New Books
What's Happening in the Mathematical Sciences
The What's Happening in the Mathematical Sciences series explores recent mathematical discoveries in an accessible manner. The 2023 volume covers topics like artificial intelligence, with "Deep Learning: Part Math, Part Alchemy" examining machine learning advances. "Organizing the Chaos Inside the Brain" applies chaos theory to animal brain simulations. Pure math enthusiasts will enjoy chapters on tiling, sphere-packing, and multi-view geometry. "How to Draw an Alternate Universe" delves into non-Euclidean geometry, while "How Mathematicians Unearthed the Stubborn Secrets of Fano Varieties" explores algebraic geometry. Other topics include prime numbers without a "7" and fluid singularities, linking back to machine learning.
The Evolution of Mathematics: A Rhetorical Approach
G. Mitchell Reyes challenges the notion that mathematics equals absolute truth in his book, exploring the rhetorical aspects of mathematical discourse. By examining math's historical development from Plato to modern algorithms, Reyes demonstrates how mathematical innovation relies on rhetorical practices like analogy and metaphor. He argues that mathematics is not a static representation of hidden truths but a dynamic force shaping our reality and experience. This perspective aims to foster collaboration between mathematicians and scholars in rhetoric, sociology, and science to better understand our material world and public culture.
The Story of Proof: Logic and the History of Mathematics
"The Story of Proof" by John Stillwell explores the evolution of mathematical proof across various disciplines. From Euclid's geometry to modern mathematics, Stillwell demonstrates how proof has been crucial in generating knowledge and inspiring innovation. The book covers key areas such as algebra, calculus, number theory, non-Euclidean geometry, topology, and logic. It delves into the fundamental relationship between proof and arithmetic, revealing limitations on provable theorems and solvable problems. Stillwell's work offers a fresh perspective on the power and progress of mathematics through the lens of proof.
Illustrating Mathematics
This book is a comprehensive guide for anyone interested in illustrating mathematical concepts. Organized by materials rather than subject areas, it emphasizes the creative process, including discussions of failures. Readers can learn from others' experiences and find inspiration for their own illustrations. The book covers a wide range of mathematical topics, from prime numbers and fractals to complex dynamics and hyperbolic 3-manifolds. Each contributor explains the mathematics behind their illustration in an accessible manner, allowing readers to appreciate both the visual beauty and the underlying concepts. The diverse content ensures that every reader can find a mathematical topic that resonates with them.
Mathematical Intelligence: A Story of Human Superiority over Machines
In "Mathematical Intelligence," Junaid Mubeen challenges the notion that machines will surpass human intelligence. He argues that mathematics, often misunderstood and poorly taught, gives humans a creative edge over computers. Mubeen identifies seven areas where human mathematical abilities excel, including our innate sense of numerical approximation, capacity for abstraction and language, logical reasoning skills, and ability to question and imagine beyond conventional rules. While computers excel at calculations and pattern recognition, Mubeen contends that human mathematical thinking offers a unique blend of creativity, reasoning, and intuition that machines cannot replicate, positioning mathematics as a crucial tool for maintaining our intellectual advantage in the age of artificial intelligence.
Language and the Rise of the Algorithm
"Language and the Rise of the Algorithm" explores the intertwined histories of mathematics, computer science, and linguistics, focusing on the challenge of balancing computational rules with human comprehension. Jeffrey M. Binder examines four historical attempts at universal computation: Leibniz's calculus ratiocinator, Condorcet's universal algebra, Boole's logic system, and the ALGOL programming language. These examples highlight the recurring entanglement of symbolic computation with debates on communication. The book argues that as machine learning blurs the line between technical and everyday language, it challenges the traditional boundary between algorithmic processes and human communication, revealing the profound implications of this convergence.
