New books by subject
Mathematics  Concordia University Libraries Recent Acquisitions
Titles in the call number range QA 1  QA 73, QA 90  QA 699 (Mathematics) that were added to the Concordia University Libraries collection in the last 60 days.

Nonlinear systems stability analysis : Lyapunovbased approach / Seyed Kamaleddin Yadavar NikraveshQA 402.35 N555 2013The equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful regarding qualitative properties of nonlinear systems and their solutionssystem stability being the most crucial property. Without stability, a system will not have value.
Nonlinear Systems Stability Analysis: LyapunovBased Approachintroduces advanced tools for stability analysis of nonlinear systems. It presents the most recent progress in stability analysis and provides a complete review of the dynamic systems stability analysis methods using Lyapunov approaches. The author discusses standard stability techniques, highlighting their shortcomings, and also describes recent developments in stability analysis that can improve applicability of the standard methods. The text covers mostly new topics such as stability of homogonous nonlinear systems and higher order Lyapunov functions derivatives for stability analysis. It also addresses special classes of nonlinear systems including timedelayed and fuzzy systems.
Presenting new methods, this book provides a nearly complete set of methods for constructing Lyapunov functions in both autonomous and nonautonomous systems, touching on new topics that open up novel research possibilities. Gathering a body of research into one volume, this text offers information to help engineers design stable systems using practiceoriented methods and can be used for graduate courses in a range of engineering disciplines. 
Polytope projects / Octavian Iordache, President, Polystochastic, Montreal, Quebec, CanadaQA 691 I66 2014
How do you know what works and what doesn't? This book contains case studies highlighting the power of polytope projects for complex problem solving. Any sort of combinational problem characterized by a large variety of possibly complex constructions and deconstructions based on simple building blocks can be studied in a similar way. Although the majority of case studies are related to chemistry, the method is general and equally applicable to other fields for engineering or science. 
Experimental design and process optimization / Maria Isabel Rodrigues, Antonio Francisco IemmaQA 279 R63 2015Experimental Design and Process Optimization delves deep into the design of experiments (DOE). The book includes Central Composite Rotational Design (CCRD), fractional factorial, and Plackett and Burman designs as a means to solve challenges in research and development as well as a tool for the improvement of the processes already implemented. Appropriate strategies for 2 to 32 factors are covered in detail in the book.
The book covers the essentials of statistical science to assist readers in understanding and applying the concepts presented. It also presents numerous examples of applications using this methodology. The authors are not only experts in the field but also have significant practical experience. This allows them to discuss the application of the theoretical aspects discussed through various realworld case studies. 
Dynamics of the chemostat : a bifurcation theory approach / Abdelhamid Ajbar, Khalid AlhumaiziQA 380 A33 2012A ubiquitous tool in mathematical biology and chemical engineering, the chemostat often produces instabilities that pose safety hazards and adversely affect the optimization of bioreactive systems. Singularity theory and bifurcation diagrams together offer a useful framework for addressing these issues. Based on the authors' extensive work in this field, Dynamics of the Chemostat: A Bifurcation Theory Approachexplores the use of bifurcation theory to analyze the static and dynamic behavior of the chemostat.
Introduction
The authors first survey the major work that has been carried out on the stability of continuous bioreactors. They next present the modeling approaches used for bioreactive systems, the different kinetic expressions for growth rates, and tools, such as multiplicity, bifurcation, and singularity theory, for analyzing nonlinear systems.Application
The text moves on to the static and dynamic behavior of the basic unstructured model of the chemostat for constant and variable yield coefficients as well as in the presence of wall attachment. It then covers the dynamics of interacting species, including pure and simple microbial competition, biodegradation of mixed substrates, dynamics of plasmidbearing and plasmidfree recombinant cultures, and dynamics of predatorprey interactions. The authors also examine dynamics of the chemostat with product formation for various growth models, provide examples of bifurcation theory for studying the operability and dynamics of continuous bioreactor models, and apply elementary concepts of bifurcation theory to analyze the dynamics of a periodically forced bioreactor.Using singularity theory and bifurcation techniques, this book presents a cohesive mathematical framework for analyzing and modeling the macro and microscopic interactions occurring in chemostats. The text includes models that describe the intracellular and operating elements of the bioreactive system. It also explains the mathematical theory behind the models.

