Andrews G.E. — Number Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Andrews G.E. — Number Theory

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Название: Number Theory

Автор: Andrews G.E.

Аннотация:

Most mathematics majors first encounter number theory in courses on abstract algebra, for which number theory provides numerous examples of algebraic systems, such as finite groups, rings, and fields. The instructor of undergraduate number theory thus faces a predicament. He must interest advanced mathematics students, who have previously studied congruences and the fundamental theorem of arithmetic, as well as other students, mostly from education and liberal arts, who usually need a careful exposition of these basic topics.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 259

Добавлена в каталог: 02.02.2010

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Предметный указатель

Radix representation      see "Basis representation"
Ramanujan identities      see "Rogers — Ramanujan identities"
Ramanujan's congruence      150
Ramanujan, S.      149—150 156 175—176
Ratio Test      42 215
Reduced residue system      54—55 93—97
Reflexive property      50
Relatively prime      20
Residue systems      52—56
Residue, definition of      52
Riemann hypothesis      112
Riffling      56—57 see
Rings, finite      v 55
Riordan, J.      227 232
Rogers — Ramanujan identities      175—176 179—188 229
Rogers — Ramanujan identities, discovery of      156—157
Rogers — Ramanujan identities, products      188—190
Rogers — Ramanujan identities, series      188—190
Rogers, L.J.      156 175—176
Rule of nines      64
Ryser, H.      v
Schur's theorem      176 190—195 229
Schur, I.J.      156 158 176 190—191
Selberg, A.      100
Self-conjugate partitions      153
Series      see "Infinite series"
Sierpinski, W.      206
Signum of x      119
Solution of Linear Diophantine Equation      23
Square-free number      85 90 105
Sums of consecutive integers (Exercise 4)      84
Sums of divisors and divisor function      92
Sums of divisors and Moebius pairs      89—90
Sums of divisors and numerical table      48
Sums of divisors as arithmetic function      1 75
Sums of divisors as multiplicative function      85—86
Sums of divisors, formulae for      82—85
Sums of divisors, historical note      228
Sums of divisors, table of      77
Sums of squares      141—148

Sums of squares and geometric number theory      199
Sums of squares and numerical table      47
Sums of squares, four squares      143—148
Sums of squares, historical note      229
Sums of squares, three squares      148 206
Sums of squares, two squares      141—143 147—148
Sums of squares, two squares and Gauss's Circle Problem      201—206
Sums of squares, two squares and geometric number theory      199
Sums of squares, two squares and quadratic residues      138
Sums of squares, two squares, table of      202
Sun-Tsu      58 68
Symmetric property      50
Taylor series      43 73
Tchebychev's theorem      106—111
Tchebychev, P.      100
Texts, algebra      55
Texts, programming      47
Theory of numbers      see "Number theory"
Three-square problem      see "Sums of three squares"
Totient function      see "Euler's $\phi$ -function"
Transitive property      50
Tuckerman, B.      112
Twin Primes Problem      111
Two-square problem      see "Sums of two squares"
Unique modulo c      60
Units, Group of      55
Universal exponent $\lambda(m)$       65
Uspensky, J.V.      227 232
Vandermonde convolution (Exercise 3)      43—44
Vinogradov, I.M.      111 147
Waring's problem      147
Waring, E.      38 146—147
Watson, G.N.      176
Weiss, E.      230 232
Wilson's theorem, as a congruence      49
Wilson's theorem, combinatorial proof of      38—40
Wilson's theorem, historical note      227 228
Wilson's theorem, proof by congruences      61—66
Wilson, Sir John      38
World Almanac      20
Wright, E.M.      230—231

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