Studies in Number Theory

Science & Math

Mathematics

Mathematical Assn of Amer

Calculus, invented by Newton and Leibniz in the seventeenth century, has played a decisive role in the development of mathematics and the growth of our present technological society. It is an indispensable tool of both the pure and applied sciences and is one of the cornerstones of modern mathematics. It has provided ways of understanding such phenomena as the velocity of a moving object at any moment, the rate at which moving objects change their speeds and, more generally, the way in which quantities vary as factors affecting them change. In this book, the author tells what calculus is about in simple nontechnical language, understandable to any interested reader.

What Is Calculus About?

Sawyer, Walter Warwick

The word "infinity" usually elicits feelings of awe, wonder and admiration; the concept infinity has fascinated philosophers and theologians. The author of this book, mindful of the popular meanings and connotations of the word, shows how professional mathematicians tame this unwieldy concept, come to terms with it, and use its various aspects as their most powerful tools of the trade. --Back cover.

Uses of Infinity

Zippin, Leo

This book is the sequel to Geometric Transfrmations I and II, volumes 8 and 21 in this series, but can be studied independently. It is devoted to the treatment of affine and projective transformations of the plane; these transformations include the congruences and similarities investigated in the previous volumes. The simple text and the many problems are designed mainly to show how the priniciples of affine and projective geometry  may be used to furnish relatively simple solutions of large classes of problems in elementary geometry, including some straight edge construction problems. In the Supplement, the reader is introduced to hyperbolic geometry. The latter part of the book consists of detailed solutions of the problems posed throughout the text.

Geometric Transformations III (New Mathematical Library)

Yaglom, I.M.

In this monograph, Ivan Niven, provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary technique. The last third of the monograph treats normal and transcendental numbers, including the transcendence of and its generalization in the Lindemann theorem, and the Gelfond-Schneider theorem. Most of the material in the first two-thirds of the book presupposes only calculus and beginning number theory. The results needed from analysis and algebra are central, and well-known theorems, and complete references to standard works are given to help the beginner. The chapters are for the most part independent. There is a set if bites at the

Irrational Numbers

Niven, Ivan

This concise monograph in probability by Mark Kac, a well-known mathematician, presumes a familiarity with Lebesgue's theory of measure and integration, the elementary theory of Fourier integrals, and the rudiments of number theory. Readers may then follow Dr. Kac's attempt "to rescue statistical independence from the fate of abstract oblivion by showing how in its simplest form it arises in various contexts cutting across different mathematical disciplines." The treatment begins with an examination of a formula of Vieta that extends to the notion of statistical independence. Subsequent chapters explore laws of large numbers and Émile Borel's concept of normal numbers; the normal law, as expressed by Abraham de Moivre and Andrey Markov's method; and number theoretic functions as well as the normal law in number theory. The final chapter ranges in scope from kinetic theory to continued fractions. All five chapters are enhanced by problems.

Statistical Independence in Probability Analysis and Number Theory (Carus Mathematical Monographs, No 12)

Kac, Marc

Combinatorial Mathematics: 014 (Carus Mathematical Monographs No. 14)

Ryser, Herbert

Dedekind Sums (Carus Mathematical Monographs)

Grosswald, Emil

Celestial Mechanics (The Carus Mathematical Monographs ; No. 18)

Pollard, Harry

Field Theory and its Classical Problems lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular n-gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond. The logical pathway is historic, but the terminology is consistent with modern treatments. No previous knowledge of algebra is assumed. Notable topics treated along this route include the transcendence of e and Ï€, cyclotomic polynomials, polynomials over the integers, Hilbert's irreducibility theorem, and many other gems in classical mathematics. Historical and bibliographical notes complement the text, and complete solutions are provided to all problems.

Field Theory and Its Classical Problems (Carus Mathematical Monographs ; No. 19)

Hadlock, Charles Robert

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