Paperback (ISBN-13: 9780521097932)
There was also a Hardback(1960) of this title but it is no longer available
Homological algebra, because of its fundamental nature, is relevant to many branches of pure mathematics, including number theory, geometry, group theory and ring theory. Professor Northcott’s aim is to introduce homological ideas and methods and to show some of the results which can be achieved. The early chapters provide the results needed to establish the theory of derived functors and to introduce torsion and extension functors. The new concepts are then applied to the theory of global dimensions, in an elucidation of the structure of commutative Noetherian rings of finite global dimension and in an account of the homology and cohomology theories of monoids and groups. A final section is devoted to comments on the various chapters, supplementary notes and suggestions for further reading. This book is designed with the needs and problems of the beginner in mind, providing a helpful and lucid account for those about to begin research, but will also be a useful work of reference for specialists. It can also be used as a textbook for an advanced course.
Preface; 1. Generalities concerning modules; 2. Tensor products and groups of homomorphisms; 3. Categories and functors; 4. Homology functors; 5. Projective and injective modules; 6. Derived functors; 7. Torsion and extension functors; 8. Some useful identities; 9. Commutative Noetherian rings of finite global dimension; 10. Homology and cohomology theories of groups and moniods; Notes; References; Index.
Paperback (ISBN-13: 9780521095907)
Here is a textbook of intuitive calculus. The material is presented in a concrete setting with many examples and problems chosen from the social, physical, behavioural and life sciences. Chapters include core material and more advanced optional sections. The book begins with a review of algebra and graphing.
Contents
1. Prerequisites; 2. Functional relationships; 3. Rate of Change; 4. Applications of the derivative; 5. Further differentiation; 6. Antidifferentation and integration; 7. Exponential functions; 8. Logarithmic functions; 9. Differential equations; 10. Further integration; 11. Trigonometric functions.
Series: MAA Problem Book Series
Paperback (ISBN-13: 9780883858257)
For over fifty years, the Mathematical Association of America (MAA) has been engaged in the construction and administration of challenging contests for students in American and Canadian high schools at every level of ability. In the year 2000 the MAA initiated the American Mathematics Competitions 10 (AMC 10), aimed at students in the first two years of high school. The Contest Problem Book VIII is the first collection of problems assembled from that competition covering the years 2001-2007. 350 problems and solutions are contained in this volume. A Problem Index at the back of the book classifies the problems into the following major subject areas: Algebra and Arithmetic, Sequences and Series, Triangle Geometry, Circle Geometry, Quadrilateral Geometry, Polygon Geometry, Counting Coordinate Geometry, Solid Geometry, Discrete Probability, Statistics, Number Theory, and Logic. These are then broken down into subcategories and problems are cross-referenced whenever they represent several subject areas.
* Contains 350 problems and solutions compiled by outstanding members of
the mathematical community * Suitable for secondary-school students of
all levels * Problems are categorised and indexed for easy reference
Preface; Problems; Solutions; Index of problems; About the editors.
Paperback (ISBN-13: 9780521093330)
Professor Sawyer’s book is based on a course given to the majority of engineering students in their first year at Toronto University. Its aim is to present the important ideas in linear algebra to students of average ability whose principal interests lie outside the field of mathematics; as such it will be of interest to students in other disciplines as well as engineering. The emphasis throughout is on imparting an understanding of the significance of the mathematical techniques and great care has therefore been taken to being out the underlying ideas embodied in the formal calculations. In those places where a rigorous treatment would be very long and wearisome, an explanation rather than a complete proof is provided, the reader being warned that in a more formal treatment such results would need to be be proved. The book is full of physical analogies (many from fields outside the realm of engineering) and contains many worked and unworked examples, integrated with the text.
Preface; 1. Mathematics and engineers; 2. Mappings; 3. The nature of generalisation; 4. Symbolic conditions for linearity; 5. Graphical representation; 6. Vectors in a plane; 7. Bases; 8. Calculations in a vector space; 9. Change of axes; 10. Specification of a linear mapping; 11. Transformations; 12. Choice of basis; 13. Complex numbers; 14. Calculations with complex numbers; 15. Complex numbers and trigonometry; 16. Trigonometry and exponentials; 17. Complex numbers: terminology; 19. The logic of complex numbers; 20. The algebra of transformations; 21. Subtraction of transformations’ 22. Matrix notation; 23. An application of matrix multiplication; 24. An application of linearity; 25. procedure for finding invariant lines, eigenvectors and eigenvalues; 26. Determinant and inverse; 27. Properties of determinants; 28. Matrices other than square; partitions; 29. Subscript and summation notation; 30. Row and column vectors; 31. Affine and Euclidean geometry; 32. Scalar products; 33. Transpose; quadratic forms; 34. Maximum and minimum principles; 35. Formal laws of matrix algebra; 36. Orthogonal transformations; 37. Finding the simplest expressions for quadratic forms; 38. Principal axes and eigenvectors; 39. Lines, planes and subspaces; vector product; 40. Null space, column space, row space of a matrix; 42. Illustrating the importance of orthogonal matrices; 43. Linear programming; 44. Linear programming, continued; Answers; Index.