Probably Overthinking It: How to Use Data to Answer Questions, Avoid Statistical Traps, and Make Better Decisions
"Probably Overthinking It" by Allen B. Downey is a concise guide to statistical thinking for everyone. Using real-world examples from various fields, Downey illustrates how data can improve decision-making and highlights common pitfalls in statistical interpretation. The book emphasizes the importance of correct data analysis in areas such as healthcare, policy-making, and social justice. Through data visualizations and accessible explanations, Downey builds readers' understanding of statistical concepts, enabling them to recognize errors in their own thinking and media reports. This book offers valuable insights for both statistics novices and those seeking to refresh their knowledge.
Wu Wenjun: A Biography in Pictures
This book depicts the fascinating life story of Wu Wenjun, a renowned mathematician who made significant contribution in the field of topology, ancient Chinese mathematics, and mathematics mechanization. He was a recipient of the Highest Science and Technology Award, the highest scientific award in China, as well as the Shaw Prize in Mathematics.Through vivid illustrations and eloquent writing, this book recounts rarely known anecdotes and significant events from Wu Wenjun's life through his childhood, education, and scientific career, offering insights into his life values.
The SAGE Encyclopedia of Theory in Science, Technology, Engineering, and Mathematics
This encyclopedia explores the role of theories in STEM disciplines, examining how they shape understanding and learning in these fields. It delves into the construction, evolution, and significance of theories, highlighting their importance in unlocking the mysteries of the world. The work features over 200 expert-authored articles, organized thematically with a Reader's Guide. Each entry includes further readings, cross-references, and a Resource Guide listing key books, journals, associations, and websites. This comprehensive reference provides valuable insights into the theoretical foundations of science, technology, engineering, and mathematics.
The Art of More: How Mathematics Created Civilization
"The Art of More" by Michael Brooks explores the profound impact of mathematics on human civilization throughout history. From ancient tax collectors to modern astronomers, the book showcases how mathematical innovations have driven human progress. Brooks argues that mathematics was as crucial to human development as the discovery of fire, enabling advancements in trade, astronomy, architecture, and technology. The narrative spans millennia, featuring diverse characters from Egyptian priests to eccentric professors, illustrating how mathematical breakthroughs have consistently propelled humanity forward and shaped our understanding of the world.
Self-Similar and Self-Affine Sets and Measures
This book explores fractals, focusing on self-similar and self-affine sets. It covers introductory concepts and advanced topics, including overlapping self-similar sets and measures, and self-affine systems. The text highlights recent breakthroughs in fractal geometry, often presenting simplified cases of complex concepts. Aimed at mathematicians and students interested in fractal geometry, the book is suitable for graduate and advanced undergraduate courses. It provides a comprehensive overview of this field, from basic definitions to cutting-edge research topics, making it a valuable resource for both beginners and experienced researchers in fractal geometry.
A Brief History of Mathematics: A Promenade Through the Civilizations of Our World
This book offers a unique perspective on the history of mathematics across cultures and civilizations. Divided into eight chronological chapters, it explores mathematical developments from ancient Egypt and Greece to China, India, and the Arab world, up to the 20th century. The author examines the interplay between mathematics and cultural elements, including modern art, providing insights into the discipline's evolution and its impact on society. With engaging visuals and accessible writing, this translated work appeals to both general readers with a basic mathematical background and researchers in mathematics and humanities.
The Lost Scientists of World War II
This book tells the stories of scientists from Germany and other European countries who vanished during World War II. These erudite scholars contributed to diverse scientific fields and were associated with some of the world's leading universities and research institutions. Despite their proficiency, they all sought help from agencies to relocate to the UK in the 1930s, but were unable to secure the necessary assistance.The Lost Scientists of World War II explores the fascinating narratives of thirty of these scientific refugees, delving into the reasons behind the unavailability of aid and presenting fresh insights into the tragic fates or astounding survival experiences of these individuals.
