- A History of Women in Mathematics : Exploring the Trailblazers of STEM byCall Number:
**QA28 .D43 2023**From ancient Greece to medieval Baghdad, from Revolutionary France to China's Qing Dynasty, women mathematicians have worked alongside men to a degree that was denied them in most other fields of scientific inquiry. For over three thousand years, women have been a steady presence during every great mathematical era. They have contributed to the fundamentals of geometry and the expansion of algebra from the earliest days of those disciplines. They have guided us through the realms of non-Euclidean space, gifted us the mathematical models we need to understand the behavior of the metals of our buildings and the soils we construct them upon, and given us a chilling view into the fates of super-massive systems over deep time.

A History of Women in Mathematics, the first comprehensive account of women's role in mathematics in 35 years, tells the stories of over a hundred women, some of whom had to conceal their gender in correspondence, or secrete themselves behind screens during lectures to access the mathematical resources that their male counterparts took for granted. Nevertheless, many had positions of academic honor and international prestige that women in other fields would have to wait centuries to attain. From Theano of Croton to Rachel Riley, here are the tales of the women who have illuminated and demystified the profound structures upon which our reality is built.

- Methods of Geometry in the Theory of Partial Differential Equations : Principle of the Cancellation of Singularities by This monograph focuses on one of the theoretical underpinnings for mathematical models of the real world, arising in the theory of partial differential equations: cancellation of singularities derived from interactions of multiple species, which is described by the language of geometry, in particular, that of global analysis. Five topics are selected, widely spread across the sciences, but strongly connected by common geometric backgrounds: evolution of geometric quantities, models of multi-species in biology, interface vanishing of d - delta systems, the fundamental equation of electro-magnetic theory, and free boundaries arising in engineering.Call Number:
**QA614.58 .S87 2024** - Math in Drag by Unleash your inner math diva! Join sensational drag queen Kyne Santos on an extraordinary journey through the glamorous world of . . . math? This sassy book is your VIP pass, taking you behind the scenes with a TikTok superstar who shatters stereotypes and proves that math can be fascinating and fun, even for people who think they aren't good at it. With her irreverent style and unique perspective, Kyne investigates mathematical mysteries while educating us about the art of drag. She explores surprising connections, such as the elegance of ballroom culture and the nature of infinity, the rebellious joys of Pride and dividing by zero, and the role of statistics in her own experience on Drag Race. Kyne gets personal while sharing her experiences as a queer person forging a path in STEM, overcoming obstacles to stay fierce, stay real, and thrive! She empowers readers of all skill levels to break school rules, question everything, and embrace math's beauty. In Math in Drag, numbers glitter, equations sashay through history, and inclusivity is a celebration. Read it to fire your excitement and unleash your inner math diva!Call Number:
**QA93 .S26 2024** - Advanced Linear Algebra : With an Introduction to Module Theory by Certain essential concepts in linear algebra cannot be fully explained in a first course. This is due to a lack of algebraic background for most beginning students. On the other hand, these concepts are taken for granted in most of the mathematical courses at graduate school level. This book will provide a gentle guidance for motivated students to fill the gap. It is not easy to find other books fulfilling this purpose. This book is a suitable textbook for a higher undergraduate course, as well as for a graduate student's self-study. The introduction of set theory and modules would be of particular interest to students who aspire to becoming algebraists.There are three parts to this book. One is to complete the discussion of bases and dimension in linear algebra. In a first course, only the finite dimensional vector spaces are treated, and in most textbooks, it will assume the scalar field is the real number field. In this book, the general case of arbitrary dimension and arbitrary scalar fields is examined. To do so, an introduction to cardinality and Zorn's lemma in set theory is presented in detail. The second part is to complete the proof of canonical forms for linear endomorphisms and matrices. For this, a generalization of vector spaces, and the most fundamental results regarding modules are introduced to readers. This will provide the natural entrance into a full understanding of matrices. Finally, tensor products of vector spaces and modules are briefly discussed.Call Number:
**QA184.2 .C453 2024** - A Philosophical Introduction to Higher Order Logics by This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages -- their model theory and proof theory, the theory of abstraction and its generalizations -- and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics. A Philosophical Introduction to Higher-order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study. Author Andrew Bacon organizes the book's 18 chapters around four main parts: I. Typed Language II. Higher-Order Languages III. General Higher-Order Languages IV. Higher-Order Model Theory. In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources.This is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics, and introduces the basic formal tools that are needed to theorize in, and model, higher-order languages There are an abundance of simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions, as well as more difficult exercises designed to facilitate long-term learning. Annotated sections on further reading are included, pointing the reader to related literature, learning resources, and historical context.Call Number:
**BC135 .B23 2024** - A Royal Road to Topology : Convergence of Filters by Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more. The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge. Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book -- from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory. The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers. Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.Call Number:
**QA611 .D655 2024** - Felix Hausdorff by Felix Hausdorff is a singular phenomenon in the history of science. As a mathematician, he played a major role in shaping the development of modern mathematics in the 20th century. He founded general topology as an independent mathematical discipline, while enriching set theory with a number of fundamental concepts and results. His general approach to measure and dimension led to profound developments in numerous mathematical disciplines, and today Hausdorff dimension plays a central role in fractal theory with its many fascinating applications by means of computer graphics. Hausdorff 's remarkable mathematical versatility is reflected in his published work: today, no fewer than thirteen concepts, theorems and procedures carry his name. Yet he was not only a creative mathematician - Hausdorff was also an original philosophical thinker, a poet, essayist and man of letters. Under the pseudonym Paul Mongré, he published a volume of aphorisms, an epistemological study, a book of poetry, an oft-performed play, and a number of notable essays in leading literary journals. As a Jew, Felix Hausdorff was increasingly persecuted and humiliated under the National Socialist dictatorship. When deportation to a concentration camp was imminent, he, along with his wife and sister-in law, decided to take their own lives. This book will be of interest to historians and mathematicians already fascinated by the rich life of Felix Hausdorff, as well as to those readers who wish to immerse themselves in the intricate web of intellectual and political transformations during this pivotal period in European history.Call Number:
**QA29.H28 B7413 2024** - Automatic Complexity : A Computable Measure of Irregularity by Automatic complexity is a computable and visual form of Kolmogorov complexity. Introduced by Shallit and Wang in 2001, it replaces Turing machines by finite automata, and has connections to normalized information distance, logical depth, and linear diophantine equations. Automatic Complexity is the first book on the subject and includes exercises with solutions written for the proof assistant Lean, computer programs to calculate automatic complexity, and many open problems.Call Number:
**QA267.7 .K56 2024**

