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Algebra & Related Topics
Essential Textbook Lectures on Algebraic Topology
by Haynes Miller (Massachusetts Institute of Technology, USA) Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory. Readership: Ideal for a beginning graduate course, aimed at students familiar with general topology and basic modern algebra; also good for researchers who need to use the methods of algebraic topology, in mathematics at large and in theoretical physics.
300pp Oct 2021 978-981-123-285-5(pbk) US$58 £50 978-981-123-124-7 US$138 £120
Selected Chapters of Number Theory: Special Numbers
Mersenne Numbers and Fermat Numbers
by Elena Deza (Moscow State Pedagogical University, Russia) This book contains a complete detailed description of two classes of special numbers closely related to classical problems of the Theory of Primes. There is also extensive discussions of applied issues related to Cryptography. Mersenne and Fermat numbers have many other interesting properties. Long and rich history, many arithmetic connections (with perfect numbers, with construction of regular polygons etc.), numerous modern applications, long list of open problems allow us to provide a broad perspective of the Theory of these two classes of special numbers, that can be useful and interesting for both professionals and the general audience. Readership:Advanced undergraduate, graduate students, researchers and the general public interested in Arithmetic, Number Theory, General Algebra, Cryptography and related fields.
200pp 978-981-123-031-8 Sep 2021 US$108 £95
Series on Knots and Everything - Volume 72
Laws of Form
A Fiftieth Anniversary
by Louis H Kauffman (University of Illinois Chicago, USA), Fred Cummins (University College Dublin, Ireland), Randolph Dible (The New School for Social Research, USA),
Leon Conrad, Graham Ellsbury, Andrew
Crompton (University of Liverpool, UK) & Florian Grote (CODE University of Applied Sciences, Germany) Laws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8–10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019. Readership: Academic and scientific readers: undergraduate and graduate students and researchers.
700pp Feb 2022 978-981-124-742-2 US$188 £165
Computational Algebra
Course and Exercises with Solutions
by Ihsen Yengui (Université de Sfax, Tunisia) This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry. This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Readership: Postgraduates, advanced undergraduates, academics and researchers of mathematics.
284pp May 2021 978-981-123-930-4(pbk) US$58 £50 978-981-123-824-6 US$98 £85
Monographs in Number Theory - Vol 9
Modular and Automorphic Forms & Beyond
by Hossein Movasati (IMPA, Brazil) The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi – Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called “Gauss – Manin connection in disguise”. Readership: Graduate students and researchers.
280pp 978-981-123-867-3 Nov 2021 US$108 £95
Problems in Linear Algebra and Matrix Theory
by Fuzhen Zhang (Nova Southeastern University, USA) This is the revised and expanded edition of the problem book Linear Algebra: Challenging Problems for Students, now entitled Problems in Linear Algebra and Matrix Theory. This new edition contains about fifty-five examples and many new problems, based on the author’s lecture notes of Advanced Linear Algebra classes at Nova Southeastern University (NSU-Florida) and short lectures Matrix Gems at Shanghai University and Beijing Normal University.
Key Features
• This is a collection of gem problems in linear algebra and matrix theory for students • Each chapter starts with important facts and interesting results as examples to show basic skills and techniques on the topic, followed by carefully selected problems Readership:College/university students and instructors in mathematics, physics, statistics, computer science, etc. Upper division/beginning graduate level.
by Hongyu Guo (University of HoustonVictoria, USA) There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive. The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily. Readership:Researchers, professionals, academics, graduate students and undergraduate students in physics, AI, machine learning, and relativity and gravitation.
248pp 978-981-124-101-7 Jun 2021 US$58 £50
Essential Textbook A Problem Based Journey from Elementary Number Theory to an Introduction to Matrix Theory
The President Problems
by Abraham Berman (Technion-Israel Inst of Tech, Israel) The book is based on lecture notes of a course “from elementary number theory to an introduction to matrix theory” given at the Technion to gifted high school students. It is problem based, and covers topics in undergraduate mathematics that can be introduced in high school through solving challenging problems. These topics include Number theory, Set Theory, Group Theory, Matrix Theory, and applications to cryptography and search engines.
Key Features
• Challenging problems, interesting mathematics, the book will appeal to high school and university students who love mathematics and their teachers
Readership: High school students who love mathematics and mathematics teachers. Also good for professors of mathematics and maths education, students in the mathematical sciences and pre-service math teachers.
130pp 978-981-123-487-3 Sep 2021 US$38 £35
Series on Number Theory and Its Applications
Elementary Modular Iwasawa Theory
by Haruzo Hida (University of California, Los Angeles, USA) This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author’s 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry.
Key Features
• The results found in the book are at the cutting edge of the present research • The first few chapters provide the fundamentals while the latter chapters cater to first or second-year graduate students • Contains numerous open research problems for young researchers
Readership: Advanced undergraduate and graduate students, researchers and practitioners in the fields of algebraic/analytic number theory and arithmetic geometry.
Copositive and Completely Positive Matrices
by Naomi Shaked-Monderer (The Max Stern Yezreel Valley College, Israel) & Abraham Berman (Technion — Israel Institute of Technology, Israel) This book is an updated and extended version of Completely Positive Matrices (Abraham Berman and Naomi Shaked-Monderer, World Scientific 2003). It contains new sections on the cone of copositive matrices, which is the dual of the cone of completely positive matrices, and new results on both copositive matrices and completely positive matrices. The book is an up to date comprehensive resource for researchers in Matrix Theory and Optimization. It can also serve as a textbook for an advanced undergraduate or graduate course. Readership: Advanced undergraduate, graduate and researchers in matrix theory and optimization.
