TY  - BOOK
AU  - Beardon,Alan F
ED  - Cambridge University Press.
TI  - Algebra and geometry
SN  - 052181362X
AV  - QA155 .B36 2005
PY  - 2005///
CY  - Cambridge, UK, New York
PB  - Cambridge University Press
KW  - Algebra
KW  - Geometry
N1  - Includes index; Preface; -- 1. Groups and permutations; -- 1.1. Introduction; -- 1.2. Groups; -- 1.3. Permutations of a finite set; -- 1.4. The sign of a permutation; -- 1.5 Permutations of an arbitrary set; -- 2. The real numbers; -- 2.1. The integers; -- 2.2. The real numbers; -- 2.3. Fields; -- 2.4. Modular arithmetic; -- 3. The complex plane; -- 3.1. Complex numbers; -- 3.2. Polar coordinates; -- 3.3. Lines and circles; -- 3.4. Isometries of the plane; -- 3.5. Roots of unity; -- 3.6. Cubic and quartic equations; -- 3.7. The fundamental theorem of algebra; -- 4. Vectors in three-dimensional space; -- 4.1. Vectors; -- 4.2. The scalar product; -- 4.3. The vector product; -- 4.4. The scalar triple product; -- 4.5. The vector triple product; -- 4.6. Orientation and determinant s-; -- 4.7. Applications to geometry; -- 4.8. Vector equations; -- 5. Spherical geometry; -- 5.1. Spherical distance; -- 5.2. Spherical trigonometry-- 5.3. Area on the sphere; -- 5.4. Euler's formula; -- 5.5. Regular polyhedra; -- 5.6. General polyhedra; -- 6. Quaternions and isometries; -- 6.1. Isometries of Euclidean space; -- 6.2. Quaternions; -- 6.3. Reflections and rotations; -- 7. Vector spaces; -- 7.1. Vector spaces; -- 7.2. Dimension; -- 7.3. Subspaces; -- 7.4. The direct sum of two subspaces; -- 7.5. Linear difference equations; -- 7.6. The vector space of polynomials; -- 7.7. Linear transformations; -- 7.8. The kernel of a linear transformation; -- 7.9. Isomorphisms; -- 7.10. The space of linear maps; -- 8. Linear equations; -- 8.1. Hyperplanes; -- 8.2. Homogeneous linear equations; -- 8.3. Row rank and column rank; -- 8.4. Inhomogeneous linear equations; -- 8.5. Determinants and linear equations; -- 8.6. Determinants; -- 9. Matrices; -- 9.1. The vector space of matrices; -- 9.2. A matrix as a linear transformation; -- 9.3. The matrix of a linear transformation; -- 9.4. Inverse maps and matrices; -- 9.5. Change of bases; -- 9.6. The resultant of two polynomials; -- 9.7. The number of surjections; -- 10. Eigenvectors; -- 10.1. Eigenvalues and eigenvectors; -- 10.2. Eigenvalues and matrices; -- 10.3. Diagonalizable matrices; -- 10.4. The Cayley-Hamilton theorem; -- 10.5. Invariant planes; 11. Linear maps of euclidean space; -- 11.1. Distance in Euclidean space; -- 11.2. Orthogonal maps; -- 11.3. Isometries of Euclidean n-space; -- 11.4. Symmetric matrices; -- 11.5. The field axioms; -- 11.6. Vector products in higher dimensions; -- 12. Groups; -- 12.1. Groups; -- 12.2. Subgroups and cosets; -- 12.3. Lagrange's theorem; -- 12.4. Isomorphisms; -- 12.5. Cyclic groups; -- 12.6. Applications to arithmetic; -- 12.7. Product groups; -- 12.8. Dihedral groups; -- 12.9. Groups of small order; -- 12.10. Conjugation; -- 12.11. Homomorphisms; -- 12.12. Quotient groups; -- 13. Möbius transformations; -- 13.1. Möbius transformations; -- 13.2. Fixed points and uniqueness; -- 13.3. Circles and lines; -- 13.4. Cross-ratios; -- 13.5. Möbius maps and permutations; -- 13.6. Complex lines; -- 13.7. Fixed points and eigenvectors; -- 13.8. A geometric view of infinity; -- 13.9. Rotations of the sphere; -- 14. Group actions; -- 14.1. Groups of permutations; -- 14.2. symmetries of a regular polyhedron; -- 14.3. Finite rotation groups in space; -- 14.4. Groups of isometries of the plane; -- 14.5. Group actions; -- 15. Hyperbolic geometry; -- 15.1. The hyperbolic plane; -- 15.2. The hyperbolic distance; -- 15.3. Hyperbolic circles; -- 15.4. Hyperbolic trigonometry; -- 15.5. Hyperbolic three-dimensional space; -- 15.6. Finite Möbius groups; -- Index
N2  - Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry
ER  -