Check out these books below by Cambridge University Press.
Abstract Algebra - A Comprehensive Introduction
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
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Algebra - Notes from the Underground
From rings to modules to groups to fields, this undergraduate
introduction to abstract algebra follows an unconventional path. The
text emphasizes a modern perspective on the subject, with gentle
mentions of the unifying categorical principles underlying the various
constructions and the role of universal properties...
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
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Introduction to Linear Algebra
Linear algebra is something all mathematics undergraduates and many
other students, in subjects ranging from engineering to economics, have
to learn. The fifth edition of this hugely successful textbook retains
all the qualities of earlier editions, while at the same time seeing
numerous minor improvements and major additions...
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
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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
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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.
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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
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Mathematical Foundations of Infinite-Dimensional 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
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Sit in the studyroom enjoy a hot cup of ☕️coffee and a good 📚book
Source: Cambridge University Press