564pp 978-981-120-434-0 Mar 2021 US$158 £140
P-adic Analytic Functions
by Alain Escassut (Université Blaise Pascal, France) Various properties of p-adic exponentialpolynomials are examined, such as the Hermite Lindemann theorem in a p-adic field, with a new proof. The order and type of growth for analytic functions are studied, in the whole field and inside an open disk. P-adic meromorphic functions are studied, not only on the whole field but also in an open disk and on the complemental of a closed disk, using Motzkin meromorphic products. Finally, the p-adic Nevanlinna theory is widely explained, with various applications. Small functions are introduced with results of uniqueness for meromorphic functions. The question of whether the ring of analytic functions — in the whole field or inside an open disk — is a Bezout ring is also examined. Readership: The target audience consists of researchers and postgraduate students in ultrametric analysis and number theory. Also appropriate for researchers in Levi-Civita fields in p-adic physics.
348pp 978-981-122-621-2 Apr 2021 US$128 £115
Submit your paper to these journals. Recommend them to your librarian!
https://www.worldscientific.com/ijnt https://www.worldscientific.com/ijac
Details on page 37
A Textbook for Beginners
(2nd Edition)
by Marco Grandis (Universitàdi Genova, Italy)
Reviews of the First Edition:
“It’s well written and is peppered with sections titled, ‘exercises and complements’. Clearly the reader needs to take these very seriously. I personally find exercises in category theory and homological algebra very satisfying because of their architecture and their minimalist quality: it’s a lot of fun for it all to come down to dancing all over a commutative diagram or two and to draw a lot of arrows. I like the subject a great deal, and I think this is a good book to learn it from.” MAA Reviews Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.
This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads.
Readership: Undergraduate, graduate and PHD students in Mathematics, Computer Science and Physics.
392pp 978-981-123-608-2 Mar 2021 US$118 £105
Boolean Structures
Combinatorics, Codification, Representation
by Gennaro Auletta (University of Cassino and Southern Lazio, Italy & Pontifical Gregorian University, Italy)
Boolean Structures: Combinatorics, Codification, Representation offers the first analytical and architectural approach to Boolean algebras based combinatorial calculus and codification with applications in IT, quantum information and classification of data.
Key Features
• Combinatorial approach, new way to consider codification applied to Boolean algebras, connection with quantum and classical information
Readership: Graduates and researchers in mathematical logic and physicists working on quantum information. May also be of interest to IT researchers and philosophers working on logic and information theory.
316pp 978-1-80061-008-8 Apr 2021 US$118 £105
A Modern Introduction to Classical Number Theory
by Tianxin Cai (Zhejiang University, China) Natural numbers are the oldest human invention. This book describes their nature, laws, history and current status.
One feature of the book is the supplementary material after each section, there by broadening the reader’s knowledge and imagination. These contents either discuss the rudiments of some aspects or introduce new problems or conjectures and their extensions, such as perfect number problem, Egyptian fraction problem, Goldbach’s conjecture, the twin prime conjecture, the 3x + 1 problem, Hilbert Waring problem, Euler’s conjecture, Fermat’s Last Theorem, Laudau’s problem and etc. Readership: Students and professionals who are interested in number theory, also good for general public to read up.
Series on Knots and Everything - Vol 68
Volume 2: Algorithmic Measurement Theory, Fibonacci and Golden Arithmetic’s and Ternary Mirror-Symmetrical Arithmetic
by Alexey Stakhov (International Club of the Golden Section, Canada & Academy of Trinitarism, Russia)
332pp 978-981-121-346-5 Sep 2020 US$98 £85
Series on Knots and Everything - Vol 69
Volume 3: The “Golden” Paradigm of Modern Science: Prerequisite for the “Golden” Revolution in Mathematics, Computer Science, and Theoretical Natural Sciences
by Alexey Stakhov (International Club of the Golden Section, Canada & Academy of Trinitarism, Russia)
244pp 978-981-121-349-6 Sep 2020 US$88 £75
“Mathematics of Harmony” rises in its origin to the “harmonic ideas” of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the “Universe Harmony, “ the main conception of ancient Greek science, and implementation of this conception to modern science and education.
Key Feature
• Can serve as the explanation of the fact why in the number theory attention was not given to numeral systems
Readership: High school, college and university students, teachers, professionals, scientists and investors interested in history of mathematics, Fibonacci numbers, golden section and their generalization.
Elements of Linear and Multilinear Algebra
by John M Erdman (Portland State University, USA)
This set of notes is an activity-oriented introduction to linear and multilinear algebra. The great majority of the most elementary results in these subjects are straightforward and can be verified by the thoughtful student. Indeed, that is the main point of these notes — to convince the beginner that the subject is accessible. In the material that follows there are numerous indicators that suggest activity on the part of the reader: words such as “proposition”, “example”, “theorem”, “exercise”, and “corollary”, if not followed by a proof (and proofs here are very rare) or a reference to a proof, are invitations to verify the assertions made.
Readership: Upper division undergraduates, beginning graduate students, instructors of linear and multilinear algebra.
