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Algebra and geometry

Author: Alan F Beardon
Publisher: Cambridge, UK ; New York : Cambridge University Press, 2005.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Beardon, Alan F.
Algebra and geometry.
Cambridge, UK ; New York : Cambridge University Press, 2005
(DLC) 2004051865
(OCoLC)55518087
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Alan F Beardon
ISBN: 0511112769 9780511112768 0511111746 9780511111747 9780511800436 0511800436 9781139636933 1139636936
OCLC Number: 667038228
Description: 1 online resource (xii, 326 pages) : illustrations
Contents: 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.
Responsibility: Alan F. Beardon.
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Abstract:

Unified introduction to algebra and geometry, emphasising links between the topics. It is ideal for self-study.  Read more...

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Unified introduction to algebra and geometry, emphasising links between the topics. It is ideal for self-study. Describing two cornerstones of mathematics, this basic textbook presents a unified Read more...

 
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