000			04600nam a2200337 i 4500
008			040521s2005 enka 001 0 eng
010			_a2004051865
020			_a052181362X _qhardback
020			_a0521890497 _qpbk.
040			_aDLC _cDLC _dDLC _dNhCcYBP _dBAUN
049			_aBAUN_MERKEZ
050	0	4	_aQA155 _b.B36 2005
082	0	0	_222
100	1		_aBeardon, Alan F
245	1	0	_aAlgebra and geometry / _cAlan F. Beardon
264		1	_aCambridge, UK ; _aNew York : _bCambridge University Press, _c2005.
300			_axii, 326 pages : _billustrations ; _c23 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
500			_aIncludes index
505	0	0	_tPreface _t-- 1. Groups and permutations _t-- 1.1. Introduction _t-- 1.2. Groups _t-- 1.3. Permutations of a finite set _t-- 1.4. The sign of a permutation _t-- 1.5 Permutations of an arbitrary set _t-- 2. The real numbers _t-- 2.1. The integers _t-- 2.2. The real numbers _t-- 2.3. Fields _t-- 2.4. Modular arithmetic _t-- 3. The complex plane _t-- 3.1. Complex numbers _t-- 3.2. Polar coordinates _t-- 3.3. Lines and circles _t-- 3.4. Isometries of the plane _t-- 3.5. Roots of unity _t-- 3.6. Cubic and quartic equations _t-- 3.7. The fundamental theorem of algebra _t-- 4. Vectors in three-dimensional space _t-- 4.1. Vectors _t-- 4.2. The scalar product _t-- 4.3. The vector product _t-- 4.4. The scalar triple product _t-- 4.5. The vector triple product _t-- 4.6. Orientation and determinant s- _t-- 4.7. Applications to geometry _t-- 4.8. Vector equations _t-- 5. Spherical geometry _t-- 5.1. Spherical distance _t-- 5.2. Spherical trigonometry-- 5.3. Area on the sphere _t-- 5.4. Euler's formula _t-- 5.5. Regular polyhedra _t-- 5.6. General polyhedra _t-- 6. Quaternions and isometries _t-- 6.1. Isometries of Euclidean space _t-- 6.2. Quaternions _t-- 6.3. Reflections and rotations _t-- 7. Vector spaces _t-- 7.1. Vector spaces _t-- 7.2. Dimension _t-- 7.3. Subspaces _t-- 7.4. The direct sum of two subspaces _t-- 7.5. Linear difference equations _t-- 7.6. The vector space of polynomials _t-- 7.7. Linear transformations _t-- 7.8. The kernel of a linear transformation _t-- 7.9. Isomorphisms _t-- 7.10. The space of linear maps _t-- 8. Linear equations _t-- 8.1. Hyperplanes _t-- 8.2. Homogeneous linear equations _t-- 8.3. Row rank and column rank _t-- 8.4. Inhomogeneous linear equations _t-- 8.5. Determinants and linear equations _t-- 8.6. Determinants _t-- 9. Matrices _t-- 9.1. The vector space of matrices _t-- 9.2. A matrix as a linear transformation _t-- 9.3. The matrix of a linear transformation _t-- 9.4. Inverse maps and matrices _t-- 9.5. Change of bases _t-- 9.6. The resultant of two polynomials _t-- 9.7. The number of surjections _t-- 10. Eigenvectors _t-- 10.1. Eigenvalues and eigenvectors _t-- 10.2. Eigenvalues and matrices _t-- 10.3. Diagonalizable matrices _t-- 10.4. The Cayley-Hamilton theorem _t-- 10.5. Invariant planes
505	0		_a11. Linear maps of euclidean space _t-- 11.1. Distance in Euclidean space _t-- 11.2. Orthogonal maps _t-- 11.3. Isometries of Euclidean n-space _t-- 11.4. Symmetric matrices _t-- 11.5. The field axioms _t-- 11.6. Vector products in higher dimensions _t-- 12. Groups _t-- 12.1. Groups _t-- 12.2. Subgroups and cosets _t-- 12.3. Lagrange's theorem _t-- 12.4. Isomorphisms _t-- 12.5. Cyclic groups _t-- 12.6. Applications to arithmetic _t-- 12.7. Product groups _t-- 12.8. Dihedral groups _t-- 12.9. Groups of small order _t-- 12.10. Conjugation _t-- 12.11. Homomorphisms _t-- 12.12. Quotient groups _t-- 13. Möbius transformations _t-- 13.1. Möbius transformations _t-- 13.2. Fixed points and uniqueness _t-- 13.3. Circles and lines _t-- 13.4. Cross-ratios _t-- 13.5. Möbius maps and permutations _t-- 13.6. Complex lines _t-- 13.7. Fixed points and eigenvectors _t-- 13.8. A geometric view of infinity _t-- 13.9. Rotations of the sphere _t-- 14. Group actions _t-- 14.1. Groups of permutations _t-- 14.2. symmetries of a regular polyhedron _t-- 14.3. Finite rotation groups in space _t-- 14.4. Groups of isometries of the plane _t-- 14.5. Group actions _t-- 15. Hyperbolic geometry _t-- 15.1. The hyperbolic plane _t-- 15.2. The hyperbolic distance _t-- 15.3. Hyperbolic circles _t-- 15.4. Hyperbolic trigonometry _t-- 15.5. Hyperbolic three-dimensional space _t-- 15.6. Finite Möbius groups _t-- Index
520	1		_aDescribing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry
650		0	_aAlgebra _9275
650		0	_aGeometry.
710	2		_972911 _aCambridge University Press.
900			_a19530
900			_bSatın
942			_2lcc _cKT
999			_c16703 _d16703