- Tangles : A Structural Approach to Artificial Intelligence in the Empirical Sciences byCall Number:
**Q335.5 .D54 2024**Tangles offer a precise way to identify structure in imprecise data.

By grouping qualities that often occur together, they can reveal not only clusters of things but also types of their qualities: types of political views, of texts, of health conditions, or of proteins. Tangles offer a new structural approach to artificial intelligence that can help us understand, classify, and predict complex phenomena.

Tangles can be used in conjunction with existing methods based on neural networks, or offer an alternative, when more control or accountability is desired.

The mathematical theory of tangles has its origin in the ground-breaking work of Neil Robertson and Paul Seymour on graph minors in the late 20th century. Its potential for applications was realized only more recently, following the axiomatization of tangles as abstract connectivity structures independent of graphs. Such potential applications are explored here for the first time.

- The Secret Lives of Numbers : A Hidden History of Math's Unsung Trailblazers by Mathematics shapes almost everything we do. But despite mathematics' reputation as the study of fundamental truths, the stories we have been told about it are wrong -- warped like the sixteenth-century map that enlarged Europe at the expense of Africa, Asia, and the Americas. In The Secret Lives of Numbers, renowned math historian Kate Kitagawa and journalist Timothy Revell make the case that the history of math is infinitely deeper, broader, and richer than the narrative we think we know. Their story takes us from Hypatia, one of the first great female mathematicians, whose ideas revolutionized geometry and who was killed for them, to Karen Uhlenbeck, the first woman to win the Abel Prize, math's Nobel. Along the way we travel the globe to meet the brilliant Arabic scholars of the House of Wisdom, a math temple whose destruction in the siege of Baghdad in the thirteenth century was a loss arguably on par with that of the Library of Alexandria; Mādhava of Sangamagrama, the fourteenth-century Indian genius who uncovered the central tenets of calculus three hundred years before Isaac Newton was born; and the Black mathematicians of the Civil Rights era, who played a significant role in dismantling early data-based methods of racial discrimination. A thrilling tour through the richness of mathematics, The Secret Lives of Numbers is an immensely compelling narrative historyCall Number:
**QA21 .K48 2024** - Shadows of the Circle : From Conic Sections to Planetary Motion by The ancient Greeks were the first to seriously ask for scientific explanations of the panorama of the heavens based on mathematical ideas. Ever since, mathematics has played a major role for human perception and description of the outside physical world, and in a larger perspective for comprehending the universe. This second edition pays tribute to this line of thought and takes the reader on a journey in the mathematical universe from conic sections to mathematical modelling of planetary systems. In the second edition, the four chapters in the first edition on conic sections (two chapters), isoperimetric problems for plane figures, and non-Euclidean geometry, are treated in four revised chapters with many new exercises added. In three new chapters, the reader is taken through mathematics in curves, mathematics in a Nautilus shell, and mathematics in the panorama of the heavens. In all chapters of the book, the circle plays a prominent role. This book is addressed to undergraduate and graduate students as well as researchers interested in the geometry of conic sections, including the historical background and mathematical methods used. It features selected important results, and proofs that not only proves but also explains the results.Call Number:
**QA485 .H36 2024** - An Introduction to Real Analysis by An Introduction to Real Analysis gives students of mathematics and related sciences an introduction to the foundations of calculus, and more generally, to the analytic way of thinking. The authors' style is a mix of formal and informal, with the intent of illustrating the practice of analysis and emphasizing the process as much as the outcome. The book is intended for use in a one- or two-term course for advanced undergraduates in mathematics and related fields who have completed two or three terms of a standard university calculus sequence.Call Number:
**QA331.5 .K38 2024**

