'Differential Topology' by Victor Guillemin and Alan Pollack unveils the intricate relationship between geometry and calculus, exploring the manifold structures that shape our understanding of space. This text dives into the fundamental concepts of differentiable functions, providing readers with a solid foundation for advanced mathematical theories. With its clear explanations and thought-provoking examples, the book challenges you to rethink what you know about topology. The authors guide you through complex ideas with elegance and precision, making this a key resource for aspiring mathematicians. Are you ready to explore the seamless connections of shapes and forms in a world where dimension is just the beginning?
By Victor Guillemin, Alan Pollack
Published: 2010
"In the intricate dance of shapes and spaces, we uncover not just mathematics, but the very essence of understanding our universe."
Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.
Showing 8 of 25 similar books
Neil deGrasse Tyson is a renowned astrophysicist, author, and science communicator, best known for his work in popularizing science through various media. As the director of the Hayden Planetarium in New York City, he has played a pivotal role in bringing astronomical discoveries to the public. Tyson has authored several bestselling books, including "Astrophysics for People in a Hurry" and "The Pluto Files," which have made complex scientific concepts accessible to a broad audience. He is also the host of the popular science TV show "Cosmos: A Spacetime Odyssey," a continuation of Carl Sagan's groundbreaking series. Tyson's contributions have significantly enhanced public understanding and appreciation of the universe.
Naval Ravikant is an entrepreneur, angel investor, and philosopher, best known as the co-founder of AngelList, a platform that connects startups with investors. Ravikant is a prolific thinker and writer on topics such as startups, investing, and personal well-being, sharing his wisdom through essays, podcasts, and social media. He has invested in over 100 companies, including Uber, Twitter, and Yammer, making him one of Silicon Valley’s most successful angel investors. Ravikant is also known for his philosophical musings on wealth, happiness, and the meaning of life, which have garnered him a large and dedicated following.
Patrick Collison is an Irish entrepreneur and co-founder of Stripe, a global technology company that enables businesses to accept online payments. Along with his brother John, Patrick has transformed Stripe into one of the most valuable private tech companies in the world. Stripe’s innovative approach to online payments has made it a key player in the financial technology space. Collison is known for his deep interest in science, technology, and policy, often engaging in conversations about innovation, progress, and how to improve societal outcomes. He is an advocate for scientific advancement and the intersection of technology and public policy.
Caroline Paul is an American author and former firefighter, best known for her non-fiction works that explore adventure, courage, and resilience. Her books, including The Gutsy Girl and Fighting Fire, highlight her experiences and encourage readers, especially women, to take risks and embrace challenges. Paul is a passionate advocate for gender equality and breaking stereotypes, particularly around women in fields like adventure and emergency services. She frequently speaks about empowerment, bravery, and finding joy in the unknown. Her writing and advocacy inspire readers to step outside their comfort zones and lead bold, fearless lives.
David Deutsch is a British physicist and philosopher, widely known for his contributions to quantum mechanics, particularly in the area of quantum computation. He is the author of The Fabric of Reality and The Beginning of Infinity, where he explores the nature of knowledge, progress, and the future of human civilization. Deutsch’s work in quantum computing laid the groundwork for the development of quantum algorithms, positioning him as a pioneer in this emerging field. He is a proponent of the multiverse theory and has offered profound insights into the nature of reality, science, and human potential. Deutsch’s philosophical work emphasizes the power of reason and creativity in solving problems and expanding human understanding. His ideas have had a significant impact on the fields of theoretical physics and epistemology, making him a leading thinker on the future of science and technology. He continues to inspire both scientists and lay readers with his optimistic vision of a world shaped by knowledge and innovation.
Astro Teller is an American entrepreneur, scientist, and the CEO of X (formerly Google X), Alphabet’s innovation lab dedicated to developing groundbreaking technologies. Often referred to as "Captain of Moonshots," Teller leads a team focused on tackling some of the world’s biggest challenges through radical solutions. Under his leadership, X has worked on projects like self-driving cars (Waymo), internet balloons (Loon), and delivery drones (Wing). Teller holds a PhD in artificial intelligence and has a deep background in science and technology, blending his technical expertise with a passion for innovation. He is a proponent of a fail-fast approach, encouraging experimentation and learning from failure as integral parts of the innovation process. Teller’s work at X has placed him at the forefront of the tech world’s quest for transformative technologies. Outside of his work at X, he is an accomplished author, having written both fiction and non-fiction, and is an advocate for the future of AI and robotics.
Cleo Abram is a distinguished journalist and content creator known for her incisive storytelling and engaging multimedia presentations. She gained widespread recognition as a producer and host for Vox's acclaimed series, "Glad You Asked," where she explored complex topics with clarity and depth. Abram's work often intersects with technology and culture, making intricate subjects accessible to a broad audience. In addition to her journalistic endeavors, she has contributed thought-provoking essays and articles to various esteemed publications. Her innovative approach to storytelling continues to influence and inspire both readers and aspiring journalists.
Eric Weinstein is an accomplished American mathematician, economist, and writer, known for his influential work in the fields of geometric unity and economic theory. As the Managing Director of Thiel Capital, he has significantly impacted the financial and technological sectors. Weinstein is also renowned for his thought-provoking discussions on the podcast "The Portal," where he explores complex scientific and social issues. He has written extensively on a variety of topics, contributing to both academic and popular literature. His unique perspectives and interdisciplinary approach have earned him recognition as a leading intellectual voice of his generation.
Showing 8 of 12 related collections
“In the intricate dance of shapes and spaces, we uncover not just mathematics, but the very essence of understanding our universe.”
Differential Topology
By Victor Guillemin, Alan Pollack
Discover a world of knowledge through our extensive collection of book summaries.
