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Check out these books below by Cambridge University Press.
Abstract Algebra - A Comprehensive Introduction
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Abstract Algebra |
Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence...
Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Date Published: April 2021
Algebra - Notes from the Underground
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Algebra |
Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naïve set theory.
- Treats all standard topics for a first course in detail, moving from rings to modules to groups to fields, which allows for a more gradual entry into the subject
- Emphasizes a modern perspective, with hints toward category theory, exposing students to advanced topics and preparing them for graduate courses and applications of algebra in other subjects
- Includes 400+ exercises, with 150 worked-out problems from the main text, and plenty of examples to help students better understand the material
- Uses a conversational style and strong narrative flow that makes the material easier for students to follow and appreciate as a whole
Publication planned for: June 2021
Introduction to Linear Algebra
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| Introduction to Linear Algebra |
A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (including practice problems, exams, and development of textbook examples), plus codes in MATLAB®, Julia, and Python.
- This fifth edition contains numerous minor improvements and major additions
- Provides a new chapter on singular values and singular vectors, as well as a revised chapter on computing in linear algebra
- A dedicated and active website offers solutions to exercises, new exercises from several sources, and codes in MATLAB®, Julia, and Python
Date Published: August 2016
Singularities, Bifurcations and Catastrophes
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| Singularities, Bifurcations and Catastrophes |
Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence...
Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided.
- Builds up the mathematical background for a new approach to the foundations of bifurcation theory
- The first two parts are of independent interest and can be the basis for an advanced undergraduate or graduate course
- Contains many colour figures and exercises, with some
solutions included and a manual for selected others available for
teachers
Publication planned for: June 2021
Computer Age Statistical Inference, Student Edition - Algorithms, Evidence, and Data Science
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| Computer Age Statistical Inference, Student Edition Algorithms, Evidence, and Data Science |
The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and influence. 'Data science' and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce...
The distinctly modern approach integrates methodology and algorithms with statistical inference. Each chapter ends with class-tested exercises, and the book concludes with speculation on the future direction of statistics and data science.
- Now in paperback and fortified with exercises, this book provides a course in modern statistical thinking written by two world-leading researchers
- 130 class-tested exercises covering theory, methods, and computation help students make the link to scientific knowledge (and uncertainty)
- Clarifies both traditional methods and current, popular algorithms (e.g. neural nets, random forests), giving students a broad and modern appreciation of the topic
Publication planned for: June 2021
Mathematical Foundations of Infinite-Dimensional Statistical Models
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| Mathematical Foundations of Infinite-Dimensiona Statistical Models |
In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces...
In the final chapter, the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions.
- Describes the theory of statistical inference in statistical models with an infinite-dimensional parameter space
- Develops a mathematically coherent and objective approach to statistical inference
- Much of the material arises from courses taught by the authors at the beginning and advanced graduate level; each section ends with exercises
Date Published: February 2016
Sit in the studyroom enjoy a hot cup of ☕️coffee and a good 📚book
Source: Cambridge University Press
