Undergraduate Texts in Contemporary Physics – serie

This text stems from a course I have taught a number of times, attended by students of material science, electrical engineering, physics, chemistry, physical chemistry and applied mathematics. It is intended as an intro­ ductory discourse to give the reader a first encounter with group theory. The work concentrates on point and space groups as these groups have the principal application in technology. Here is an outline of the salient features of the chapters. In Chapter 1, basic notions and definitions are introduced including that of Abelian groups, cyclic groups, Sylow's theorems, Lagrange's subgroup theorem and the rearrangement theorem. In Chapter 2, the concepts of classes and direct products are discussed. Applications of point groups to the Platonic solids and non-regular dual polyhedra are described. In Chapter 3, matrix representation of operators are introduced leading to the notion of irreducible representations ('irreps'). The Great Orthogonal­ ity Theorem (GOT) is also introduced, followed by six important rules relating to dimensions of irreps. Schur's lemma and character tables are described. Applications to quantum mechanics are discussed in Chapter 4 including descriptions of the rotation groups in two and three dimensions, the symmetric group, Cayley's theorem and Young diagrams. The relation of degeneracy of a quantum state of a system to dimensions of irreps of the group of symmetries of the system are discussed, as well as the basis properties of related eigenfunctions.

Computer algebra systems have the potential to revolutionize the teaching of and learning of science. Not only can students work thorough mathematical models much more efficiently and with fewer errors than with pencil and paper, they can also work with much more complex and computationally intensive models. Thus, for example, in studying the flight of a golf ball, students can begin with the simple parabolic trajectory, but then add the effects of lift and drag, of winds, and of spin. Not only can the program provide analytic solutions in some cases, it can also produce numerical solutions and graphic displays. Aimed at undergraduates in their second or third year, this book is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, physics, chemistry. The text is organized along a spiral, revisiting general topics such as graphics, symbolic computation, and numerical simulation in greater detail and more depth at each turn of the spiral. The heart of the text is a large number of computer algebra recipes.These have been designed not only to provide tools for problem solving, but also to stimulate the reader's imagination. Associated with each recipe is a scientific model or method and a story that leads the reader through steps of the recipe. The recipes are also included on the CD-ROM enclosed with the book. Each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further.

Intended for advanced undergraduates and graduate students, this book is a practical guide to the use of probability and statistics in experimental physics. The emphasis is on applications and understanding, on theorems and techniques actually used in research. The text is not a comprehensive text in probability and statistics; proofs are sometimes omitted if they do not contribute to intuition in understanding the theorem. The problems, some with worked solutions, introduce the student to the use of computers; occasional reference is made to routines available in the CERN library, but other systems, such as Maple, can also be used. Topics covered include: basic concepts; definitions; some simple results independent of specific distributions; discrete distributions; the normal and other continuous distributions; generating and characteristic functions; the Monte Carlo method and computer simulations; multi-dimensional distributions; the central limit theorem; inverse probability and confidence belts; estimation methods; curve fitting and likelihood ratios; interpolating functions; fitting data with constraints; robust estimation methods. This second edition introduces a new method for dealing with small samples, such as may arise in search experiments, when the data are of low probability. It also includes a new chapter on queuing problems (including a simple, but useful buffer length example). In addition new sections discuss over- and under-coverage using confidence belts, the extended maximum-likelihood method, the use of confidence belts for discrete distributions, estimation of correlation coefficients, and the effective variance method for fitting y = f(x) when both x and y have measurement errors.

Intended as a companion for textbooks in mathematical methods for science and engineering, this book presents a large number of numerical topics and exercises together with discussions of methods for solving such problems using Mathematica(R). Although it is primarily designed for use with the author's "Mathematical Methods: For Students of Physics and Related Fields," the discussions in the book sufficiently self-contained that the book can be used as a supplement to any of the standard textbooks in mathematical methods for undergraduate students of physical sciences or engineering.

This book, a companion to the textbook, Understanding Physics, is your guide to observations and explorations in the world of physics. Prepare for ch- lenging work, fun, and some surprises. One of the best ways to learn physics is by doing physics, in the laboratory and everywhere. One cannot rely on reading and class work alone. The explorations in this book are your - portunity to gain some actual, hands-on experience with physics. Many of these explorations will assist you to design your own experiments and to discover many of the important ideas of science yourself. As you will see from the Contents, this Student Guide provides a variety of potentially helpful materials. Following the Introduction is a review of units, mathematics, and scientific notation, and a list of suggested further reading and Web Sites. However, a large portion of the Student Guide c- tains further materials relating to many of the textbook chapters, as well as to laboratory explorations. In the section containing “Further Chapter - terials” you will find elaborations on topics in many of the chapters, as well as derivations of important equations. A complete list of the suggested mi- and major-laboratory explorations is also given in the Contents. Each - ploration is keyed to specific portions of the textbook, and lists are also provided of the explorations pertaining to each part of the text.

