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andrews g number theory 1971

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Textbook in PDF format Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more. Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic. In this book, the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. Among the topics covered in this accessible, carefully designed introduction are: •Multiplicativity-divisibility, including the fundamental theorem of arithmetic •Combinatorial and computational number theory •Congruences, arithmetic functions, primitive roots and prime numbers •Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory), and geometric number theory Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated. George Andrews is the reigning expert on partitions in the mathematical community who has written many seminal papers on the subject over the past half-century! If you don't know what partitions are in the theoretical sense, don't worry, the text provides ample introduction. You can find here an elementary introduction to the difficult, but extraordinarily powerful and elegant theory of partitions. The book covers the basics of number theory well, but it is the chapters on partitions that make this text stand out. It covers the Rogers-Ramanujan identities as well as the Jacobi triple product identity. It is rare in the mathematical community that an expert in a subject also writes a ground-level introductory text - but that's what you have here. Multiplicativity-Divisibility Basis Representation The Fundamental Theorem of Arithmetic Combinatorial and Computational Number Theory Fundamentals of Congruences Solving Congruences Arithmetic Functions Primitive Roots Prime Numbers Quadratic Congruences Quadratic Residues Distribution of Quadratic Residues Additivity Sums of Squares Elementary Partition Theory Partition Generating Functions Partition Identities Geometric Number Theory Lattice Points Appendices

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