- Differential Equations : Solving Ordinary and Partial Differential Equations with Mathematica® by This book explores solutions for nearly 650 ordinary and partial differential equations. Each equation has at least one solution and one colored graph for each solution. Some graphs are dynamical, as for Clairaut differential equations. Thus, one can study the general and the singular solutions. All the equations are solved by Mathematica. The first chapter contains mathematical notions and results that are used later through the book. The book is useful for undergraduate and graduate students, for researchers in engineering, physics, chemistry, and statistics. Subjects covered chapter by chapter include parabolic partial differential equations, third and higher order nonlinear partial differential equations, both with modern methods. Chapter 10 discusses the Korteweg-de Vries, Dodd-Bullough-Mikhailov, Tzitzeica-Dodd-Bullough, Benjamin, Kadomtsev-Petviashvili, Sawada-Kotera, and Kaup-Kupershmidt equations.Call Number:
**QA371 .M87 2024** - Elementary Linear Algebra with Applications : Matlab, Mathematica and Maplesoft by This text offers a unique balance of theory and a variety of standard and new applications along with solved technology-aided problems. The book includes the fundamental mathematical theory, as well as a wide range of applications, numerical methods, projects, and technology-assisted problems and solutions in Maple, Mathematica, and MATLAB. Some of the applications are new, some are unique, and some are discussed in an essay. There is a variety of exercises which include True/False questions, questions that require proofs, and questions that require computations. The goal is to provide the student with is a solid foundation of the mathematical theory and an appreciation of some of the important real-life applications. Emphasis is given on geometry, matrix transformations, orthogonality, and least-squares. Designed for maximum flexibility, it is written for a one-semester/two semester course at the sophomore or junior level for students of mathematics or science.Call Number:
**QA184.2 .N35 2024** - Stochastic Interacting Systems in Life and Social Sciences by This volume provides an overview of two of the most important examples of interacting particle systems, the contact process, and the voter model, as well as their many variants introduced in the past 50 years. These stochastic processes are organized by domains of application (epidemiology, population dynamics, ecology, genetics, sociology, econophysics, game theory) along with a flavor of the mathematical techniques developed for their analysis.Call Number:
**QA274 .L36 2024** - The Numerical Jordan Form by The Numerical Jordan Form is the first book dedicated to exploring the algorithmic and computational methods for determining the Jordan form of a matrix, as well as addressing the numerical difficulties in finding it. Unlike the 'pure' Jordan form, the numerical Jordan form preserves its structure under small perturbations of the matrix elements so that its determination presents a well-posed computational problem. If this structure is well conditioned, it can be determined reliably in the presence of uncertainties and rounding errors.This book addresses the form's application in solving some important problems such as the estimation of eigenvalue sensitivity and computing the matrix exponential. Special attention is paid to the Jordan-Schur form of a matrix which, the author suggests, is not exploited sufficiently in the area of matrix computations. Since the mathematical objects under consideration can be sensitive to changes in the elements of the given matrix, the book also investigates the perturbation analysis of eigenvalues and invariant subspaces. This study is supplemented by a collection over 100 M-files suitable for MATLAB in order to implement the state-of-the art algorithms presented in the book for reducing a square matrix into the numerical Jordan form.Researchers in the fields of numerical analysis and matrix computations and any scientists who utilise matrices in their work will find this book a useful resource, and it is also a suitable reference book for graduate and advance undergraduate courses in this subject area.Call Number:
**QA188 .P455 2024** - Applications of Complex Variables : Asymptotics and Integral Transforms by The subject of applied complex variables is so fundamental that most of the other topics in advanced engineering mathematics (AEM) depend on it. The present book contains complete coverage of the subject, summarizing the more elementary aspects that you find in most AEM textbooks and delving into the more specialized topics that are less commonplace. The book represents a one-stop reference for complex variables in engineering analysis. The applications of conformal mapping in this book are significantly more extensive than in other AEM textbooks. The treatments of complex integral transforms enable a much larger class of functions that can be transformed, resulting in an expanded use of complex-transform techniques in engineering analysis. The inclusion of the asymptotics of complex integrals enables the analysis of models with irregular singular points. The book, which has more than 300 illustrations, is generous with realistic example problems.Call Number:
**TA347.C64 L33 2024** - Navigating the Math Major : Charting your Course by Are you a mathematics major or thinking about becoming one? This friendly guidebook is for you, no matter where you are in your studies. For those just starting out, there are: interactive exercises to help you chart your personalized course, brief overviews of the typical courses you will encounter during your studies, recommended extracurricular activities that can enrich your mathematical journey. Mathematics majors looking for effective ways to support their success will discover: practical examples of dealing with setbacks and challenges in mathematics, a primer on study skills, including particular advice like how to effectively read mathematical literature and learn mathematically focused programming. Students thinking about life after graduation will find: advice for seeking jobs outside academia, guidance for applying to graduate programs, a collection of interviews with former mathematics majors now working in a wide variety of careers-they share their experience and practical advice for breaking into their field. Packed with a wealth of information, Navigating the Math Major is your comprehensive resource to the undergraduate mathematics degree program.Call Number:
**QA10.5 .E28 2024** - Foundations of Logic : Completeness, Incompleteness, Computability by A comprehensive introduction to logic's central concepts. This book provides a concise but detailed account of modern logic's three cornerstones: the completeness of first-order logic, Gödel's Incompleteness Theorems, and Turing's analysis of computability. In addition to the central text, an appendix explains the required technical terminology and facts. The main ideas behind the three cornerstones are explained in a simple, easy-to-grasp manner, and it is possible to select among the chapters and sections so that the reader becomes familiar with these ideas, even if some technicalities are skipped or postponed. A wealth of exercises accompany a wide selection of materials, including the histories and philosophical implications of the three main premises, making it useful as a textbook for undergraduate or graduate courses focusing on any of the three main themes. The material is rigorous and detailed but keeps the main ideas in sight, and there are numerous excursions into more advanced material for curious readers to explore. Call Number:
**BC128 .W47 2023** - Differential Equations, Fourier Series, and Hilbert Spaces : Lecture Notes at the University of Siena. by This book is intended to be used as a rather informal, and surely not complete, textbook on the subjects indicated in the title. It collects my Lecture Notes held during three academic years at the University of Siena for a one semester course on "Basic Mathematical Physics," and is organized as a short presentation of few important points on the arguments indicated in the title. It aims at completing the students' basic knowledge on Ordinary Differential Equations (ODE) - dealing in particular with those of higher order - and at providing an elementary presentation of the Partial Differential Equations (PDE) of Mathematical Physics, by means of the classical methods of separation of variables and Fourier series. For a reasonable and consistent discussion of the latter argument, some elementary results on Hilbert spaces and series expansion in othonormal vectors are treated with some detail in Chapter 2. Prerequisites for a satisfactory reading of the present Notes are not only a course of Calculus for functions of one or several variables, but also a course in Mathematical Analysis where - among others - some basic knowledge of the topology of normed spaces is supposed to be included. For the reader's convenience some notions in this context are explicitly recalled here and there, and in particular as an Appendix in Section 1.4. An excellent reference for this general background material is W. Rudin's classic Principles of Mathematical Analysis. On the other hand, a complete discussion of the results on ODE and PDE that are here just sketched are to be found in other books, specifically and more deeply devoted to these subjects, some of which are listed in the Bibliography. In conclusion and in brief, my hope is that the present Notes can serve as a second quick reading on the theme of ODE, and as a first introductory reading on Fourier series, Hilbert spaces, and PDE.Call Number:
**QC20.7.D5 C45 2023**

