8 minute read
Mathematical Analysis
Bestseller Lectures on the Geometry of
Manifolds (3rd Edition)
by Liviu I Nicolaescu (University of Notre Dame, USA) Review of the 2nd Edition: “... advanced graduate students will find the present book a fine text and reference. Virtually everything is created from scratch and presented in a thoughtful manner ... the chapter on cohomology is really a tourde-force, involving geometry, topology and analysis in a fashion that every graduate student should see ... All-in-all, this is an excellent book for the right audience ... this book has everything for a full year-long course introducing students to the modern workings of global analysis.”
Zentralblatt MATH
The book starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. Readership: Graduate students and researchers in global analysis, differential geometry.
700pp Oct 2020 978-981-121-595-7(pbk) US$98 £85 978-981-121-481-3 US$198 £175
Algebraic Surfaces in Positive Characteristics
Purely Inseparable Phenomena in Curves and Surfaces
by Masayoshi Miyanishi (Osaka University, Japan) & Hiroyuki Ito (Tokyo University of Science, Japan) This is the first book which explains the phenomena arising from purely inseparable coverings and Artin – Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces. Readership: Graduate students and researchers in the fields of Algebraic Geometry, Fields and Rings, and Commutative Algebra.
456pp 978-981-121-520-9 Aug 2020 US$138 £120
MATHEMATICAL ANALYSIS
Essential Textbook Introduction to Analysis with Complex Numbers
by Irena Swanson (Purdue University, USA) This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series. The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer’s head. The book contains many examples and exercises to solidify the understanding. Readership: Introduction to proofs and analysis on real and complex functions for undergraduates.
Special Techniques for Solving Integrals
Examples and Problems
by Khristo N Boyadzhiev (Ohio Northern University, USA) This volume contains techniques of integration which are not found in standard calculus and advanced calculus books. It can be considered as a map to explore many classical approaches to evaluate integrals. It is intended for students and professionals who need to solve integrals or like to solve integrals and yearn to learn more about the various methods they could apply. The volume contains numerous solved examples and problems for the reader. Readership: Graduate and undergraduate students, professors and researchers in mathematics related to calculus, advanced calculus, mathematical analysis, real analysis, and mathematical physics; physics, and engineering.
390pp Mar 2022 978-981-123-625-9(pbk) US$58 £50 978-981-123-575-7 US$98 £85
(2nd Edition)
by Min Ru (University of Houston, USA) This book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas: one in complex analysis and one in number theory, it has been discovered that a number of striking similarities exist between these two subjects. A growing understanding of these connections has led to significant advances in both fields. Outstanding conjectures from decades ago are being solved.
Key Features
• Uniquely combined Nevanlinna theory and Diophantine approximation together in the book. Each chapter was divided into Part A and Part B. The Part A deals with Nevanlinna theory and Part B covers Diophantine approximation. At the end of each chapter, a table is provided to indicate the clear correspondence of the theorems Readership:Researchers and graduate students in the area of complex analysis (including several complex variables and complex geometry), number theory, algebraic/differential geometry.
444pp 978-981-123-350-0 Apr 2021 US$148 £130
Mathematical Analysis
A Concise Introduction
by Jiongmin Yong (University of Central Florida, USA) Mathematical analysis serves as a common foundation for many research areas of pure and applied mathematics. It is also an important and powerful tool used in many other fields of science, including physics, chemistry, biology, engineering, finance, and economics. In this book, some basic theories of analysis are presented, including metric spaces and their properties, limit of sequences, continuous function, differentiation, Riemann integral, uniform convergence, and series. After going through a sequence of courses on basic calculus and linear algebra, it is desirable for one to spend a reasonable length of time (ideally, say, one semester) to build an advanced base of analysis sufficient for getting into various research fields. This book is written to meet such a demand. Readership:Upper-level undergraduate students and first-year graduate students of mathematics, applied mathematics, and other mathematical related majors, such as statistics and industrial engineering.
276pp 978-981-122-163-7
Krzyz • Conjecture: Theory and Methods
A Research Diary of a Mathematician
by Ronen Peretz (Ben Gurion University of the Negev, Israel) This book is about one of the beautiful topics in mathematics. It describes an on-going research on bounded analytic functions which are defined on the unit disc. This is a very active topic that belongs to the theory of complex analysis in a single complex variable. The book includes much more than just a review on the The Krzyż Conjecture. It includes topics on inner functions within the context of problems that are different from the The Krzyż Conjecture as well as other topics on general bounded analytic functions. Progress in mathematical research is frequently fuelled by efforts to solve open problems. The book also includes a few important open problems and some partial solutions of these. Readership: Complex Analysis, Geometric Function Theory, Extremal problems, for graduate students and experts in those areas.
