematics Department of the Suraj Degree College, Mahendergarh, Haryana in 2016. She has been an Assistant Professor in the Mathematics Department of the Garg Degree College, Laksar, Haridwar from 2017 to October 2018. She has been an Assistant Professor and Head of the Department of Applied Science and Humanities Department, Roorkee Institute of Technology, Roorkee from 2018 to January 2020. Currently, she is an Assistant Professor in department of Mathematics, Graphic Era Deemed to be University, Dehradun, India. She is a reviewer of various international journals including Springer, Emerald and IEEE, IJMEMS. She has published 30 plus research papers in various reputed national and international journals, book chapters including Springer, Emerald, Taylor & Francis, Inderscience and many other and also presented her research works at national and international conferences. She is the guest editor in many special issues of some journals. She is associate editor in the International Journal of Mathematical, Engineering and Management Sciences. She is editing one book in CRC Press- Taylor & Francis group. She has been a member of the organizing committee of a number of international and national conferences, seminars, and workshops.
Piotr Kulczycki graduated in Electrical Engineering from the AGH University of Science and Technology, and in Applied Mathematics from the Jagiellonian University. He currently holds the professor positions at the Systems Research Institute of the Polish Academy of Sciences, where he is the Head of the Centre of Information Technology for Data Analysis Methods, as well as the AGH University of Science and Technology, where he is the Head of the Division for Information Technology and Systems Research.
Mangey Ram received the Ph.D. degree major in Mathematics and minor in Computer Science from G. B. Pant University of Agriculture and Technology, Pantnagar, India. He has been a Faculty Member for around twelve years and has taught several core courses in pure and applied mathematics at undergraduate, postgraduate, and doctorate levels. He is currently the Research Professor at Graphic Era (Deemed to be University), Dehradun, India. Before joining the Graphic Era, he was a Deputy Manager (Probationary Officer) with Syndicate Bank for a short period. He is Editor-in-Chief of International Journal of Mathematical, Engineering and Management Sciences, Journal of Reliability and Statistical Studies, Editor-in-Chief of six Book Series with Elsevier, CRC Press-A Taylor and Frances Group, Walter De Gruyter Publisher Germany, River Publisher and the Guest Editor & Member of the editorial board of various journals. He has published 225 plus research publications (journal articles/books/book chapters/conference articles) in IEEE, Taylor & Francis, Springer, Elsevier, Emerald, World Scientific and many other national and international journals and conferences. Also, he has published more than 50 books (authored/edited) with international publishers like Elsevier, Springer Nature, CRC Press-A Taylor and Frances Group, Walter De Gruyter Publisher Germany, River Publisher. His fields of research are reliability theory and applied mathematics. Dr. Ram is a Senior Member of the IEEE, Senior Life Member of Operational Research Society of India, Society for Reliability Engineering, Quality and Operations Management in India, Indian Society of Industrial and Applied Mathematics, He has been a member of the organizing committee of a number of international and national conferences, seminars, and workshops. He has been conferred with "Young Scientist Award" by the Uttarakhand State Council for Science and Technology, Dehradun, in 2009. He has been awarded the "Best Faculty Award" in 2011; "Research Excellence Award" in 2015; and recently "Outstanding Researcher Award" in 2018 for his significant contribution in academics and research at Graphic Era Deemed to be University, Dehradun, India.