Topology of Numbers
by Allen Hatcher
Publisher: Cornell University 2014
Number of pages: 122
An introductory textbook on elementary number theory from a geometric point of view, as opposed to the usual strictly algebraic approach. A fair amount of the book is devoted to studying Conway's topographs associated to quadratic forms in two variables.
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by Thomas Taylor, A. J. Valpy
The substance of all that has been written on this subject by Nicomachus, Iamblichus, and Boetius, together with some particulars respecting perfect, amicable, and other numbers, which are not to be found in the writings of modern mathematicians.
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The book on elementary number theory: compositions and partitions, arithmetic functions, distribution of primes, irrational numbers, congruences, Diophantine equations; combinatorial number theory, and geometry of numbers.
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The purpose of this book is to give the reader a convenient introduction to the theory of numbers. The treatment throughout is made as brief as is possible consistent with clearness and is confined entirely to fundamental matters.
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One might think that of all areas of mathematics arithmetic should be the simplest, but it is a surprisingly deep subject. It is assumed that students have some familiarity with set theory, calculus, and a certain amount of mathematical maturity.