The Power of q

The Power of q PDF Author: Michael D. Hirschhorn
Publisher: Springer
ISBN: 9783319577616
Category : Mathematics
Languages : en
Pages : 0

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Book Description
This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and life-long study—inspired by Ramanujan—of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises. After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange’s four-squares theorem and Gauss’s two-squares theorem. Attention then turns to partitions and Ramanujan’s partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across the Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction, the famous “forty identities” of Ramanujan, and the representation results of Jacobi, Dirichlet and Lorenz, not to mention many other interesting and beautiful results. We also meet a challenge of D.H. Lehmer to give a formula for the number of partitions of a number into four squares, prove a “mysterious” partition theorem of H. Farkas and prove a conjecture of R.Wm. Gosper “which even Erdős couldn’t do.” The book concludes with a look at Ramanujan’s remarkable tau function.

The Power of q

The Power of q PDF Author: Michael D. Hirschhorn
Publisher: Springer
ISBN: 331957762X
Category : Mathematics
Languages : en
Pages : 422

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Book Description
This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and life-long study—inspired by Ramanujan—of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises. After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange’s four-squares theorem and Gauss’s two-squares theorem. Attention then turns to partitions and Ramanujan’s partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across the Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction, the famous “forty identities” of Ramanujan, and the representation results of Jacobi, Dirichlet and Lorenz, not to mention many other interesting and beautiful results. We also meet a challenge of D.H. Lehmer to give a formula for the number of partitions of a number into four squares, prove a “mysterious” partition theorem of H. Farkas and prove a conjecture of R.Wm. Gosper “which even Erdős couldn’t do.” The book concludes with a look at Ramanujan’s remarkable tau function.

The Power of q

The Power of q PDF Author: Michael D. Hirschhorn
Publisher: Springer
ISBN: 9783319577616
Category : Mathematics
Languages : en
Pages : 0

Get Book Here

Book Description
This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and life-long study—inspired by Ramanujan—of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises. After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange’s four-squares theorem and Gauss’s two-squares theorem. Attention then turns to partitions and Ramanujan’s partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across the Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction, the famous “forty identities” of Ramanujan, and the representation results of Jacobi, Dirichlet and Lorenz, not to mention many other interesting and beautiful results. We also meet a challenge of D.H. Lehmer to give a formula for the number of partitions of a number into four squares, prove a “mysterious” partition theorem of H. Farkas and prove a conjecture of R.Wm. Gosper “which even Erdős couldn’t do.” The book concludes with a look at Ramanujan’s remarkable tau function.

The Q Continuum

The Q Continuum PDF Author: Greg Cox
Publisher: Simon and Schuster
ISBN: 0743491823
Category : Fiction
Languages : en
Pages : 370

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Book Description
The unpredictable cosmic entity known only as Q has plagued Captain Jean-Luc Picard and the crew of the Starship Enterprise™ since their very first voyage together. But little was known of Q's mysterious past or of the unearthly realm from which he hails. Until now. A brilliant scientist may have found a way to breach the energy barrier surrounding the Milky Way galaxy, and the Enterprise is going to put it to the test. The last thing Captain Picard needs is a surprise visit from Q, but the omnipotent trickster has more in mind than his usual pranks. Kidnapping Picard, he takes the captain back through time to the moment the Q Continuum faced its greatest threat. Now Picard must learn Q's secrets -- or all of reality may perish!

I, Q

I, Q PDF Author: John de Lancie
Publisher: Simon and Schuster
ISBN: 0671024442
Category : Interplanetary voyages
Languages : en
Pages : 276

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Book Description
Science fiction roman.

Star Trek: Q Squared

Star Trek: Q Squared PDF Author: Peter David
Publisher: Simon and Schuster
ISBN: 1471108732
Category : Fiction
Languages : en
Pages : 336

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Book Description
In all of his travels Captain Jean-Luc Picard has never faced an opponent more powerful than Q, a being from another continuum that Picard encountered on his very first mission as Captain of the Starship EnterpriseTM. In the years since, Q has returned again and again to harass Picard and his crew. Sometimes dangerous, sometimes merely obnoxious, Q has always been mysterious and seemingly all-powerful. But this time, when Q appears, he comes to Picard for help. Apparently another member of the Q continuum has tapped into an awesome power source that makes this being more powerful than the combined might of the entire Q continuum. This renegade Q is named Trelane, also known as the Squire of Gothos, who Captain Kirk and his crew first encountered over one hundred years ago. Q explains that, armed with this incredible power, Trelane has become unspeakably dangerous. Now Picard must get involved in an awesome struggle between super beings. And this time the stakes are not just Picard's ship, or the galaxy, or even the universe, this time the stakes are all of creation.

