'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 28 similar books
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.
Dwayne "The Rock" Johnson is an American actor, producer, and former professional wrestler who has become one of the most bankable stars in Hollywood. After rising to fame in WWE, where he became a fan favorite for his charisma and athleticism, Johnson transitioned to acting in the early 2000s. His breakout role came in The Scorpion King and he has since starred in major franchises like Fast & Furious and Jumanji. Known for his larger-than-life personality, work ethic, and versatility, Johnson has successfully built a career in action, comedy, and family films. Outside of acting, Johnson is a philanthropist and entrepreneur, launching his own production company, Seven Bucks Productions, and wellness brands like ZOA energy drink. He is also a social media powerhouse, using his platform to motivate millions and engage with fans. Forbes frequently lists him as one of the highest-paid actors globally, and he remains one of the most influential figures in entertainment.
Barack Obama is the 44th President of the United States, serving from 2009 to 2017. As the first African American president, Obama’s leadership marked a historic moment in American history. His administration focused on healthcare reform, economic recovery from the Great Recession, and environmental policies. He is best known for the Affordable Care Act, as well as his efforts to expand civil rights and restore diplomatic relations with Cuba. Since leaving office, Obama has continued to engage in public life through his foundation, focusing on leadership development, civic engagement, and global issues.
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.
Sophie Bakalar is a distinguished author and venture capitalist known for her adept storytelling and insightful exploration of contemporary issues. Her debut novel received critical acclaim for its nuanced portrayal of complex characters and societal dynamics. In addition to her literary achievements, Bakalar is a co-founder of a successful venture firm, where she leverages her keen understanding of market trends and innovation. Her essays and articles, often featured in prominent publications, reflect her deep engagement with cultural and technological shifts. Bakalar's multifaceted career bridges the worlds of literature and entrepreneurship, making her a unique voice in both fields.
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.
Showing 8 of 14 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 'Freakonomics,' Steven D. Levitt and Stephen J. Dubner explore the hidden side of everything, revealing the surprising truths behind human behavior and decision-making. Through a series of intriguing case studies, they uncover the economic forces that shape our lives in ways we never expected. What do schoolteachers and sumo wrestlers have in common? How do incentives drive the behavior of people in powerful positions? Prepare to challenge your assumptions and see the world through a lens of data and unconventional thinking.
In 'The Coddling of the American Mind,' authors Greg Lukianoff and Jonathan Haidt explore the troubling trends of emotional fragility and avoidance of discomfort among today's youth. They argue that overprotection and the decline of critical thinking in education are eroding resilience and fostering divisions. The book delves into the psychological and cultural shifts that have led to this phenomenon, revealing how it impacts free speech and democracy. With compelling anecdotes and rigorous research, the authors challenge readers to reconsider the implications of their parenting and educational choices. A thought-provoking read that raises questions about the future of society and the importance of mental toughness.
In 'The Big Picture', physicist Sean Carroll invites readers to explore the fascinating intersections of science, philosophy, and the meaning of life. He delves into the fundamental nature of reality, presenting complex concepts in a captivating and accessible manner. With a blend of narratives and profound insights, Carroll challenges us to consider our place in the universe. As he unravels the mysteries of existence, readers are urged to reflect on the implications of science for understanding consciousness and our everyday experiences. This thought-provoking journey leaves us questioning: what does it truly mean to be human in a cosmos governed by natural laws?
In 'Gang Leader for a Day,' sociologist Sudhir Venkatesh takes readers on a riveting journey through the streets of Chicago, where he plunges into the world of gang life. Captivated by the complexities of urban poverty, he forms an unlikely partnership with the notorious Black Kings gang leader. Through gripping anecdotes, Venkatesh reveals the intricate social dynamics and struggles that shape the community's reality. As he navigates this underworld, the boundaries between researcher and subject blur, challenging societal norms and perceptions. This eye-opening narrative invites readers to rethink what they know about gang culture and the human spirit.
In 'Save the Cat!', Blake Snyder reveals the secrets of successful screenwriting through a unique formula for storytelling. He emphasizes the importance of creating relatable characters and compelling plots that resonate with audiences. Snyder introduces the concept of the 'Save the Cat' moment, where protagonists earn audience sympathy through an act of kindness. With practical advice and engaging anecdotes, this guide empowers aspiring writers to craft screenplays that capture attention and hearts. Discover how to make your stories irresistible and ensure your characters stay in the spotlight.
Dive into the fascinating world of Differential Forms in Algebraic Topology, where the elegant interplay between geometry and algebra unfolds. Authors Raoul Bott and Loring W. Tu guide readers through complex concepts with clarity and insight, revealing the beauty behind these mathematical structures. With a perfect blend of theory and application, this book illuminates how differential forms serve as powerful tools in various contexts of topology. Each chapter invites readers to engage with profound ideas that challenge and inspire. Are you ready to embark on a journey that transforms your understanding of the mathematical universe?
No summary available
Download our mobile app to enjoy your favorite books on the go. Get access to exclusive features, offline listening, and personalized recommendations.
