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Undergraduate courses in mathematics are commonly of two types.
Onthe one hand are courses in subjects - such as linear algebra or
realanalysis - with which it is considered that every student of
mathematicsshould be acquainted. On the other hand are courses
given by lecturersin their own areas of specialization, which are
intended to serve as apreparation for research. But after taking
courses of only these twotypes, students might not perceive the
sometimes surprisinginterrelationships and analogies between
different branches ofmathematics, and students who do not go on to
become professionalmathematicians might never gain a clear
understanding of the natureand extent of mathematics.
This two-volume book is a modern introduction to the theory of
numbers, emphasizing its connections with other branches of
mathematics. Part A is accessible to first-year undergraduates and
deals with elementary number theory. Part B is more advanced and
gives the reader an idea of the scope of mathematics today. The
connecting theme is the theory of numbers. By exploring its many
connections with other branches a broad picture is obtained. The
book contains a treasury of proofs, several of which are gems
seldom seen in number theory books.
Number Theory is more than a comprehensive treatment of the
subject. It is an introduction to topics in higher level
mathematics, and unique in its scope; topics from analysis, modern
algebra, and discrete mathematics are all included.
The book is divided into two parts. Part A covers key concepts
of number theory and could serve as a first course on the subject.
Part B delves into more advanced topics and an exploration of
related mathematics. The prerequisites for this self-contained text
are elements from linear algebra. Valuable references for the
reader are collected at the end of each chapter. It is suitable as
an introduction to higher level mathematics for undergraduates, or
for self-study.
This work on the foundations of Euclidean geometry aims to present
the subject from the point of view of mathematics at the end of the
20th century, taking advantage of all the developments since the
appearance of Hilbert's classic work. Here real affine space is
characterized by a small number of axioms involving points and line
segments making the treatment self-contained and thorough, many
results being established under weaker hypotheses than usual. The
treatment should be accessible for final year undergraduates and
graduate students, and can also serve as an introduction to other
areas of mathematics such as matroids and antimatroids,
combinatorial convexity, the theory of polytopes, projective
geometry and functional analysis.
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