Due 2018-07-15
1st ed. 2018, XXI, 298 p. 77 illus., 15 illus. in color.
Softcover
ISBN 978-3-319-90319-4
Series : Springer Undergraduate Mathematics Series
Provides general and maths-specific problem-solving strategies
Contains many motivating examples and exercises
Engages the reader to explore mathematics and solve fun problems
Introduces fundamental ideas useful in all areas of mathematics
Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps
you had an idea but got stuck halfway through? This book guides you in developing your
creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only
learn strategies for solving problems and logical reasoning, but they will also learn about the
importance of proofs and various proof techniques. Other topics covered include recursion,
mathematical induction, graphs, counting, elementary number theory, and the pigeonhole,
extremal and invariance principles. Designed to help students make the transition from
secondary school to university level, this book provides readers with a refreshing look at
mathematics and deep insights into universal principles that are valuable far beyond the scope
of this book. Aimed especially at undergraduate and secondary school students as well as
teachers, this book will appeal to anyone interested in mathematics. Only basic secondary
school mathematics is required, including an understanding of numbers and elementary
geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is
suitable for self-study and use alongside lecture courses.
Due 2018-07-16
1st ed. 2018, VIII, 382 p.
16 illus., 12 illus. in color.
Hardcover
ISBN 978-3-319-90914-1
Teaches number theory through problem solving, making it perfect for selfstudy
and Olympiad preparation
Contains over 260 challenging problems and 110 homework exercises in
number theory with hints and detailed solutions
Encourages the creative applications of methods, rather than memorization
Through its engaging and unusual problems, this book demonstrates methods of reasoning
necessary for learning number theory. Every technique is followed by problems (as well as
detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of
abstract problems in a systematic, creative manner. New solutions often require the ingenious
use of earlier mathematical concepts - not the memorization of formulas and facts. Questions
also often permit experimental numeric validation or visual interpretation to encourage the
combined use of deductive and intuitive thinking. The first chapter starts with simple topics like
even and odd numbers, divisibility, and prime numbers and helps the reader to solve quite
complex, Olympiad-type problems right away. It also covers properties of the perfect, amicable,
and figurate numbers and introduces congruence. The next chapter begins with the Euclidean
algorithm, explores the representations of integer numbers in different bases, and examines
continued fractions, quadratic irrationalities, and the Lagrange Theorem. The last section of
Chapter Two is an exploration of different methods of proofs. The third chapter is dedicated to
solving Diophantine linear and nonlinear equations and includes different methods of solving
Fermat’s (Pell’s) equations. It also covers Fermat’s factorization techniques and methods of
solving challenging problems involving exponent and factorials. Chapter Four reviews the
Pythagorean triple and quadruple and emphasizes their connection with geometry,
trigonometry, algebraic geometry, and stereographic projection. A special case of Waring’s
problem as a representation of a number by the sum of the squares or cubes of other
numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and
interesting word problems related to the properties of numbers.
Due 2018-08-24
2nd ed. 2018, XII, 436 p. 110 illus.
Hardcover
ISBN 978-3-319-91754-2
Series : Graduate Texts in Mathematics
Easy for instructors to adapt the topical coverage to suit their course
Develops an intimate acquaintance with the geometric meaning of curvature
Gives students strong skills via numerous exercises and problem sets
Adapted from Riemannian Manifolds, the new edition has been aptly
expanded to cover one or two semesters
This textbook is designed for a one or two semester graduate course on Riemannian geometry
for students who are familiar with topological and differentiable manifolds. The second edition
has been adapted, expanded, and aptly retitled from Lee’s earlier book, Riemannian Manifolds:
An Introduction to Curvature. Numerous exercises and problem sets provide the student with
opportunities to practice and develop skills; appendices contain a brief review of essential
background material. While demonstrating the uses of most of the main technical tools needed
for a careful study of Riemannian manifolds, this text focuses on ensuring that the student
develops an intimate acquaintance with the geometric meaning of curvature. The reasonably
broad coverage begins with a treatment of indispensable tools for working with Riemannian
metrics such as connections and geodesics. Several topics have been added, including an
expanded treatment of pseudo-Riemannian metrics, a more detailed treatment of
homogeneous spaces and invariant metrics, a completely revamped treatment of comparison
theory based on Riccati equations, and a handful of new local-to-global theorems, to name just
a few highlights. Reviews of the first edition: Arguments and proofs are written down precisely
and clearly. The expertise of the author is reflected in many valuable comments and remarks
on the recent developments of the subjects. Serious readers would have the challenges of
solving the exercises and problems. The book is probably one of the most easily accessible
introductions to Riemannian geometry. (M.C. Leung,MathReview) The book’s aim is to develop
tools and intuition for studying the central unifying theme in Riemannian geometry, which is
the notion of curvature and its relation with topology.
Due 2018-07-17
XIV, 614 p. 47 illus.
Hardcover
ISBN 978-3-319-90901-1
Important complement to the existing literature on continuum theory
Provides the requisite background so often missing in journal papers
New edition adds a thorough study of induced maps on n-fold hyperspaces
and n-fold hyperspace suspensions
Many topics included in the book are not presented in any other textbook on
continuum theory
This book is a significant companion text to the existing literature on continuum theory. It
opens with background information of continuum theory, so often missing from the preceding
publications, and then explores the following topics: inverse limits, the Jones set function T,
homogenous continua, and n-fold hyperspaces. In this new edition of the book, the author
builds on the aforementioned topics, including the unprecedented presentation of n-fold
hyperspace suspensions and induced maps on n-fold hyperspaces. The first edition of the book
has had a remarkable impact on the continuum theory community. After twelve years, this
updated version will also prove to be an excellent resource within the field of topology.
Due 2018-07-27
2nd ed. 2018, XVI, 191 p.
Softcover
Series : Universitext
Contains over 300 exercises
Assumes only basic abstract algebra
Covers topics leading up to class field theory
Requiring no more than a basic knowledge of abstract algebra, this textbook presents the
basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids
local methods, for example, and presents proofs in a way that highlights key arguments. There
are several hundred exercises, providing a wealth of both computational and theoretical
practice, as well as appendices summarizing the necessary background in algebra. Now in a
newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will
continue to provide lecturers and their students with an invaluable resource and a compelling
gateway to a beautiful subject. From the reviews: “A thoroughly delightful introduction to
algebraic number theory” ? Ezra Brown in the Mathematical Reviews “An excellent basis for an
introductory graduate course in algebraic number theory” ? Harold Edwards in the Bulletin of
the American Mathematical Society