Understanding Physics provides a thorough grounding in contemporary physics while placing physics into its social and historical context. Based in large part on the highly respected Project Physics Course developed by two of the authors, it also integrates the results of recent pedagogical research. The text thus: - teaches about the basic phenomena in the physical world and the concepts developed to explain them - shows that science is a rational human endeavor with a long and continuing tradition, involving many different cultures and people - develops facility in critical thinking, reasoned argumentation, evaluation of evidence, mathematical modeling, and ethical values The treatment emphasizes not only what we know but also how we know it, why we believe it, and what effects that knowledge has: - Why do we believe the Earth and planets revolve around the Sun? - Why do we believe that matter is made of atoms? - How do relativity theory and quantum mechanics alter our conception of Nature and in what ways do they leave the classical concepts unchanged? - What impact does the knowledge of finite energy resources have on our society? - How have applications of fundamental science (such as the steam engine, the laser, the electric generator, the transistor) affected our lives? - How does the evidence for non-scientific ideas, such as UFOs, ESP, and the like, differ from the evidence for accepted scientific results?

This text stems from a course I have taught a number of times, attended by students of material science, electrical engineering, physics, chemistry, physical chemistry and applied mathematics. It is intended as an intro­ ductory discourse to give the reader a first encounter with group theory. The work concentrates on point and space groups as these groups have the principal application in technology. Here is an outline of the salient features of the chapters. In Chapter 1, basic notions and definitions are introduced including that of Abelian groups, cyclic groups, Sylow's theorems, Lagrange's subgroup theorem and the rearrangement theorem. In Chapter 2, the concepts of classes and direct products are discussed. Applications of point groups to the Platonic solids and non-regular dual polyhedra are described. In Chapter 3, matrix representation of operators are introduced leading to the notion of irreducible representations ('irreps'). The Great Orthogonal­ ity Theorem (GOT) is also introduced, followed by six important rules relating to dimensions of irreps. Schur's lemma and character tables are described. Applications to quantum mechanics are discussed in Chapter 4 including descriptions of the rotation groups in two and three dimensions, the symmetric group, Cayley's theorem and Young diagrams. The relation of degeneracy of a quantum state of a system to dimensions of irreps of the group of symmetries of the system are discussed, as well as the basis properties of related eigenfunctions.

Intended for advanced undergraduates and graduate students, this book is a practical guide to the use of probability and statistics in experimental physics. The emphasis is on applications and understanding, on theorems and techniques actually used in research. The text is not a comprehensive text in probability and statistics; proofs are sometimes omitted if they do not contribute to intuition in understanding the theorem. The problems, some with worked solutions, introduce the student to the use of computers; occasional reference is made to routines available in the CERN library, but other systems, such as Maple, can also be used. Topics covered include: basic concepts; definitions; some simple results independent of specific distributions; discrete distributions; the normal and other continuous distributions; generating and characteristic functions; the Monte Carlo method and computer simulations; multi-dimensional distributions; the central limit theorem; inverse probability and confidence belts; estimation methods; curve fitting and likelihood ratios; interpolating functions; fitting data with constraints; robust estimation methods. This second edition introduces a new method for dealing with small samples, such as may arise in search experiments, when the data are of low probability. It also includes a new chapter on queuing problems (including a simple, but useful buffer length example). In addition new sections discuss over- and under-coverage using confidence belts, the extended maximum-likelihood method, the use of confidence belts for discrete distributions, estimation of correlation coefficients, and the effective variance method for fitting y = f(x) when both x and y have measurement errors.

Computer algebra systems have the potential to revolutionize the teaching of and learning of science. Not only can students work thorough mathematical models much more efficiently and with fewer errors than with pencil and paper, they can also work with much more complex and computationally intensive models. Thus, for example, in studying the flight of a golf ball, students can begin with the simple parabolic trajectory, but then add the effects of lift and drag, of winds, and of spin. Not only can the program provide analytic solutions in some cases, it can also produce numerical solutions and graphic displays. Aimed at undergraduates in their second or third year, this book is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, physics, chemistry. The text is organized along a spiral, revisiting general topics such as graphics, symbolic computation, and numerical simulation in greater detail and more depth at each turn of the spiral.The heart of the text is a large number of computer algebra recipes. These have been designed not only to provide tools for problem solving, but also to stimulate the reader's imagination. Associated with each recipe is a scientific model or method and a story that leads the reader through steps of the recipe. Each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further.