Introduction to Topology and Geometry

Discover a unique and modern treatment of topology employing a cross-disciplinary approach Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research. Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs. This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation. The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological groups The fundamental group and homology Special «core intuition» segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the publisher's Web site.

An invaluable introduction to nanomaterials and their applications Offering the unique approach of applying traditional physics concepts to explain new phenomena, Introduction to Nanomaterials and Devices provides readers with a solid foundation on the subject of quantum mechanics and introduces the basic concepts of nanomaterials and the devices fabricated from them. Discussion begins with the basis for understanding the basic properties of semiconductors and gradually evolves to cover quantum structures—including single, multiple, and quantum wells—and the properties of nanomaterial systems, such as quantum wires and dots. Written by a renowned specialist in the field, this book features: An introduction to the growth of bulk semiconductors, semiconductor thin films, and semiconductor nanomaterials Information on the application of quantum mechanics to nanomaterial structures and quantum transport Extensive coverage of Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein stastistics An in-depth look at optical, electrical, and transport properties Coverage of electronic devices and optoelectronic devices Calculations of the energy levels in periodic potentials, quantum wells, and quantum dots Introduction to Nanomaterials and Devices provides essential groundwork for understanding the behavior and growth of nanomaterials and is a valuable resource for students and practitioners in a field full of possibilities for innovation and invention.

Introduction to Nanoscience and Nanotechnology explains nanotechnology to an audience that does not necessarily have a scientific background. It covers all aspects, including the new areas of biomedical applications and the use of nanotechnology to probe the «quantum vacuum.» After discussing the present state of the art in nanotechnology, the book makes estimates of where these technologies are going and what will be possible in the future.

Introduction to Astronomy & Cosmology is a modern undergraduate textbook, combining both the theory behind astronomy with the very latest developments. Written for science students, this book takes a carefully developed scientific approach to this dynamic subject. Every major concept is accompanied by a worked example with end of chapter problems to improve understanding Includes coverage of the very latest developments such as double pulsars and the dark galaxy. Beautifully illustrated in full colour throughout Supplementary web site with many additional full colour images, content, and latest developments.

The book presents nanoscience and nanotechnology to a broad audience that does not necessarily have a scientific background. This book starts with the fundamental physicochemical properties of nanoparticles and nanostructures, and discusses how these special properties can be manipulated to produce high-performance materials and devices. In the following chapters, the scope is broadened to cover naturally occurring nanoparticles and artificially-engineered carbon nanoparticles, their mechanical properties, and their importance to the rest of nanotechnology. The book also covers the two design ideologies for manufacturing nanostructures, the bottom-up and top-down methods, and discusses how these two can be combined to allow for the imaging, probing and manipulation of nanostructures. The remainder of the book surveys the current state of nanotechnology, including the use of single-nanoparticle devices in data storage, electronics, optics, and solar power; advances in nanoparticle manufacturing and biotechnology that can lead to powerful new cancer treatments; and the use of nanotechnology to study the “quantum vacuum”.

A well-balanced introduction to probability theory and mathematical statistics Featuring updated material, An Introduction to Probability and Statistics, Third Edition remains a solid overview to probability theory and mathematical statistics. Divided intothree parts, the Third Edition begins by presenting the fundamentals and foundationsof probability. The second part addresses statistical inference, and the remainingchapters focus on special topics. An Introduction to Probability and Statistics, Third Edition includes: A new section on regression analysis to include multiple regression, logistic regression, and Poisson regression A reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics Additional topical coverage on bootstrapping, estimation procedures, and resampling Discussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals Over 550 problems and answers to most problems, as well as 350 worked out examples and 200 remarks Numerous figures to further illustrate examples and proofs throughout An Introduction to Probability and Statistics, Third Edition is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.

The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors. Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which «capstone» best suits his or her students. Topology: Point-Set and Geometric features: A short introduction in each chapter designed to motivate the ideas and place them into an appropriate context Sections with exercise sets ranging in difficulty from easy to fairly challenging Exercises that are very creative in their approaches and work well in a classroom setting A supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs

Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals. Key features: Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains. Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver. Examines optimal filtering methods and their consequences. Presents a detailed discussion of the topic of Poisson processes and shot noise. An excellent resource for professional engineers developing communication systems, semiconductor devices, and audio and video equipment, this book is also ideal for senior undergraduate and graduate students in Electronic and Electrical Engineering.

Introduction to Aircraft Aeroelasticity and Loads, Second Edition is an updated new edition offering comprehensive coverage of the main principles of aircraft aeroelasticity and loads. For ease of reference, the book is divided into three parts and begins by reviewing the underlying disciplines of vibrations, aerodynamics, loads and control, and then goes on to describe simplified models to illustrate aeroelastic behaviour and aircraft response and loads for the flexible aircraft before introducing some more advanced methodologies. Finally, it explains how industrial certification requirements for aeroelasticity and loads may be met and relates these to the earlier theoretical approaches used. Key features of this new edition include: Uses a unified simple aeroelastic model throughout the book Major revisions to chapters on aeroelasticity Updates and reorganisation of chapters involving Finite Elements Some reorganisation of loads material Updates on certification requirements Accompanied by a website containing a solutions manual, and MATLAB® and SIMULINK® programs that relate to the models used For instructors who recommend this textbook, a series of lecture slides are also available Introduction to Aircraft Aeroelasticity and Loads, Second Edition is a must-have reference for researchers and practitioners working in the aeroelasticity and loads fields, and is also an excellent textbook for senior undergraduate and graduate students in aerospace engineering.

Learn the basics of the five core areas of community and public health Introduction to Community and Public Health covers the basics in each area of community and public health as identified by the Association of Schools of Public Health. In a student-friendly approach, authors Manoj Sharma, Paul W. Branscum, and Ashutosh Atri discuss epidemiology, biostatistics, social and behavioral sciences, environmental health, and healthy policy and management. Written to serve both graduate and undergraduate public health students, as well as to help prepare for the Certified in Public Health (CPH) exam, Certified Health Education Specialist (CHES) exam and Master certified in Health Education Specialist (MCHES) exam, the book covers each of these five core disciplines, plus other important topics such as: Population dynamics and control Air, water, and noise pollution, and other environmental issues Program planning, budgeting, management, and evaluation Systems thinking and leadership in community and public health Students will gain insight into the descriptive, inferential, and analytical aspects of community and public health, as well as models, methods, and theories in health education and health promotion. Introduction to Community and Public Health provides the foundation necessary to build the skills of tomorrow's community and public health leaders.