Wednesday, June 19, 2019

Number Theory An Introduction to Mathematics (2nd Edition)

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Undergraduate courses in mathematics are commonly of two types. On the one hand there are courses in subjects, such as linear algebra or real analysis, with which it is considered that every student of mathematics should be acquainted. On the other hand there are courses given by lecturers in their own areas of specialization, which are intended to serve as a preparation for research. There are, I believe, several reasons why students need more than this.

First, although the vast extent of mathematics today makes it impossible for any individual to have a deep knowledge of more than a small part, it is important to have some understanding and appreciation of the work of others. Indeed the sometimes surprising interrelationships and analogies between different branches of mathematics are both the basis for many of its applications and the stimulus for further development. Secondly, different branches ofmathematics appeal in differentways and require different talents. It is unlikely that all students at one university will have the same interests and aptitudes as their lecturers. Rather, they will only discover what their own interests and aptitudes are by being exposed to a broader range. Thirdly, many students of mathematics will become, not professional mathematicians, but scientists, engineers or schoolteachers. It is useful for them to have a clear understanding of the nature and extent of mathematics, and it is in the interests of mathematicians that there should be a body of people in the community who have this understanding.

Preface to the Second Edition
Part A
I. The Expanding Universe of Numbers
II. Divisibility
III. More on Divisibility
IV. Continued Fractions and Their Uses
V. Hadamard’s Determinant Problem
VI. Hensel’s p-adic Numbers
Part B
VII. The Arithmetic of Quadratic Forms
VIII. The Geometry of Numbers
IX. The Number of Prime Numbers
X. A Character Study
XI. Uniform Distribution and Ergodic Theory
XII. Elliptic Functions
XIII. Connections with Number Theory

Author Details
"W.A. Coppel"

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