- Elements of Discrete Mathematics : Numbers and Counting, Groups, Graphs, Orders and Lattices by This book treats the elements of discrete mathematics that have important applications in computer science, thus providing the necessary tools for the reader to come to a competent mathematical judgement of modern developments in the age of information. Almost all assertions are shown with full proofs. Exercises are provided, with solutions presented in full detail.Call Number:
**QA297.4 .D54 2024** - Krasner Hyperring Theory Hb by The theory of algebraic hyperstructures, in particular the theory of Krasner hyperrings, has seen a spectacular development in the last 20 years, which is why a book dedicated to the study of these is so vital. Krasner hyperrings are a generalization of hyperfields, introduced by Krasner in order to study complete valued fields. A Krasner hyperring (R, +, .) is an algebraic structure, where (R, +) is a canonical hypergroup, (R, .) is a semigroup having zero as a bilaterally absorbing element and the multiplication is distributive with respect to the hyperoperation +. Krasner Hyperring Theory presents an elaborate study on hyperstructures, particularly Krasner hyperrings, across 10 chapters with extensive examples. It contains the results of the authors, but also of other researchers in the field, focusing especially on recent research. This book is especially addressed to doctoral students or researchers in the field, as well as to all those interested in this interesting part of algebra, with applications in other fields.Call Number:
**QA174.2 .D3785 2024** - Lectures on Fractal Geometry by This book is based on a series of lectures at the Mathematics Department of the University of Jena, developed in the period between 1995 and 2015. It is completed by additional material and extensions of some basic results from the literature to more general metric spaces. This book provides a clear introduction to classical fields of fractal geometry, which provide some background for modern topics of research and applications. Some basic knowledge on general measure theory and on topological notions in metric spaces is presumed.Call Number:
**QA614.86 .Z34 2024** - Partial Differential Equations by This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes, Navier-Stokes equations, and more. The "Problems and Complements" sections have also been updated to feature new exercises, examples, and hints toward solutions, making this a timely resource for students. Partial Differential Equations is ideal for graduate students interested in exploring the theory of PDEs and how they connect to contemporary research. It can also serve as a useful tool for more experienced readers who are looking for a comprehensive reference.Call Number:
**QA377 .D624 2023** - Slowly Varying Oscillations and Waves : From Basics to Modernity by The beauty of the theoretical science is that quite different physical, biological, etc. phenomena can often be described as similar mathematical objects, by similar differential (or other) equations. In the 20th century, the notion of "theory of oscillations" and later "theory of waves" as unifying concepts, meaning the application of similar methods and equations to quite different physical problems, came into being. In the variety of applications (quite possibly in most of them), the oscillatory process is characterized by a slow (as compared with the characteristic period) variation of its parameters, such as the amplitude and frequency. The same is true for the wave processes. This book describes a variety of problems associated with oscillations and waves with slowly varying parameters. Among them the nonlinear and parametric resonances, self-synchronization, attenuated and amplified solitons, self-focusing and self-modulation, and reaction-diffusion systems. For oscillators, the physical examples include the van der Pol oscillator and a pendulum, models of a laser. For waves, examples are taken from oceanography, nonlinear optics, acoustics, and biophysics. The last chapter of the book describes more formal asymptotic perturbation schemes for the classes of oscillators and waves considered in all preceding chapters.Call Number:
**QA865 .O863 2022**