The series of expository lectures intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Topics: applications of noncommutative geometry to problems in ordinary geometry and topology, Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory, residue index theorem of Connes and Moscovici, etc.
This book is a concise, self-contained introduction to abstract algebra which stresses its unifying role in geometry and number theory. There is a strong emphasis on historical motivation- both to trace abstract concepts to their concrete roots, but also to show the power of new ideas to solve old problems. This approach shows algebra as an integral part of mathematics and makes this text more informative to both beginners and experts than others. Classical results of geometry and number theory are used to motivate and illustrate algebraic techniques, and classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory.
Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads
The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).
The Grail legends have been appropriated by novelists as diverse as Umberto Eco and Dan Brown yet very few have read for themselves the original stories from which they came. All the mystery and drama of the Arthurian world are embodied in the extraordinary tales of Perceval, Gawain, Lancelot and Galahad in pursuit of the Holy Grail. The original romances, full of bewildering contradictions and composed by a number of different writers, dazzle with the sheer wealth of their conflicting imagination.
Core Clinical Cases in Paediatrics: A Problem-Solving Approach
The core areas of undergraduate study are covered in a logical sequence of learning activities: each case is followed by a detailed answer, along with a number of OSCE-style questions to help you practise for the exam.