- Math Mind : The Simple Path to Loving Math by In Math Mind, Shalinee Sharma shows how complex problem-solving, puzzle-solving, abstract and logical thinking, and cultivating a growth mindset are crucial skills for success that can be taught to everyone. Mathematics, far from being a dry, dull exercise, shares common ground with art, creativity, and wonder. She also explodes the myths that hold us back from enjoying math, with chapters dedicated to the three roadblocks that hold both kids and adults back and discourage them from learning. With instructive line drawings throughout, Sharma explains the math instinct that all humans have from birth, and better, more intuitive ways to solve math problems.Call Number:
**QA93 .S458 2024** - Numbers and Functions : Theory, Formulation and Python Codes by This unique volume covers two fundamental elements of computational methods - numbers and functions. It provides an in-depth discussion of the behaviors of numbers, including both real and complex numbers. The discussion leads to the important closure properties of numbers, ensuring solution consistence and existence, and also possible failure in numerical computations in science and engineering. This text then introduces types of functions that take numbers as independent variables and produce a single number. Approaches for constructing inverse functions are also provided. Frequently used basis functions are introduced, with detailed studies on their properties and behaviors. Techniques are presented for constructing basis functions and their use in function approximation in computational methods.Call Number:
**QA255 .L58 2024** - Nonautonomous Fractional Evolution Equations by Fractional evolution equations describe various complex and nonlocal systems with memory. This volume investigates fractional evolution equations, in infinite intervals. The book covers a range of topics, including the existence, uniqueness, attractivity, and applications to fractional diffusion equations and fractional Schrodinger equations. Researchers and graduate students in pure and applied mathematics will find this a useful reference.Call Number:
**QA377.3 .Z46 2024** - Vector : A Surprising Story of Space, Time, and Mathematical Transformation by A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions--sparking both controversy and discovery. The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word "vector" might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough--and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn't have such a deep understanding of our world. Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it's not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional "spaces," and why you're likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone. In exploring the evolution of vectors and tensors--and introducing the fascinating people who gave them to us--Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. She shows the genius required to reimagine the world--and how a clever mathematical construct can dramatically change discovery's direction.Call Number:
**QA433 .A75 2024** - Mathematical Logic : On Numbers, Sets, Structures, and Symmetry by This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.Call Number:
**QA9 .K67 2024** - Proven Impossible : Elementary Proofs of Profound Impossibility from Arrow, Bell, Chaitin, Gödel, Turing and More by In mathematics, it simply is not true that "you can't prove a negative." Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic - and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training - all you need is the discipline to follow logical arguments and a pen in your hand.Call Number:
**QA9.54 .G87 2024**