By B. Booss, D.D. Bleecker
Published: 1985
The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi ness for extra-mathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most far-reaching conclusions from a single mathe matical idea than to cover a subject or problem area tentatively by a proper "variety" of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differ ent mathematical approaches, and must have experience with their inter connections. The Atiyah-Singer Index Formula, "one of the deepest and hardest results in mathematics", "probably has wider ramifications in topology and analysis than any other single result" (F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to "Mathematics": In spi te of i ts difficulty and immensely rich interrela tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle * semesters. In fact, the Atiyah-Singer Index Formula has become progressively "easier" and "more transparent" over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the many facetted and always new presentations of the material by M. F.
Showing 8 of 27 similar books
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.
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.
Bill Gates, co-founder of Microsoft Corporation, is a pioneering figure in the tech industry, having played a key role in the personal computer revolution. His work at Microsoft, particularly the development of Windows, transformed software and computing globally. Beyond his technology contributions, Gates is also a prolific author, with notable works such as "The Road Ahead" and "Business @ the Speed of Thought," which offer insights into the future of technology and business. Additionally, his philanthropic efforts through the Bill & Melinda Gates Foundation have had a profound impact on global health, education, and poverty. Gates continues to influence both technology and literature with his forward-thinking perspectives and innovative ideas.
Brian Cox is a Scottish actor and director, best known for his roles in films like Braveheart and Adaptation, as well as for his portrayal of media mogul Logan Roy in the hit HBO series Succession. Cox is renowned for his commanding screen presence and his ability to convey complex, often morally ambiguous characters. He has had a distinguished career in both film and theater, earning numerous awards, including a Golden Globe for his performance in Succession. In addition to his acting work, Cox is a vocal advocate for arts education and has been involved in various charitable initiatives. His longevity and versatility have made him a respected and influential figure in the entertainment industry.
Brian Armstrong is a renowned entrepreneur and author best known for co-founding and leading Coinbase, a major cryptocurrency exchange. His literary contributions include insightful writings on the future of digital currencies and blockchain technology. Armstrong's work has been pivotal in demystifying complex financial systems for a broader audience. Beyond his business acumen, his thought leadership in publications and public speaking engagements has cemented his status as a key voice in the fintech revolution. His dedication to innovation continues to influence the trajectory of global financial systems.
Discover a world of knowledge through our extensive collection of book summaries.
B. Booss is a talented author known for their thought-provoking narratives and compelling character development. With a keen ability to explore complex themes, their notable works include 'The Silent Echoes' and 'Winds of Fortune,' which have garnered critical acclaim and a dedicated readership. Booss's writing style blends lyrical prose with elements of realism, drawing readers into richly crafted worlds that often challenge societal norms and explore the fabric of human experience.
D.D. Bleecker is an acclaimed author known for their gripping narratives and profound character development. Their notable works include 'The Rise of Secrets' and 'Whispers in the Dark', both of which explore intricate themes of identity and the human condition. Bleecker's writing style is characterized by vivid imagery and a keen psychological insight, engaging readers with a blend of suspense and emotional depth.
Key information about the book.
Buy on Amazon
Buy via BookShopSupport local bookstores: BookShop gives a portion of each sale to independent bookshops!
In "Astrophysics for People in a Hurry," Neil deGrasse Tyson takes readers on a whirlwind journey through the cosmos, unveiling the complex wonders of the universe in bite-sized pieces. He distills complex theories about black holes, dark matter, and the Big Bang into accessible narratives that spark curiosity and awe. With his signature wit and clarity, Tyson makes the grand tapestry of the universe relatable, inviting readers to ponder their place within it. This captivating exploration not only enlightens but also ignites a sense of wonder about the infinite possibilities of existence. Are you ready to embrace the mysteries of the universe, one brief chapter at a time?
In 'Know My Name', Chanel Miller bravely shares her deeply personal journey after surviving a highly publicized sexual assault. Once known only as "Emily Doe," she reclaims her identity and voice, exposing the trauma and resilience that come from her experience. Miller masterfully weaves her story with raw honesty, illuminating the flaws in the justice system and societal perceptions of victimhood. As she explores themes of identity, healing, and empowerment, readers are compelled to rethink how we recognize and support survivors. This powerful memoir invites us to understand the strength in vulnerability and the importance of making every name known.
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 'Naked Statistics', Charles Wheelan demystifies the world of statistics and reveals its crucial role in everyday decision-making. Through engaging anecdotes and humorous insights, he illustrates how statistical concepts can be both intriguing and practical. Wheelan empowers readers to interpret data with confidence, highlighting common pitfalls in reasoning. This accessible guide transforms what many see as a dry subject into a captivating exploration of the power of numbers. Dive into the world of statistics and discover how it can illuminate your understanding of the world!
Set in a sprawling future where humanity has colonized the stars, 'The Reality Dysfunction' unfolds a tale of cosmic horror as an ancient evil awakens. As the boundaries of life and death blur, a diverse cast of characters—ranging from spacefaring rebels to a religious prophecy—must confront their worst nightmares. Amidst epic battles and political intrigue, the fabric of reality itself begins to unravel. This gripping narrative explores themes of existence, belief, and the consequences of humanity's hubris. Dive into a universe teetering on the brink of chaos, where every choice could lead to salvation or doom.
In 'Indistractable', Nir Eyal uncovers the hidden psychology behind distraction and how our modern environment plays a role in it. He offers practical strategies to reclaim focus, emphasizing that becoming indistractable is not about elimination of all distractions, but about managing them effectively. With compelling anecdotes and scientific research, Eyal shows readers how to align their actions with their values and objectives. The journey toward greater productivity is not merely about willpower; it's about understanding the triggers that lead us astray. Could mastering the art of focus lead to a more fulfilled life?
In 'Imagine It Forward', Beth Comstock shares her transformative journey within GE, revealing how imagination can drive innovation and change. The book delves into the power of bold thinking and taking risks in a rapidly evolving world. Comstock's insights challenge conventional wisdom and encourage readers to embrace their creativity. With personal anecdotes and practical advice, she illustrates how to cultivate a mindset that fosters resilience and adaptability. This compelling narrative inspires readers to envision a future filled with limitless possibilities.
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?
Download our mobile app to enjoy your favorite books on the go. Get access to exclusive features, offline listening, and personalized recommendations.
