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Author: R. Bruce King
Publisher: Springer Science & Business Media
ISBN: 0817648496
Category : Mathematics
Languages : en
Pages : 159
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Book Description
The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians. The book includes an initial introductory chapter on group theory and symmetry, Galois theory and Tschirnhausen transformations, and some elementary properties of elliptic function in order to make some of the key ideas more accessible to less sophisticated readers. The book also includes a discussion of the much simpler algorithms for roots of the general quadratic, cubic, and quartic equations before discussing the algorithm for the roots of the general quintic equation. A brief discussion of algorithms for roots of general equations of degrees higher than five is also included. "If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations." --New Scientist
Author: R. Bruce King
Publisher: Springer Science & Business Media
ISBN: 0817648496
Category : Mathematics
Languages : en
Pages : 159
Get Book Here
Book Description
The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians. The book includes an initial introductory chapter on group theory and symmetry, Galois theory and Tschirnhausen transformations, and some elementary properties of elliptic function in order to make some of the key ideas more accessible to less sophisticated readers. The book also includes a discussion of the much simpler algorithms for roots of the general quadratic, cubic, and quartic equations before discussing the algorithm for the roots of the general quintic equation. A brief discussion of algorithms for roots of general equations of degrees higher than five is also included. "If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations." --New Scientist
Author: Ron Irving
Publisher: American Mathematical Soc.
ISBN: 147045176X
Category : Education
Languages : en
Pages : 246
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Book Description
The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial's coefficients can be used to obtain detailed information on its roots. The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.
Author: John Clift
Publisher: John Clift
ISBN:
Category : Mathematics
Languages : en
Pages : 148
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Book Description
Nine investigations into Algebra topics normally relegated to university courses, but written in a way that should be comprehensible to a Sixth-Form mathematician motivated to find out more about the subject. Areas featured include cubic equations, modular arithmetic, permutation groups, the Euclidean algorithm, determinants, quaternions and cryptography.
Author: Peter Pesic
Publisher: MIT Press
ISBN: 0262338955
Category : Technology & Engineering
Languages : en
Pages : 222
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Book Description
The intellectual and human story of a mathematical proof that transformed our ideas about mathematics. In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra—which even Newton resisted—and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.
Author: Stephen Siklos
Publisher:
ISBN: 9781783747764
Category : Mathematics
Languages : en
Pages : 188
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Book Description
This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.
Author: John P. Boyd
Publisher: SIAM
ISBN: 161197352X
Category : Mathematics
Languages : en
Pages : 446
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Book Description
Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute--not always needed, but indispensible when it is. The author's goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations.
Author: Mario Livio
Publisher: Simon and Schuster
ISBN: 0743274628
Category : Mathematics
Languages : en
Pages : 367
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Book Description
What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.
Author: Robin Hartshorne
Publisher: Springer Science & Business Media
ISBN: 0387226761
Category : Mathematics
Languages : en
Pages : 535
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Book Description
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Author: Sownak Bose
Publisher: Springer
ISBN: 3319967614
Category : Science
Languages : en
Pages : 207
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Book Description
This book employs computer simulations of ‘artificial’ Universes to investigate the properties of two popular alternatives to the standard candidates for dark matter (DM) and dark energy (DE). It confronts the predictions of theoretical models with observations using a sophisticated semi-analytic model of galaxy formation. Understanding the nature of dark matter (DM) and dark energy (DE) are two of the most central problems in modern cosmology. While their important role in the evolution of the Universe has been well established—namely, that DM serves as the building blocks of galaxies, and that DE accelerates the expansion of the Universe—their true nature remains elusive. In the first half, the authors consider ‘sterile neutrino’ DM, motivated by recent claims that these particles may have finally been detected. Using sophisticated models of galaxy formation, the authors find that future observations of the high redshift Universe and faint dwarf galaxies in the Local Group can place strong constraints on the sterile neutrino scenario. In the second half, the authors propose and test novel numerical algorithms for simulating Universes with a ‘modified’ theory of gravity, as an alternative explanation to accelerated expansion. The authors’ techniques improve the efficiency of these simulations by more than a factor of 20 compared to previous methods, inviting the readers into a new era for precision cosmological tests of gravity.
Author: Adam Ross Solomon
Publisher: Springer
ISBN: 3319466216
Category : Science
Languages : en
Pages : 239
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Book Description
This work investigates the theoretical and cosmological implications of modifying Einstein's theory of general relativity. It explores two classes of modifications to gravity: those in which the graviton is given a small mass, and those in which Lorentz invariance is spontaneously broken. It elucidates the nature of cosmological perturbations in theories of massive bimetric gravity, including a potentially deadly instability. Theories of gravity beyond general relativity could explain why the expansion of the Universe is accelerating, obviating the need for a dark energy, and can also affect the evolution of the early Universe. Next, it investigates the nature of spacetime in massive gravity theories that contain two different spacetime metrics. Lastly, the strongest constraints to date are placed on the size of Lorentz-violating effects in the gravity sector during inflation.
