Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of pro
Unique in its clarity, examples, and range, Physical Mathematics explains simply and succinctly the mathematics that graduate students and professional physicists need to succeed in their courses and research. The book illustrates the mathematics with numerous physical examples drawn from contemporary research. This second edition has new chapters on vector calculus, special relativity and artificial intelligence and many new sections and examples. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations, Bessel functions, and spherical harmonics, the book explains topics such as the singular value decomposition, Lie algebras and group theory, tensors and general relativity, the central limit theorem and Kolmogorov's theorems, Monte Carlo methods of experimental and theoretical physics, Feynman's path integrals, and the standard model of cosmology.
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every cha
The third edition of this successful textbook will supply advanced undergraduate and graduate students with the tools they need to understand modern glaciological research. Practicing glacial geologists and glaciologists will also find the volume useful as a reference book. Since the second edition, three-quarters of the chapters have been updated, and two new chapters have been added. Included in this edition are noteworthy new contributions to our understanding of important concepts, with over 170 references to papers published since the second edition went to press. The book develops concepts from the bottom up: a working knowledge of calculus is assumed, but beyond that, the important physical concepts are developed from elementary principles. Emphasis is placed on connections between modern research in glaciology and the origin of features of glacial landscapes. Student exercises are included.
Rakesh V. Vohra offers a unique approach to studying and understanding intermediate microeconomics by reversing the conventional order of treatment, starting with topics that are mathematically simpler and progressing to the more complex. The book begins with monopoly, which requires single variable rather than multivariable calculus and allows students to focus clearly on the fundamental trade-off at the heart of economics: margin versus volume. Imperfect competition and the contrast with monopoly follows, introducing the notion of Nash equilibrium. Perfect competition is addressed toward the end of the book, and framed as a model of non-strategic behavior by firms and agents. The last chapter is devoted to externalities, with an emphasis on how one might design competitive markets to price externalities and linking the difficulties to the problem of efficient provision of public goods. Real-life examples engage the reader while encouraging them to think critically about the interplay
Anchored in simple and familiar physics problems, the author provides a focused introduction to mathematical methods in a narrative driven and structured manner. Ordinary and partial differential equation solving, linear algebra, vector calculus, complex variables and numerical methods are all introduced and bear relevance to a wide range of physical problems. Expanded and novel applications of these methods highlight their utility in less familiar areas, and advertise those areas that will become more important as students continue. This highlights both the utility of each method in progressing with problems of increasing complexity while also allowing students to see how a simplified problem becomes 're-complexified'. Advanced topics include nonlinear partial differential equations, and relativistic and quantum mechanical variants of problems like the harmonic oscillator. Physics, mathematics and engineering students will find 300 problems treated in a sophisticated manner. The insig
This textbook offers a rigorous, calculus based presentation of the complexities of urban economics, which is suitable for students who are new to the subject. It focuses on structural details and exp
Advanced Calculus: Theory and Practice, Second Edition, expands on the material covered in elementary calculus and presents this material in a rigorous manner. The text improves students’ problem
Rakesh V. Vohra offers a unique approach to studying and understanding intermediate microeconomics by reversing the conventional order of treatment, starting with topics that are mathematically simpler and progressing to the more complex. The book begins with monopoly, which requires single variable rather than multivariable calculus and allows students to focus clearly on the fundamental trade-off at the heart of economics: margin versus volume. Imperfect competition and the contrast with monopoly follows, introducing the notion of Nash equilibrium. Perfect competition is addressed toward the end of the book, and framed as a model of non-strategic behavior by firms and agents. The last chapter is devoted to externalities, with an emphasis on how one might design competitive markets to price externalities and linking the difficulties to the problem of efficient provision of public goods. Real-life examples engage the reader while encouraging them to think critically about the interplay
The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required computing power to analyse them have rendered classical tools outdated and insufficient. Tools such as random matrix theory and the study of large sample covariance matrices can efficiently process these big data sets and help make sense of modern, deep learning algorithms. Presenting an introductory calculus course for random matrices, the book focusses on modern concepts in matrix theory, generalising the standard concept of probabilistic independence to non-commuting random variables. Concretely worked out examples and applications to financial engineering and portfolio construction make this unique book an essential tool for physicists, engineers, data analysts, and economists.