620pp 978-981-122-637-3 Apr 2021 US$168 £150
Lectures on Functional Analysis and Applications (2nd Edition)
by V S Pugachev & I N Sinitsyn (Russian Academy of Sciences, Russia) This volume is not only intended for mathematicians who deal with applications of functional analysis, but also for those having only a moderate background in mathematics in their areas of work. The materials covered, which includes practically all the information on functional analysis that may be necessary for those working in various areas of mathematics applications, as well as the simplicity of presentation, differentiates this book from others. The method and style of presentation of materials make it digestible and easily understood by readers. This second edition includes new and updated 300 examples and more than 500 problems to help readers understand and master the theories presented. In addition, necessary improvements for bringing the contents more up to date with current fundamental and applied developments in Chapters 1 – 10 were made. Readership: Undergraduate and graduate students as well as researchers in applied mathematics, and engineers.
800pp Jul 2021 978-981-3203-17-4 US$178 £148 978-981-3203-18-1(pbk) US$88 £73
Bestseller The Fractional Laplacian
by Wenxiong Chen (Yeshiva University, USA), Yan Li (Yeshiva University, USA) & Pei Ma (Nanjing Forestry University, China) This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared recently in research literature, which researchers would find helpful. It focuses on introducing direct methods on the nonlocal problems without going through extensions, such as the direct methods of moving planes, direct method of moving spheres, direct blowing up and rescaling arguments, and so on. Readership: Graduate students and researchers interested in analysis and differential equations.
344pp Jul 2020 978-981-3223-99-8 US$128 £113
Essential Textbook Casual Calculus
(In 3 Volumes) Vol. I: A Friendly Student Companion Vol. II: A Friendly Student Companion Vol. III: Multivariable
by Kenneth H Luther (Valparaiso University, USA) Yes, this is another Calculus book. However, I think it fits in a niche between the two predominant types of such texts. It could be used as a textbook, albeit a streamlined one — it contains exposition on each topic, with an introduction, rationale, train of thought, and solved examples with accompanying suggested exercises. Exercises are structured in three sets to force multiple encounters with each topic. The text is intended to be fully consumed; it is designed so that students become engaged with every topic and every exercise presented. The book is written in a very conversational tone. Readership: Undergraduate students currently taking or refreshing themselves on Calculus.
1764pp Dec 2021 978-981-124-264-9(Set)(pbk) US$188 £165 978-981-124-263-2(Set) US$448 £395 Vol. 1 692pp 978-981-122-392-1 US$188 £165 978-981-122-488-1(pbk) US$78 £70 Vol. 2 446pp 978-981-124-197-0 US$148 £130 978-981-124-198-7(pbk) US$58 £50 Vol. 3 626pp 978-981-122-395-2 US$188 £165 978-981-122-489-8(pbk) US$78 £70
Bounded Symmetric Domains in Banach Spaces
by Cho-Ho Chu (Queen Mary, University of London, UK) This timely book exposes succinctly recent advances in the geometric and analytic theory of bounded symmetric domains. A unique feature is the unified treatment of both finite and infinite dimensional symmetric domains, using Jordan theory in tandem with Lie theory. The highlights include a generalized Riemann mapping theorem, which realizes a bounded symmetric domain as the open unit ball of a complex Banach space with a Jordan structure. Far-reaching applications of this realization in complex geometry and function theory are discussed. Readership: Graduate students and researchers in diverse mathematical fields including complex geometry, function theory, functional analysis and operator theory.
408pp 978-981-121-410-3 Sep 2020 US$138 £120
Correct Antidifferentiation
The Change of Variable Well Done
by Antonio Martínez-Abejón (University of Oviedo, Spain) This book is monographically focused on elementary antidifferentiation and reasonably self-contained, yet it is written in a “hand-book” style: it has plenty of examples and graphics in an increasing level of difficulty; the most standard changes of variable are studied and the hardest theoretic parts are included in a final Appendix. Each practical chapter has a list of exercises and solutions. There is plenty of graphics which help the student to understand better the process of antidifferentiation while most of the books do not.
Readership: Instructors and university students of Mathematics of first and second year, University students of technical branches that include Calculus and/or Mathematical Analysis in their curriculum.
