- Probably Overthinking It : How to Use Data to Answer Questions, Avoid Statistical Traps, and Make Better Decisions byCall Number:
**QA276 .D67 2023**An essential guide to the ways data can improve decision making.

Statistics are everywhere: in news reports, at the doctor's office, and in every sort of forecast, from the stock market to the weather. Blogger, teacher, and computer scientist Allen B. Downey knows well that people have an innate ability both to understand statistics and to be fooled by them. As he makes clear in this accessible introduction to statistical thinking, the stakes are big. Simple misunderstandings have led to incorrect medical prognoses, underestimated the likelihood of large earthquakes, hindered social justice efforts, and resulted in dubious policy decisions. There are right and wrong ways to look at numbers, and Downey will help you see which are which.

Probably Overthinking It uses real data to delve into real examples with real consequences, drawing on cases from health campaigns, political movements, chess rankings, and more. Downey lays out common pitfalls--like the base rate fallacy, length-biased sampling, and Simpson's paradox--and shines a light on what we learn when we interpret data correctly, and what goes wrong when we don't. Using data visualizations instead of equations, he builds understanding from the basics to help you recognize errors, whether in your own thinking or in media reports. Even if you have never studied statistics--or if you have and forgot everything you learned--this book will offer new insight into the methods and measurements that help us understand the world.

- Spin/Pin-structures and Real Enumerative Geometry by Spin/Pin-structures on vector bundles have long featured prominently in differential geometry, in particular providing part of the foundation for the original proof of the renowned Atiyah-Singer Index Theory. More recently, they have underpinned the symplectic topology foundations of the so-called real sector of the mirror symmetry of string theory. This semi-expository three-part monograph provides an accessible introduction to Spin- and Pin-structures in general, demonstrates their role in the orientability considerations in symplectic topology, and presents their applications in enumerative geometry. Part I contains a systematic treatment of Spin/Pin-structures from different topological perspectives and may be suitable for an advanced undergraduate reading seminar. This leads to Part II, which systematically studies orientability problems for the determinants of real Cauchy-Riemann operators on vector bundles. Part III introduces enumerative geometry of curves in complex projective varieties and in symplectic manifolds, demonstrating some applications of the first two parts in the process. Two appendices review the Cech cohomology perspective on fiber bundles and Lie group covering spaces.Call Number:
**QA612.63 .C44 2024** - Stirling Numbers by Stirling numbers are one of the most well-known classes of special numbers in Mathematics, especially in combinatorics and algebra. They were introduced by Scottish mathematician James Stirling (1692-1770) in his most important work, Differential Method with a Tract on Summation and Interpolation of Infinite Series (1730). Stirling numbers have a rich history; many arithmetic, number-theoretical, analytical and combinatorial connections, numerous classical properties, and many modern applications. This book collects much of the scattered material on the two subclasses of Stirling numbers to provide a holistic overview of the topic. From the combinatorial point of view, Stirling numbers of the second kind, S(n, k), count the number of ways to partition a set of n different objects (i.e., a given n-set) into k non-empty subsets. Stirling numbers of the first kind, s(n, k), give the number of permutations of n elements with k disjoint cycles. Both subclasses of Stirling numbers play an important role in algebra: they form the coefficients, connecting well-known sets of polynomials. This book is suitable for students and professionals, providing a broad perspective of the theory of this class of special numbers, and many generalizations and relatives of Stirling numbers, including Bell numbers and Lah numbers. Throughout the book, readers are provided exercises to test and cement their understanding.Call Number:
**QA164 .D49 2024** - Aspiring and Inspiring : Tenure and Leadership in Academic Mathematics by Aspiring and Inspiring is a collection of essays from successful women and gender minority mathematicians on what it takes to build a career in mathematics. The individual essays are intended to advise, encourage, and inspire mathematicians throughout different stages of their careers. Themes emerge as these prominent individuals describe how they managed to persist and rise to positions of leadership in a field which can still be forbidding to many. We read, repeatedly, that individual mentorship matters, that networks of support can be critical, and that finding fulfillment can mean formulating one's own definition of success. Those who aspire to leadership in the field will find much useful advice here. The cumulative power of the collection carries a strong impact. The glass ceiling is very real in mathematics and is the result of cultural and sociological factors at work in our community. The book makes clear that we won't achieve equality of