The Newman lectures on mathematics / John Newman, Vincent BattagliaQA 11.2 N49 2018Prof. Newman is considered one of the great chemical engineers of his time. His reputation derives from his mastery of all phases of the subject matter, his clarity of thought, and his ability to reduce complex problems to their essential core elements. He is a member of the National Academy of Engineering, Washington, DC, USA, and has won numerous national awards including every award offered by the Electrochemical Society, USA. His motto, as known by his colleagues, is "do it right the first time." He has been teaching undergraduate and graduate core subject courses at the University of California, Berkeley (UC Berkeley), USA, since joining the faculty in 1966. His method is to write out, in long form, everything he expects to convey to his class on a subject on any given day. He has maintained and updated his lecture notes from notepad to computer throughout his career. This book is an exact reproduction of those notes.
This book shows a clean and concise way on how to use different analytical techniques to solve equations of multiple forms that one is likely to encounter in most engineering fields, especially chemical engineering. It provides the framework for formulating and solving problems in mass transport, fluid dynamics, reaction kinetics, and thermodynamics through ordinary and partial differential equations. It includes topics such as Laplace transforms, Legendre's equation, vector calculus, Fourier transforms, similarity transforms, coordinate transforms, conformal mapping, variational calculus, superposition integrals, and hyperbolic equations. The simplicity of the presentation instils confidence in the readers that they can solve any problem they come across either analytically or computationally.

Applied parameter estimation for chemical engineers / Peter Englezos, Nicolas KalogerakisQA 274.4 E54 2001
This book determines adjustable parameters in mathematical models that describe steady state or dynamic systems, presenting the most important optimization methods used for parameter estimation. It focuses on the GaussNewton method and its modifications for systems and processes represented by algebraic or differential equation models. 
Equations and inequalities : elementary problems and theorems in algebra and number theory / Jiří Herman, Radan Kučera, Jaromír Šimša ; translated by Karl DilcherQA 218 H4713 2000
A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises. 
Applying the classification of finite simple groups : a user's guide / Stephen D. SmithQA 177 S645 2018
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the ``quasithin'' part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a secondyear graduate course for students who have had firstyear graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources. 
Analysis in banach spaces. Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz WeisQA 322.2 H988 2017ebThis second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and LittlewoodPaley Theory. It presents a thorough study of the fundamental randomisation techniques and the operatortheoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, Kconvexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of Rboundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bisectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operatortheoretic approach to deterministic and stochastic evolution equations.

R for data science : import, tidy, transform, visualize, and model data / Hadley Wickham and Garrett GrolemundQA 276.45 R3 W53 2016Learn how to use R to turn raw data into insight, knowledge, and understanding. This book introduces you to R, RStudio, and the tidyverse, a collection of R packages designed to work together to make data science fast, fluent, and fun. Suitable for readers with no previous programming experience, R for Data Science is designed to get you doing data science as quickly as possible.
Authors Hadley Wickham and Garrett Grolemund guide you through the steps of importing, wrangling, exploring, and modeling your data and communicating the results. You'll get a complete, bigpicture understanding of the data science cycle, along with basic tools you need to manage the details. Each section of the book is paired with exercises to help you practice what you've learned along the way.
You'll learn how to:
Wrangle transform your datasets into a form convenient for analysis Program learn powerful R tools for solving data problems with greater clarity and ease Explore examine your data, generate hypotheses, and quickly test them Model provide a lowdimensional summary that captures true "signals" in your dataset Communicate learn R Markdown for integrating prose, code, and results 
An introduction to number theory with cryptography / James S. Kraft, Lawrence C. WashingtonQA 241 K73 2018Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory.
The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum.