Victor Guillemin is a renowned author celebrated for his contributions to contemporary literature. Known for his thought-provoking narratives and eloquent prose, Guillemin's works often explore themes of identity, resilience, and the human experience. Among his notable publications are "The Echo of Silence," which delves into the intricacies of personal loss, and "Fragments of Tomorrow," a poignant reflection on the passage of time. Guillemin's writing style is characterized by its lyrical quality and profound emotional depth, making him a distinctive voice in modern fiction.
Alan Pollack is a renowned American author and musicologist, celebrated for his in-depth analysis of the Beatles' music and culture. He is best known for his series of essays titled 'The Beatles' and his book 'The Beatles: A Compact Documentary', which provide insightful commentary and exploration of the band's impact on popular music. Pollack's writing is characterized by its analytical rigor and accessible prose, making complex musical concepts understandable to a broad audience. His work not only examines the artistic elements of the Beatles' compositions but also their cultural significance, solidifying his reputation as an authoritative voice in music literature.
Key information about the book.
Buy on Amazon
Buy via BookShopSupport local bookstores: BookShop gives a portion of each sale to independent bookshops!
In "American Gods," Neil Gaiman weaves a mesmerizing tale of Shadow Moon, an ex-convict drawn into a hidden world where ancient gods clash with modern deities created by society's obsessions. As Shadow travels across the country with the enigmatic Mr. Wednesday, he uncovers a rich tapestry of myth and magic interwoven with contemporary America. Every bizarre encounter reveals the past's lingering power and the cost of forgotten beliefs amidst a rapidly changing landscape. With each page, readers are drawn deeper into a battle for the soul of a nation, where the stakes are nothing less than the survival of the old gods. Will Shadow embrace his true identity, or will he be lost to the chaos of a world that no longer remembers them?
In "Cosmos," Carl Sagan embarks on a thrilling expedition through space and time, weaving together the threads of science, history, and philosophy. With stunning prose, he unveils the wonders of the universe, exploring the birth of stars, the evolution of life, and the intricacies of human existence. Sagan’s passion for discovery ignites a sense of awe, inviting readers to ponder our place within the vast cosmos. As he delves into topics from alien civilizations to the origins of consciousness, each page beckons you to rethink what you know about the universe. Prepare to be captivated by a journey that challenges the boundaries of human understanding, leaving you eager to uncover the mysteries that lie beyond the stars.
In "How to Raise Successful People," educator and psychologist Julie Lythcott-Haims unveils transformative insights on nurturing autonomous, resilient children in a world obsessed with achievement. Drawing from her experiences as a former dean at Stanford University, she challenges conventional parenting approaches that prioritize pressure over purpose. With compelling anecdotes and practical strategies, Lythcott-Haims reveals the vital importance of instilling grit, curiosity, and self-efficacy in the next generation. This book is a heartfelt call to rethink what it truly means to be successful and how we can foster that success in others. Prepare to be inspired and equipped to empower the children in your life to thrive authentically!
In 'Keep Going', Austin Kleon inspires readers to cultivate creativity in everyday life amidst challenges and distractions. He offers pragmatic advice on maintaining momentum and nurturing passion, turning mundane routines into vibrant expressions of art. With witty anecdotes and engaging illustrations, Kleon emphasizes the importance of perseverance and connection in creative endeavors. Each chapter serves as a motivational guide, encouraging readers to embrace their unique journeys. By fusing hard work with play, Kleon unlocks the secrets to sustaining creativity over time, leaving readers eager to explore their own passions.
In 'Relentless', Tim S. Grover unveils the mindset that drives the world’s most elite athletes to succeed against all odds. Through gripping anecdotes and powerful insights, Grover exposes the relentless pursuit of greatness that separates the 'coolers' from the 'cleaners.' He challenges readers to embrace discomfort and push beyond their limits in the quest for excellence. With no room for mediocrity, this book is a provocative call to action for anyone looking to elevate their performance and mindset. Are you ready to unleash your inner cleaner and redefine what’s possible?
In 'The Hidden Life of Trees,' Peter Wohlleben unveils the fascinating and intricate world beneath our feet, revealing that trees communicate, share resources, and even help raise their young. This groundbreaking exploration challenges our perceptions of nature, illustrating a social network among trees that thrives in the shadows. Discover how trees possess memory and resilience, adapting to their environment in extraordinary ways. Wohlleben's passionate storytelling invites readers to reconsider the importance of preserving forests for future generations. Delve into this captivating journey to understand the silent yet profound lives of these majestic beings.
In 'The Success Equation', Michael J. Mauboussin explores the intricate interplay between skill and luck in achieving success. He dismantles the myth of pure meritocracy, illustrating how randomness can shape outcomes in unexpected ways. Through engaging anecdotes and thought-provoking analysis, Mauboussin reveals insights on decision-making that challenge conventional wisdom. Readers will discover how to identify and cultivate true talent while understanding the limits of their control. This book invites you to rethink what it means to succeed—are you ready to redefine your own path?
In 'The Curse of the Mogul,' a trio of sharp economic minds dissect the turbulent saga of the media moguls who rose to power and fell from grace. With a mix of historical insight and incisive analysis, Knee, Greenwald, and Seave expose the flawed strategies that led to disastrous outcomes for these titans. Readers will uncover the inherent pitfalls of ambition and the temptations of the media landscape. This compelling narrative weaves together personal stories with economic theories, revealing the true cost of success. Can the lessons learned from these moguls’ downfalls shed light on the future of media management?
Download our mobile app to enjoy your favorite books on the go. Get access to exclusive features, offline listening, and personalized recommendations.
