Algebra : a computational introduction /: a computational introduction. (2018)

• Record Type: Book
• Further Information: Note: John Scherk.
• Authors: Scherk, John
• Contents: CONGRUENCES; Basic Properties; Divisibility Tests; Common Divisors; Solving Congruences; The Integers Modulo n; Introduction to Software; PERMUTATIONS; Permutations as Mappings; Cycles; Sign of a Permutation; PERMUTATION GROUPS; Definition; Cyclic Groups; Generators; Software and Calculations; LINEAR GROUPS; Definitions and Examples; Generators; Software and Calculations; GROUPS; Basic Properties and More Examples; Homomorphisms; SUBGROUPS; Definition; Orthogonal Groups; Cyclic Subgroups and Generators; Kernel and Image of a Homomorphism; SYMMETRY GROUPS; Symmetries of Regular Polygons; Symmetries of Platonic Solids; Improper Symmetries; Symmetries of Equations; GROUP ACTIONS; Examples; Orbits and Stabilizers; Fractional Linear Transformations; Cayley's Theorem; Software and Calculations; COUNTING FORMULAS; The Class Equation; A First Application; Burnside's Counting Lemma; Finite Subgroups of SO(3); COSETS; Lagrange's Theorem; Normal Subgroups; Quotient Groups; The Canonical Isomorphism; Software and Calculations; SYLOW SUBGROUPS; The Sylow Theorems; Groups of Small Order; A List; A Calculation; SIMPLE GROUPS; Composition Series; Simplicity of An; Simplicity of PSL(2, Fp); ABELIAN GROUPS; Free Abelian Groups; Row and Column Reduction of Integer Matrices; Classification Theorems; Invariance of Elementary Divisors; The Multiplicative Group of the Integers Mod n; POLYNOMIAL RINGS; Basic Properties of Polynomials; Unique Factorization into Irreducibles; Finding Irreducible Polynomials; Commutative Rings; Congruences; Factoring Polynomials over a Finite Field; Calculations; SYMMETRIC POLYNOMIALS; Polynomials in Several Variables; Symmetric Polynomials and Functions; Sums of Powers; Discriminants; Software; ROOTS OF EQUATIONS; Introduction; Extension Fields; Degree of an Extension; Splitting Fields; Cubics; Cyclotomic Polynomials; Finite Fields; Plots and Calculations; GALOIS GROUPS; Introduction; Definition; How Large is the Galois Group?; The Galois Correspondence; Discriminants; QUARTICS; Galois Groups of Quartics; The Geometry of the Cubic Resolvent; Software; THE GENERAL EQUATION OF THE nth DEGREE; Examples; Symmetric Functions; The Fundamental Theorem of Algebra; SOLUTION BY RADICALS; Formulas for a Cubic; Cyclic Extensions; Solution by Radicals in Higher Degrees; Calculations; RULER-AND-COMPASS CONSTRUCTIONS; Introduction; Algebraic Interpretation; Construction of Regular Polygons; Periods; APPENDIX: MATHEMATICA COMMANDS
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 512; Algebra; Algebra -- Computer programs
• Languages: English
• ISBNs: 9781351989688
• Related ISBNs: 9781482295696; 9781351992534; 9781315273167
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.