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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.
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