Q-Squared

Q-Squared PDF Author: Peter David
Publisher: Simon and Schuster
ISBN: 0671041002
Category : Fiction
Languages : en
Pages : 339

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Book Description
In all of his travels Captain Jean-Luc Picard has never faced an opponent more powerful that Q, a being from another continuum that Picard encountered on his very first mission as Captain of the Starship Enterprise™. In the years since, Q has returned again and again to harass Picard and his crew. Sometimes dangerous, sometimes merely obnoxious, Q has always been mysterious and seemingly all-powerful. But this time, when Q appears, he comes to Picard for help. Apparently another member of the Q continuum has tapped into an awesome power source that makes this being more powerful than the combined might of the entire Q continuum. This renegade Q is named Trelane -- also known as the Squire of Gothos, who Captain Kirk and his crew first encountered over one hundred years ago. Q explains that, armed with this incredible power, Trelane has become unspeakably dangerous. Now Picard must get involved in an awesome struggle between super beings. And this time the stakes are not just Picard's ship, or the galaxy, or even the universe -- this time the stakes are all of creation...

An Introduction to q-analysis

An Introduction to q-analysis PDF Author: Warren P. Johnson
Publisher: American Mathematical Soc.
ISBN: 1470456230
Category : Education
Languages : en
Pages : 537

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Book Description
Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to q q-analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view. The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for self-study in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.

The Quantum Leap: Exploring the Power and Potential of Q-Star AI in Academia and Beyond

The Quantum Leap: Exploring the Power and Potential of Q-Star AI in Academia and Beyond PDF Author: KHRITISH SWARGIARY
Publisher: EdTech Research Association, Scottsdale, Arizona, US
ISBN:
Category : Education
Languages : en
Pages : 90

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Book Description
In the ever-evolving landscape of artificial intelligence, we find ourselves at the brink of a new era marked by unprecedented technological advancements. Quantum-driven AI, specifically Q-Star AI, represents one of the most transformative innovations in this field. This book, "The Quantum Leap: Exploring the Power and Potential of Q-Star AI in Academia and Beyond," is a comprehensive examination of this groundbreaking technology, focusing on its applications within academia and its potential to shape the future of education, research, and industry. The journey to create this book began with a fascination for the possibilities of quantum computing and its application to artificial intelligence. As quantum mechanics entered the AI domain, opening doors to unparalleled computational power, I realized the profound implications for academic fields that rely heavily on data processing, modeling, and complex problem-solving. Q-Star AI stands as a unique milestone that combines the depth of quantum mechanics with the versatility of AI, capable of enhancing both scientific and social research. However, for academics, educators, and students to fully embrace and utilize Q-Star AI, a clear understanding of its capabilities, applications, and ethical implications is essential. This book aims to be more than an introduction; it is a guide that provides readers with practical tools, real-world applications, and critical perspectives on Q-Star AI. In exploring its academic applications, we delve into how Q-Star AI optimizes research methodologies across disciplines and reshapes teaching practices, learning outcomes, and data analysis. The book also addresses ethical considerations, acknowledging the need for responsible use of this technology in educational contexts.

Q-in-Law

Q-in-Law PDF Author: Peter David
Publisher: Simon and Schuster
ISBN: 0671040995
Category : Fiction
Languages : en
Pages : 246

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Book Description
A celebration of love between two powerful rival families is cut short when the all powerful being called Q arrives and challenges the very concept of love. When two powerful rival families of the spacefaring merchant race called the Tizarin are to be joined through marriage, the U.S.S. Enterprise is chosen as the site for the wedding. Though Captain Picard is pleased by the happy duty, his pleasure is cut short by the arrival of the Federation delegate from Betazed: Lwaxana Troi—the mother of ship's counsellor, Deanna Troi. Despite Lwaxana Troi's romantic overtures toward the captain, the celebration seems to go smoothly until the situation is further complicated by the arrival of the notorious and all powerful being called Q—who has come to examine and challenge the human concept of love. Suddenly, the festivities are in turmoil, the powerful Tizarin families are on the verge of war, and Lwaxana Troi is determined to teach Q a lesson in love that he will never forget...

The Story of Q.

The Story of Q. PDF Author: N. M. Freeman
Publisher: iUniverse
ISBN: 1450276989
Category : Fiction
Languages : en
Pages : 313

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Book Description
Two thousand years ago, a boy named Mateo entered an underground cave known as the Sanctuary to learn of stories 'older than the memory of man'.