Mathematics Titles for Colleges and Undergrads 2020 – 2021 World Scientific Connecting Great Minds Connecting Great Minds Essential Textbooks in Physics How to Derive a Formula Volume 1: Basic Analytical Skills and Methods for Physical Scientists By Alexei A Kornyshev & Dominic O'Lee (Imperial College London, UK) Apr 2020 ▪ 704pp ▪ ISBN: 978-1-78634-644-5 (pbk) US$88 £75 | ISBN: 978-1-78634-634-6 US$158 £140 "For many science undergraduates, the teaching of mathematics is divorced from the real business of learning about science. For them, mathematics is just a mental hurdle that has to be overcome in exams. In contrast, this book shows the student that mathematics is, and has always been, the language of science because it is only through mathematical analysis that a model for phenomenon or process can be constructed and tested against experiment. By embedding the leaning of mathematics in science, this book shows the student how understanding in science is developed and what it entails” Adrian Sutton FRS Emeritus Professor of Physics Imperial College London A First Look at Stochastic Processes By Jeffrey S Rosenthal (University of Toronto, Canada) Oct 2019 ▪ 212pp ▪ ISBN: 978-981-120-897-3 (pbk) US$38 £35 | ISBN: 978-981-120-790-7 US$78 £70 This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory. Linear Algebra Core Topics for the First Course By Dragu Atanasiu (University of Borås, Sweden), Piotr Mikusiński (University of Central Florida, USA) May 2020 ▪ 464pp ▪ ISBN: 978-981-121-596-4 (pbk) US$68 £60 | ISBN: 978-981-121-502-5 US$128 £115 The book is an introduction to linear algebra intended as a textbook for the first course in linear algebra. In the first six chapters we present the core topics: matrices, the vector space n, orthogonality in n determinants, eigenvalues and eigenvectors, and linear transformations. The book gives students an opportunity to better understand linear ℝ ℝ algebra in the next three chapters: Jordan forms by examples, singular value decomposition, and quadratic forms and positive definite matrices. Introduction to Analysis with Complex Numbers By Irena Swanson (Purdue University, USA) Mar 2021 ▪ 390pp ▪ ISBN: 978-981-122-769-1 (pbk) US$68 £60 | ISBN: 978-981-122-585-7 US$118 £105 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, 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. An Introduction to Numerical Computation (2nd Edition) By Wen Shen (Penn State University, USA) Sep 2019 ▪ 340pp ▪ ISBN: 978-981-120-518-7 (pbk) US$48 £40 | ISBN: 978-981-120-441-8 US$98 £85 Reviews of the First Edition: "For a compact volume, the homework is ample and well-conceived. Homework problems concluding each chapter include applications, programming tasks, and a list of items to turn in. A complete set of solutions is available for instructor upon request... This is an excellent resource as a semester-long text, textbook adjunct, introduction for self- instruction, or a handy reference for practical implementations." MAA Reviews 1 Essential Textbooks in Physics Series on University Mathematics - Vol 10 How to Derive a Formula Linear Algebra and its Applications Volume 1: Basic Analytical Skills and Methods for Physical Scientists By Tzuong-Tsieng Moh (Purdue University, USA) By Alexei A Kornyshev & Dominic O'Lee (Imperial College London, UK) Nov 2020 ▪ 316pp ▪ ISBN: 978-981-3235-42-7 US$98 £86 Apr 2020 ▪ 704pp ▪ ISBN: 978-1-78634-644-5 (pbk) US$88 £75 | ISBN: 978-1-78634-634-6 US$158 £140 From Tzuong-Tsieng Moh, a long-time expert in algebra, comes a new book for students to better understand linear "For many science undergraduates, the teaching of mathematics is divorced from the real business of learning about algebra. Writing from an experienced standpoint, Moh touches on the many facets surrounding linear algebra, science. For them, mathematics is just a mental hurdle that has to be overcome in exams. In contrast, this book including but not limited to, echelon forms, matrix algebra, linear transformations, determinants, dual space, inner shows the student that mathematics is, and has always been, the language of science because it is only through products, the Gram – Schmidt Theorem, Hilbert space, and more. It is ideal for both newcomers and seasoned mathematical analysis that a model for phenomenon or process can be constructed and tested against experiment. readers who want to attain a deeper understanding on both the basics and advanced topics of linear algebra and its By embedding the leaning of mathematics in science, this book shows the student how understanding in science is vast applications. The wide range of topics combined with the depth of each discussion make it essential to be on the developed and what it entails” shelf of every mathematical beginner and enthusiast. Adrian Sutton FRS Emeritus Professor of Physics Understanding Game Theory (2nd Edition) Imperial College London Introduction to the Analysis of Many Agent Systems with Competition and Cooperation By Vassili N Kolokoltsov (The University of Warwick, UK & St. Petersburg State University, Russia), Oleg A Malafeyev (St. Petersburg State University, Russia) A First Look at Stochastic Processes By Jeffrey S Rosenthal (University of Toronto, Canada) Sep 2020 ▪ 412pp ▪ ISBN: 978-981-121-485-1 US$128 £115 Oct 2019 ▪ 212pp ▪ ISBN: 978-981-120-897-3 (pbk) US$38 £35 | ISBN: 978-981-120-790-7 US$78 £70 This book on game theory, its applications and mathematical methods, is written with this objective in mind. The book This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using gives a concise but wide-ranging introduction to games including older (pre-game theory) party games and more concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through recent topics like elections and evolutionary games and is generously spiced with excursions into philosophy, history, simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence literature and politics. A distinguished feature is the clear separation of the text into two parts: elementary and criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter advanced, which makes the book ideal for study at various levels. provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory. Basic Insights in Vector Calculus With a Supplement on Mathematical Understanding By Terrance J Quinn (Middle Tennessee State University, USA), Zine Boudhraa & Sanjay Rai (Montgomery Linear Algebra Core Topics for the First Course College, Maryland, USA) By Dragu Atanasiu (University of Borås, Sweden), Piotr Mikusiński (University of Central Florida, USA) Aug 2020 ▪ 252pp ▪ ISBN: 978-981-122-256-6 US$98 £85 May 2020 ▪ 464pp ▪ ISBN: 978-981-121-596-4 (pbk) US$68 £60 | ISBN: 978-981-121-502-5 US$128 £115 This book provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem The book is an introduction to linear algebra intended as a textbook for the first course in linear algebra. In the first and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a six chapters we present the core topics: matrices, the vector space n, orthogonality in n determinants, eigenvalues natural way. As in classical physics, we begin with descriptions of flows. and eigenvectors, and linear transformations. The book gives students an opportunity to better understand linear ℝ ℝ Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi- algebra in the next three chapters: Jordan forms by examples, singular value decomposition, and quadratic forms variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi- and positive definite matrices. variable calculus needed for the three main theorems of vector calculus. Introduction to Analysis with Complex Numbers Basic Probability By Irena Swanson (Purdue University, USA) What Every Math Student Should Know By Henk Tijms (Vrije University, The Netherlands) Mar 2021 ▪ 390pp ▪ ISBN: 978-981-122-769-1 (pbk) | ISBN: 978-981-122-585-7 US$68 £60 US$118 £105 Jun 2019 ▪ 132pp ▪ ISBN: 978-981-120-376-3 (pbk) US$28 £25 | ISBN: 978-981-120-235-3 US$48 £40 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, also handles complex-valued functions, sequences, and series. "What makes this book unique among books of similar size and scope is that when the author decided to include something in the book, he has treated it in a way similar to the common practice in textbooks, with very detailed and The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and reader-friendly explanations, fully worked-out examples, and even numerous exercises ..