Number theory

George E. Andrews

270 pages, parution le 01/10/1994

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Résumé

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.

Int this book the author solves the problem of maintaining the interest at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insight, while over students benefit from the consequent simplicity of the proofs for many theorems.

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.

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

L'auteur - George E. Andrews

is Evan Pugh Professor of Mathematics at the Pennsylvania State University. He is the author of many books in mathematics, including The Theory o/Partitions (Cambridge University Press). He is a member of the American Academy of Arts and Sciences. In 2003, he was elected to the National Academy of Sciences (USA).

Caractéristiques techniques

	PAPIER
Éditeur(s)	Dover
Auteur(s)	George E. Andrews
Parution	01/10/1994
Nb. de pages	270
Format	13,5 x 21,5
Couverture	Broché
Poids	290g
Intérieur	Noir et Blanc
EAN13	9780486682525
ISBN13	978-0-486-68252-5