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This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.
This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questio ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.
True Islam's 1997 cult classic is back in print in a new, revised edition. The Book of God has been called 'the bible of the Black God,' as it presents a wide range of scientific, historical, and scriptural evidence demonstrating that the Original Black Man is the God of the world's religious traditions, from the religious traditions of the Ancient Near and Far East such as Kemet (Egypt) and India to the Biblical religions and Islam. The Book of God answers such questions as: How is the Black Man God and what does this mean? What is God's relationship to spirit and matter? What does Albert Einstein's mathematical revelation E=mc2 have to do with the Reality of God? If the Original Black Man is God, Who is the Original Black Woman? Is there evidence of the reality of the Twenty Four Scientists? Who is Master Fard Muhammad? Was he actually an ex-con named Wallie Ford who served time in San Quentin on a drug charge? And more. The Book of God also demonstrates that: The God of the ancient religious traditions around the world was a self-created Black God. The Six Days of Creation in the book of Genesis chronicles the Black God's Six Trillion year evolution. The ancient sacred texts of the Original Man and Woman from around the world agree with the Hon. Elijah Muhammad's Teaching on God. The fields of Genetics and Hebrew Sacred Tradition converge to reveal that the Essence of the Creator inhabits the very genetic makeup of the Original Man and Woman. The Secret of the ancient Mysteries, the Masonic Lodge and Shrine, and the Church of Rome is the Reality of the Black God. Astrophysical evidence and ancient tradition converge to support the Hon. Elijah Muhammad's teaching on the Deportation of the Moon by a Black God. And much more.
Shares an account of his religiously transformative near-death experience and revealing week-long coma, describing his scientific study of near-death phenomena while explaining what he learned about the nature of human consciousness.
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

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