opportunity merely by exhorting those who are often excluded to change their behaviors and their goals. The need for systemic cultural change is vividly, at times painfully, evident in these stories. As Dr. Erica Graham says in her powerful and moving essay, we need "a different kind of academy,'' and we'll only get it by working for it. We can start by reading this book and recognizing the kind of academy we currently have.Call Number:
**QA11.2 .A87 2023** - The Less Is More Linear Algebra of Vector Spaces and Matrices by Designed for a proof-based course on linear algebra, this rigorous and concise textbook intentionally introduces vector spaces, inner products, and vector and matrix norms before Gaussian elimination and eigenvalues so students can quickly discover the singular value decomposition (SVD)-arguably the most enlightening and useful of all matrix factorizations. Gaussian elimination is then introduced after the SVD and the four fundamental subspaces and is presented in the context of vector spaces rather than as a computational recipe. This allows the authors to use linear independence, spanning sets and bases, and the four fundamental subspaces to explain and exploit Gaussian elimination and the LU factorization, as well as the solution of overdetermined linear systems in the least squares sense and eigenvalues and eigenvectors. This unique textbook also includes examples and problems focused on concepts rather than the mechanics of linear algebra. The problems at the end of each chapter and in an associated website encourage readers to explore how to use the notions introduced in the chapter in a variety of ways. Additional problems, quizzes, and exams will be posted on an accompanying website and updated regularly. The Less Is More Linear Algebra of Vector Spaces and Matrices is for students and researchers interested in learning linear algebra who have the mathematical maturity to appreciate abstract concepts that generalize intuitive ideas. The early introduction of the SVD makes the book particularly useful for those interested in using linear algebra in applications such as scientific computing and data science. It is appropriate for a first proof-based course in linear algebra.Call Number:
**QA184.2 .C35 2023** - Matrix Analysis and Applied Linear Algebra by Matrix Analysis and Applied Linear Algebra circumvents the traditional definition-theorem-proof format, and includes topics not normally found in undergraduate textbooks. Taking readers from elementary to advanced aspects of the subject, the author covers both theory and applications. The theoretical development is rigorous and linear, obviating the need for circular or non-sequential references. An abundance of examples and a rich variety of applications will help students gain further insight into the subject. A study and solutions guide is also available.Call Number:
**QA188 .M495 2023** - Mathematics and Tools for Financial Engineering by Based on a master's program course at the University of Southern California, the main goal of Mathematics and Tools for Financial Engineering is to train students to use mathematical and engineering tools to understand and solve financial problems. The book contains numerous examples and problems and is divided into two parts: Part I covers mathematical preliminaries (set theory, linear algebra, sequences and series, real functions and analysis, numerical approximations and computations, basic optimization theory, and stochastic processes). Part II addresses financial topics, ranging from low- to high-risk investments. Mathematics and Tools for Financial Engineering is intended for senior undergraduate or graduate students in finance or financial engineering. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. Readers with no prior knowledge in finance can use the book to learn about various mathematical theories and tools.Call Number:
**HF5691 .I58 2021** - Integral Representation : Choquet Theory for Linear Operators on Function Spaces by This book presents a wide-ranging approach to operator-valued measures and integrals of both vector-valued and set-valued functions. It covers convergence theorems and an integral representation for linear operators on spaces of continuous vector-valued functions on a locally compact space. These are used to extend Choquet theory, which was originally formulated for linear functionals on spaces of real-valued functions, to operators of this type.Call Number:
**QA323 .R68 2023**

- Affine Algebraic Geometry : Geometry of Polynomial Rings by Algebraic geometry is more advanced with the completeness condition for projective or complete varieties. Many geometric properties are well described by the finiteness or the vanishing of sheaf cohomologies on such varieties. For non-complete varieties like affine algebraic varieties, sheaf cohomology does not work well and research progress used to be slow, although affine spaces and polynomial rings are fundamental building blocks of algebraic geometry. Progress was rapid since the Abhyankar-Moh-Suzuki Theorem of embedded affine line was proved, and logarithmic geometry was introduced by litaka and Kawamata. Readers will find the book covers vast basic material on an extremely rigorous level: It begins with an introduction to algebraic geometry which comprises almost all results in commutative algebra and algebraic geometry. Arguments frequently used in affine algebraic geometry are elucidated by treating affine lines embedded in the affine plane and automorphism theorem of the affine plane. There is also a detailed explanation on affine algebraic surfaces which resemble the affine plane in the ring-theoretic nature and for actions of algebraic groups. The Jacobian conjecture for these surfaces is also considered by making use of the results and tools already presented in this book. The conjecture has been thought as one of the most unattackable problems even in dimension two. Advanced results are collected in appendices of chapters so that readers can understand the main streams of arguments. There are abundant problems in the first three chapters which come with hints and ideas for proof.Call Number:
**QA251.3 .M593 2024** - Elementary Classical Mechanics by This book develops elementary classical mechanics in a setting that is appropriate for beginning university mathematics students without requiring a background in physics. It is an ideal first look at the subject for those who will go on to study more advanced aspects of the subject, such as Lagrangian, Hamiltonian, and quantum mechanics. These more advanced developments of mechanics are at the forefront of research in modern mathematics. Certainly, topics such as symplectic geometry, Lagrangian intersection theory, spectral theory, pseudodifferential operators, etc. do not require a background in classical mechanics, but studies in these areas are greatly enriched by a knowledge of their roots and how some of their motivational issues arose.Call Number:
**QA807 .W63 2023** - Equitable and Engaging Mathematics Teaching : A Guide to Disrupting Hierarchies in the Classroom by Teaching college mathematics is a monumental task. Today’s instructors are increasingly asked to do more with less, juggling numerous professional demands while also trying to teach effectively. What if learning to teach better didn’t have to be more work? What if effective practices could make your teaching more equitable and efficient? Equitable and Engaging Mathematics Teaching provides an extensive toolkit of teaching strategies and practices that are brought to life with a wide array of examples and language that you can apply to your own teaching. You'll come to understand the root causes of how and why hierarchies emerge in mathematics classrooms, identify equity issues common to mathematics classrooms, and develop effective methods suited to your personal teaching style.Call Number:
**QA11.2 .R4465 2023** - Numerical Linear Algebra with Julia by Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient. The style is friendly and approachable and cartoon characters guide the way. Inside this book, readers will find detailed descriptions of algorithms, implementations in Julia that illustrate concepts and allow readers to explore methods on their own, and illustrations and graphics that emphasize core concepts and demonstrate algorithms. Numerical Linear Algebra with Julia is a textbook for undergraduate and graduate students. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. The book may also serve as a reference for researchers in various fields such as computational engineering, statistics, data-science, and machine learning, who depend on numerical solvers in linear algebra.Call Number:
**QA185.D37 D37 2021** - Glimpses into the World of Mathematics : A Cognitive Perspective by Essays collected in this volume deal with various problems from the philosophy of mathematics. What connects them are two questions: how mathematics is created and how it is acquired. In "Three Worlds of Mathematics" we are familiarized with David Tall's ideas pertaining to the embodied, symbolic and formal worlds of mathematics. In "Basic Ideas of Intuitionism," we focus on an epistemological approach to mathematics which is distinctive to constructive mathematics. The author focuses on the computational content of intuitionistic logic and shows how it relates to functional programming. "The Brave Mathematical Ant" carefully selects mathematical puzzles related to teaching experiences in a way that the solution requires creativity and is not obtainable by following an algorithm. Moreover the solution gives us some new insight into the underlying idea. "Degrees Of Accessibility Of Mathematical Objects" discusses various criteria which can be used to judge accessibility of mathematical objects. We find logical complexity, range of applications, existence of a physical model as well as aesthetic values.Call Number:
**QA8.4 .G55 2021** - Deep Learning with Python by Deep learning is applicable to a widening range of artificial intelligence problems, such as image classification, speech recognition, text classification, question answering, text-to-speech, and optical character recognition. Deep Learning with Python is structured around a series of practical code examples that illustrate each new concept introduced and demonstrate best practices. By the time you reach the end of this book, you will have become a Keras expert and will be able to apply deep learning in your own projects. KEY FEATURES * Practical code examples * In-depth introduction to Keras * Teaches the difference between Deep Learning and AI ABOUT THE TECHNOLOGY Deep learning is the technology behind photo tagging systems at Facebook and Google, self-driving cars, speech recognition systems on your smartphone, and much more.Call Number:
**QA76.73 .P98 C46 2018**