Weapons of Math Destruction
In "Weapons of Math Destruction," Cathy O'Neil warns about the pervasive use of mathematical models in decision-making processes. These algorithms, often opaque and unregulated, can reinforce discrimination and widen societal gaps. O'Neil argues that instead of promoting fairness, these models can trap individuals in vicious cycles, particularly affecting the underprivileged. She examines how these "weapons of math destruction" impact various aspects of life, from education and employment to credit and criminal justice. O'Neil calls for increased accountability from modelers, stricter regulation, and greater public awareness to challenge and change these potentially harmful systems.
The Secret Lives of Numbers: A Hidden History of Math's Unsung Trailblazers
"The Secret Lives of Numbers" by Kate Kitagawa and Timothy Revell reframes mathematics' history, highlighting overlooked contributors across six continents and millennia. The book challenges the Eurocentric narrative, showcasing diverse mathematicians like Hypatia, Karen Uhlenbeck, and scholars from the "House of Wisdom." It explores groundbreaking work by Madhava of Sangamagrama and Black mathematicians during the Civil Rights era. This comprehensive narrative spans thousands of years and various mathematical disciplines, offering a fresh perspective on the global development of mathematics and its unsung heroes.
Visual Complex Analysis: 25th Anniversary Edition
Complex Analysis merges complex numbers with calculus, forming a crucial scientific tool for over two centuries. This book revolutionizes the subject by employing geometry instead of calculations to explain concepts, featuring 501 diagrams that replace traditional computational methods. The visual approach provides intuitive access to the underlying mathematical principles, departing from the standard, often obscure calculations used for 200 years. The 25th Anniversary Edition introduces new captions that thoroughly elucidate the geometric reasoning, transforming the work into a sophisticated, visually-driven exploration of complex analysis.
Sharing Our Science: How to Write and Speak STEM
"Sharing Our Science" by Brandon Brown is a comprehensive guide for STEM professionals seeking to improve their written and oral communication skills. The book addresses the growing need for scientists and engineers to effectively convey their work through various media. Brown covers fundamental writing principles, scientific-specific considerations, and social aspects of communication. Drawing from his experience as a scientist and writing instructor, he provides practical advice on crafting engaging narratives, conveying complex ideas, and presenting information across different formats. This accessible handbook is an invaluable resource for STEM practitioners aiming to enhance their communication abilities and share their work with both technical and general audiences.
Being Human in STEM: Partnering with Students to Shape Inclusive Practices and Communities
This book presents the Being Human in STEM Initiative (HSTEM), a model for creating inclusive environments in undergraduate STEM education. Born from student protests at Amherst College, HSTEM challenges assumptions about who belongs in STEM fields. The authors provide a framework for developing HSTEM courses, evaluating inclusive change initiatives, and adapting the model to various institutions. The book offers strategies for making any course more inclusive through active listening, validation, and reflective practice. It emphasizes the importance of institutional culture shifts and provides resources for educators to implement these changes. Each chapter includes reflective questions and practical exercises to foster inclusivity in STEM classrooms and laboratories.
How to Derive a Formula
This book argues for the continued importance of scientific formulae alongside AI advancements. It explores the process of deriving formulas, emphasizing their role in understanding nature's laws. The authors aim to make mathematics more accessible to physical science students by focusing on practical skills and intuition rather than technical knowledge. The book uses relevant examples from various scientific fields, incorporating historical facts and humor to engage learners. It offers a fresh approach to mathematics education, addressing common obstacles students face and demonstrating the subject's relevance and applicability.
Modern Mathematical Logic
This modern textbook provides a comprehensive introduction to mathematical logic, employing contemporary notation and perspectives. It covers basic concepts, completeness, compactness, and incompleteness, while also delving into model theory, set theory, and computability. Suitable for upper-undergraduate or beginning-graduate courses, it requires only modest mathematical background. The text features numerous examples and classroom-tested exercises to reinforce key ideas and applications. With its fresh approach, this engaging book offers a thorough exploration of this enduringly fascinating and important subject, emphasizing its interactions with other areas of mathematics.