| 期刊全稱 | Beyond the Quartic Equation | | 影響因子2023 | R. Bruce King | | 視頻video | http://file.papertrans.cn/186/185357/185357.mp4 | | 發(fā)行地址 | An affordable softcover edition of a classic text.Complete algorithm for roots of the general quintic equation.Key ideas accessible to non-specialists.Indroductory chapter covers group theory and symm | | 學科分類 | Modern Birkh?user Classics | | 圖書封面 |  | | 影響因子 | One of the landmarks in the history of mathematics is the proof of the nonex- tence of algorithms based solely on radicals and elementary arithmetic operations (addition, subtraction, multiplication, and division) for solutions of general al- braic equations of degrees higher than four. This proof by the French mathema- cian Evariste Galois in the early nineteenth century used the then novel concept of the permutation symmetry of the roots of algebraic equations and led to the invention of group theory, an area of mathematics now nearly two centuries old that has had extensive applications in the physical sciences in recent decades. The radical-based algorithms for solutions of general algebraic equations of degrees 2 (quadratic equations), 3 (cubic equations), and 4 (quartic equations) have been well-known for a number of centuries. The quadratic equation algorithm uses a single square root, the cubic equation algorithm uses a square root inside a cube root, and the quartic equation algorithm combines the cubic and quadratic equation algorithms with no new features. The details of the formulas for these equations of degree d(d = 2,3,4) relate to the properties of the corresponding | | Pindex | Book 1996 |
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