Hardback
Series: Spectrum
ISBN:9780883855768
Dimensions: 247 x 174 mm
available from February 2012
Mathematical ideas have an aesthetic appeal that can be appreciated by anyone who has the time and dedication to investigate. Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions and unsolved problems. Readers will discover exciting mathematics topics from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared. Who should read this book? There is something new for any mathematically minded person. High school and college students will find motivation for their mathematical studies. Professional mathematicians will find fresh examples of mathematical beauty to pass along to others. Within each chapter, the topics require progressively more prerequisite knowledge. An appendix gives background definitions and theorems, while another gives challenging exercises (with solutions).
Preface
1. Imaginative words
2. Intriguing images
3. Captivating formulas
4. Delightful theorems
5. Pleasing proofs
6. Elegant solutions
7. Creative problems
Appendix A. Harmonious foundations
Appendix B. Eye-opening explorations.
Paperback
Series: London Mathematical Society Lecture Note Series(No. 396)
ISBN:9781107674141
Dimensions: 228 x 152 mm
available from January 2012
1. Introduction
2. The p-adic numbers Q_p
3. Some classical analysis on Q_p
4. Analytic functions on Z_p
5. Arithmetic differential operators on Z_p
6. A general view of arithmetic differential operators
7. Analyticity of arithmetic differential operators
8. Characteristic functions: standard p-adic coordinates
9. Characteristic functions: harmonic arithmetic coordinates
10. Differences between arithmetic differential operators over Z_p and Z_p^{unr}
References.
Hardback
ISBN:9781107020832
430 b/w illus. 15 tables 375 exercises
Dimensions: 247 x 174 mm
available from March 2012
With hundreds of worked examples, exercises and illustrations, this detailed exposition of the theory of Vassiliev knot invariants opens the field to students with little or no knowledge in this area. It also serves as a guide to more advanced material. The book begins with a basic and informal introduction to knot theory, giving many examples of knot invariants before the class of Vassiliev invariants is introduced. This is followed by a detailed study of the algebras of Jacobi diagrams and 3-graphs, and the construction of functions on these algebras via Lie algebras. The authors then describe two constructions of a universal invariant with values in the algebra of Jacobi diagrams: via iterated integrals and via the Drinfeld associator, and extend the theory to framed knots. Various other topics are then discussed, such as Gauss diagram formulae, before the book ends with Vassiliev's original construction.
1. Knots and their relatives
2. Knot invariants
3. Finite type invariants
4. Chord diagrams
5. Jacobi diagrams
6. Lie algebra weight systems
7. Algebra of 3-graphs
8. The Kontsevich integral
9. Framed knots and cabling operations
10. The Drinfeld associator
11. The Kontsevich integral: advanced features
12. Braids and string links
13. Gauss diagrams
14. Miscellany
15. The space of all knots
Appendix
References
Notations
Index.
2 Hardback books
Series: The Cambridge China Library
ISBN:9781107020016
Dimensions: 247 x 174 mm
available from March 2012
The self-taught mathematician Hua Loo-Keng (1910?1985) spent most of his working life in China and suffered at first hand the turbulence of twentieth-century Chinese politics. His influence has been credited with inspiring generations of mathematicians, while his papers on number theory are regarded as 'virtually an index to the major activities in that subject during the first half of the twentieth century.' Introduction to Higher Mathematics is based on the lectures given by Hua at the University of Science and Technology of China from 1958. The course reflects Hua's instinctive technique, using the simplest tools to tackle even the most difficult problems, and contains both pure and applied mathematics, emphasising the interdependent relationships between different branches of the discipline. With hundreds of diagrams, examples and exercises, this is a wide-ranging reference text for university mathematics and a testament to the teaching of one of the most eminent mathematicians of his generation.
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Paperback
ISBN:9780521279482
20 b/w illus. 150 exercises
Dimensions: 247 x 174 mm
available from April 2012
Any student studying linear algebra will welcome this textbook, which provides a thorough, yet concise, treatment of key topics in university linear algebra courses. The authors, who have extensive teaching experience, provide hundreds of examples and exercises with a complete list of solutions, to enable students to practise and master the standard methods. Crucially, the authors also give clear explanations of how the methods really work, so that readers can gain a sound understanding of the underlying theory. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book. At every stage the authors take care to ensure that the discussion is no more complicated or abstract than it needs to be and focuses only on the fundamental topics. Instructors can draw on the many examples and exercises to supplement their own assignments.
Preface
Preliminaries: before we begin
1. Matrices and vectors
2. Systems of linear equations
3. Matrix inversion and determinants
4. Rank, range and linear equations
5. Vector spaces
6. Linear independence, bases and dimension
7. Linear transformations and change of basis
8. Diagonalisation
9. Applications of diagonalisation
10. Inner products and orthogonality
11. Orthogonal diagonalisation and its applications
12. Direct sums and projections
13. Complex matrices and vector spaces
14. Comments on exercises
Index.
Hardback
Series: Spectrum
ISBN:9780883855751
Dimensions: 247 x 174 mm
available from June 2012
Calculus answers questions that had been explored for centuries before calculus was born. Calculus and Its Origins begins with these ancient questions and details the remarkable story of how subsequent scholars wove these inquiries into a unified theory. This book does not presuppose knowledge of calculus, it requires only a basic knowledge of geometry and algebra (similar triangles, polynomials, factoring). Inside you will find the accounts of how Archimedes discovered the area of a parabolic segment, ibn Al-Haytham calculated the volume of a revolved area, Jyesthadeva explained the infinite series for sine and cosine, Wallis deduced the link between hyperbolas and logarithms, Newton generalized the binomial theorem, Leibniz discovered integration by parts, and much more. Each chapter ends with further results, in the form of exercises, by such luminaries as Pascal, Maclaurin, Barrow, Cauchy and Euler.
Preface
1. The Ancients
2. East of Greece
3. Motion
4. Indivisibles
5. Quadrature
6. The Fundamental Theorem of Calculus
7. Notation
8. Chords
9. Zero over zero
10. Rigor.