An experimental introduction to number theory / Benjamin HutzQA 241 H88 2018
This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) openended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration. 
Euler's pioneering equation : the most beautiful theorem in mathematics / Robin WilsonQA 241 W55 2018
In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twentyfour theorems were listed and readers were invited to award each a "score for beauty". While there were many worthy competitors, the winner was"Euler's equation". In 2004 Physics World carried out a similar poll of "greatest equations", and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like aShakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, eix + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a majordevelopment in mathematics, and opened up the idea of negative numbers; pi an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of 1, the basis of complex numbers. Followinga chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula. 
Hilbert schemes of points and infinite dimensional lie algebras / Zhenbo QinQA 564 Q56 2018
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes $X^{{[n]}}$ of collections of $n$ points (zerodimensional subschemes) in a smooth algebraic surface $X$. Schemes $X^{{[n]}}$ turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others.
This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of $X^{{[n]}}$, including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of $X^{{[n]}}$ and the GromovWitten correspondence. The last part of the book presents results about quantum cohomology of $X^{{[n]}}$ and related questions.
The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics. 
Sugawara operators for classical Lie algebras / Alexander MolevQA 252.3 M6495 2018
The celebrated SchurWeyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finitedimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine KacMoody algebras.
The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical $\mathcal{{W}}$algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the HarishChandra isomorphism connects the Sugawara operators with the classical $\mathcal{{W}}$algebras, which play the role of the Weyl group invariants in the finitedimensional theory. 
Bounded cohomology of discrete groups / Roberto FrigerioQA 612.3 F75 2017
The theory of bounded cohomology, introduced by Gromov in the late 1980s, has had powerful applications in geometric group theory and the geometry and topology of manifolds, and has been the topic of active research continuing to this day. This monograph provides a unified, selfcontained introduction to the theory and its applications, making it accessible to a student who has completed a first course in algebraic topology and manifold theory. The book can be used as a source for research projects for master's students, as a thorough introduction to the field for graduate students, and as a valuable landmark text for researchers, providing both the details of the theory of bounded cohomology and links of the theory to other closely related areas.
The first part of the book is devoted to settling the fundamental definitions of the theory, and to proving some of the (by now classical) results on lowdimensional bounded cohomology and on bounded cohomology of topological spaces. The second part describes applications of the theory to the study of the simplicial volume of manifolds, to the classification of circle actions, to the analysis of maximal representations of surface groups, and to the study of flat vector bundles with a particular emphasis on the possible use of bounded cohomology in relation with the Chern conjecture. Each chapter ends with a discussion of further reading that puts the presented results in a broader context. 
Game theory : breakthroughs in research and practice / Information Resources Management Association, USA [editor]QA 269 G3536 2018
Developments in the use of game theory have impacted multiple fields and created opportunities for new applications. With the ubiquity of these developments, there is an increase in the overall utilization of this approach.
Game Theory: Breakthroughs in Research and Practice contains a compendium of the latest academic material on the usage, strategies, and applications for implementing game theory across a variety of industries and fields. Including innovative studies on economics, military strategy, and political science, this multivolume book is an ideal source for professionals, practitioners, graduate students, academics, and researchers interested in the applications of game theory. 
Applied functional analysis / J. Tinsley Oden, Leszek F. DemkowiczQA 320 O29 2018Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science.
This wellreceived textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces.
The final two chapters provides readers with an indepth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory.
The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.

Notes on counting : an introduction to enumerative combinatorics / Peter J. Cameron (University of St Andrews, Scotland)QA 164 C36 2017
Enumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the RedfieldPlya theory of cycle indices, Mbius inversion, the Tutte polynomial, and species. 
Graphs, algorithms, and optimization / William L. Kocay, Donald L. KreherQA 166.245 K63 2017The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs.
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The calculus story : a mathematical adventure / David AchesonQA 303.2 A32 2017
Calculus is the key to much of modern science and engineering. It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is alsosomething of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn...In The Calculus Story David Acheson presents a wideranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, hedemonstrates how to start doing calculus, from the very beginning. 
Basic and advanced statistical tests : writing results sections and creating tables and figures / Amanda Ross, A.A. Ross Consulting and Research, USA and Victor L. Willson, Texas A&M University, USAQA 277 R67 2017This book focuses on extraction of pertinent information from statistical test outputs, in order to write result sections and/or accompanying tables and/or figures.
The book is divided into two encompassing sections: Part I  Basic Statistical Tests and Part II  Advanced Statistical Tests. Part I includes 9 basic statistical tests, and Part II includes 7 advanced statistical tests. Each chapter provides the name of a basic or advanced statistical test, a brief description, examples of when to use each, a sample scenario, and a sample results section writeup. Depending on the test and need, most chapters provide a table and/or figure to accompany the writeup.
The purpose of the book is to provide researchers with a reference manual for writing results sections and tables/figures in scholarly works. The authors fill a gap in research support manuals by focusing on sample writeups and tables/figures for given statistical tests. The book assists researchers by eliminating the need to comb through numerous publications to determine necessary information to report, as well as correct APA format to use, at the close of analyses.

Codes, cryptology and curves with computer algebra / Ruud Pellikaan, Technische Universiteit Eindhoven, The Netherlands, XinWen Wu, Griffith University, Queensland, Stanislav Bulygin, Relinde Jurrius, Université de Neuchatel, SwitzerlandQA 268 P45 2018
This wellbalanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced errorcorrecting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masterslevel students studying mathematics, computer science, electrical engineering or physics. 
Calculus : early transcendental functionsQA 303 L3274 2019
Designed for the threesemester engineering calculus course, CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 7th Edition, continues to offer instructors and students innovative teaching and learning resources. The Larson team always has two main objectives for text revisions: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student. Every edition from the first to the seventh of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas.