By Titu Andreescu
Number conception, an ongoing wealthy quarter of mathematical exploration, is famous for its theoretical intensity, with connections and purposes to different fields from illustration thought, to physics, cryptography, and extra. whereas the leading edge of quantity idea is replete with subtle and recognized open difficulties, at its beginning are easy, hassle-free principles that could stimulate and problem starting scholars. This full of life introductory textual content makes a speciality of a problem-solving method of the subject.
Key positive aspects of quantity concept: constructions, Examples, and Problems:
* A rigorous exposition starts off with the normal numbers and the basics.
* vital strategies are provided with an instance, which could additionally emphasize an software. The exposition strikes systematically and intuitively to discover deeper properties.
* issues comprise divisibility, certain factorization, modular mathematics and the chinese language the rest Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and different particular numbers, and specific sequences. Sections on mathematical induction and the pigeonhole precept, in addition to a dialogue of alternative quantity structures are covered.
* exact routines make stronger and inspire the reader, with chosen recommendations to a few of the problems.
* word list, bibliography, and entire index around out the text.
Written via exceptional examine mathematicians and well known lecturers, this article is a transparent, available advent to the topic and a resource of attention-grabbing difficulties and puzzles, from complicated highschool scholars to undergraduates, their teachers, and common readers in any respect levels.