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Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.
The field of geometric variational problems is fast-moving and influential. These problems interact with many other areas of mathematics and have strong relevance to the study of integrable systems, mathematical physics and PDEs. The workshop 'Variational Problems in Differential Geometry' held in 2009 at the University of Leeds brought together internationally respected researchers from many different areas of the field. Topics discussed included recent developments in harmonic maps and morphisms, minimal and CMC surfaces, extremal Kahler metrics, the Yamabe functional, Hamiltonian variational problems and topics related to gauge theory and to the Ricci flow. These articles reflect the whole spectrum of the subject and cover not only current results, but also the varied methods and techniques used in attacking variational problems. With a mix of original and expository papers, this volume forms a valuable reference for more experienced researchers and an ideal introduction for graduate students and postdoctoral researchers.
Chess puzzles for the Casual Player, Vol. 1 contains 50 highly instructive puzzles illustrated by 776 move by move diagrams. Each puzzle contains two parts (see sample puzzles at www.chesspuzzlebook.com ). First, you are shown a move that may seem good but is actually bad and asked how to take advantage of it. Second, you are asked what a better move would have been in the first place. This two part puzzle training technique helps you learn how to take advantage of opponents' blunders and also how to avoid them yourself. The positions come from real games between average casual players. Every solution is generated and verified by sophisticated professional chess analysis software. The solution to every puzzle is fully illustrated, and explained with easy to understand text.
Suchen Sie nach einer Starthilfe fur Ihr Bachelor- oder Lehramt-Mathematikstudium? Haben Sie mit dem Studium vielleicht schon begonnen und fuhlen sich nun von Ihrem bisherigen Lieblingsfach eher verwirrt? Keine Panik Dieser freundliche Ratgeber wird Ihnen den Ubergang in die Welt des mathematischen Denkens erleichtern. Wenn Sie das Buch durcharbeiten, werden Sie mit einem Arsenal an Techniken vertraut, mit denen Sie sich Definitionen, Satze und Beweise erschliessen konnen. Sie lernen, wie man typische Aufgaben lost und mathematisch exakt formuliert. Unter anderem sind alle wesentlichen Beweismethoden abgedeckt: direkter Beweis, Fallunterscheidungen, Induktion, Widerspruchsbeweis, Beweis durch Kontraposition. Da stets konkrete Beispiele den Stoff vertiefen, gewinnen Sie ausserdem reichhaltige praktische Erfahrung mit Themen, die in vielen einfuhrenden Vorlesungen nicht vorkommen: Aquivalenzrelationen, Injektivitat und Surjektivitat von Funktionen, Kongruenzrechnung, der euklidische Algorithmus, und vieles mehr. An uber 300 Ubungsaufgaben konnen Sie Ihren Fortschritt uberprufen so werden Sie schnell lernen, wie ein Mathematiker zu denken und zu formulieren. Studierende haben das Material uber viele Jahre hinweg getestet. Das Buch ist nicht nur unentbehrlich fur jeden Studienanfanger der Mathematik, sondern kann Ihnen auch dann weiterhelfen, wenn Sie Ingenieurwissenschaften oder Physik studieren und einen Zugang zu den Themen des mathematischen Grundstudiums benotigen, oder wenn Sie sich mit Gebieten wie Informatik, Philosophie oder Linguistik beschaftigen, in denen Kenntnisse in Logik vorausgesetzt werden. "
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