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Alexanderson G.L. (ed.), Klosinski L.F. (ed.), Larson L.C. (ed.) — William Lowell Putnam Mathematical Competition: Problems and Solutions 1965-1984
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Íàçâàíèå: William Lowell Putnam Mathematical Competition: Problems and Solutions 1965-1984Àâòîðû: Alexanderson G.L. (ed.), Klosinski L.F. (ed.), Larson L.C. (ed.)Àííîòàöèÿ: The Putnam Competition has since 1928 been providing a challenge to gifted college mathematics students. This book, the second of the Putnam Competition volumes, contains problems with their solutions for the years 1965-1984. Additional solutions are presented for many of the problems. Included is an essay on recollections of the first Putnam Exam by Herbert Robbins, as well as appendices listing the winning teams and students from 1965 through 1984. This volume offers the problem solver an enticing sample of challenging problems and their solutions. In 1980, the MAA published the first William Lowell Putnam Mathematical Competition book, covering the contest from 1938 to 1964. In 2002 the third of the Putnam problem books appeared, covering the years 1985 through 2000. All three of these books belong on the bookshelf of students, teachers, and all interested in problem solving.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1995Êîëè÷åñòâî ñòðàíèö: 147Äîáàâëåíà â êàòàëîã: 10.12.2009Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Abstract algebra, binary operations 1971 B—1 1972 A-2 1978 A—4 Abstract algebra, extension fields 1968 B—3 1980 A-4 Abstract algebra, finite fields 1979 B—3 Abstract algebra, group theory 1968 B—2 1969 B—2 1972 B—3 1975 B—1 1976 B—2 1977 B-6 Abstract algebra, mappings 1966 A—5 Area 1978 B—1 1979 B—5 1981 B—6 1984 A—4 1984 B-6 Arithmetic geometric mean inequality 1968 A—6 1975 B—6 1978 A-3 Arithmetic progressions 1972 A-1 1978 1979 A—3 Balanced triples 1977 B—3 Bernoulli polynomials 1981 B—1 1982 A-2 Binary operations 1971 B—1 1972 A—2 1978 A—4 1984 B-3 Binary representation 1981 B—5 1973 B—1 1984 B-5 Binomial coefficients 1965 B—4 1967 B—5 1971 A—4 1972 A-1 1974 A—4 1974 B-6 1977 A—5 1983 A-4 Calculus see Differential calculus Integral Real Cauchy — Schwarz inequality 1977 B—5 1978 A—6 1979 B—6 1982 B-6 Centroids 1982 A-1 1984 B—4 Chessboard 1981 A—2 clocks 1983 A—2 Coloring problems 1979 A—4 Combinatorial identities 1965 A—2 1974 A-4 Combinatorics 1965 A—5 1965 B—5 1967 A—6 1973 A—6 1974 A-1 1980 B—4 Combinatorics, inequalities 1978 A—6 Combinatorics, optimization 1974 B—1 complex numbers 1967 B—1 1973 B—2 1979 B-6 Complex numbers, algebra 1975 A—4 Complex numbers, graphing 1975 A—2 Complex variables 1972 B—6 Continuous functions 1966 A—5 1978 B-5 1982 B—5 Convex sets 1967 A—5 1969 B—4 1979 B-5 Decimal representation 1984 A—6 Determinants 1969 A—2 1978 A—2 1984 A-3 Difference equations 1980 B—3 Differences 1971 A—6 1974 A—6 1976 B-5 1983 A—4 Differential calculus, differentiation 1967 A—1 Differential calculus, maxima & minima 1970 A—2 1973 B-6 1981 B—2 Differential calculus, partial derivatives 1967 B—6 Differential calculus, rates 1970 B—4 1972 B-2 Differential equations 1975 A—5 1983 B-3 Differential equations, higher order 1966 B—6 Differential equations, homogeneous linear 1979 B—4 Differential equations, nonhomogeneous linear 1979 B—4 Differential equations, systems 1969 A—5 1971 B—5 1973 A-5 1982 A—4 Diophantine equations 1971 A—5 1978 B-4 1979 A—5 Dissections 1982 B—1 Equations, functional 1971 B—2 1979 A-2 Equations, systems 1967 A—6 1977 A—2 1980 A-5 Euler’s formula for polyhedra 1969 A—3 Extension fields 1968 B—3 1980 A-4 Factorials 1984 A—6 1984 B-1 Fermat’s theorem 1983 A—3 Fields, characteristic 1979 B—3 Finite fields 1979 B—3 Functions 1977 A—3 Functions, continuous 1966 A—5 1982 B-5 Functions, convex 1980 B—5 Functions, linear 1980 B—2 Games 1971 A—5 Gamma function 1984 A—5 Geometry see Plane geometry Plane Solid graphs 1965 A—4 Graphs, coloring 1979 A—4 Graphs, Hamiltonian circuits 1968 A—3 Graphs, incidence matrices 1965 A—4 Greatest integer function 1973 A—3 1979 A—5 1983 A—5 1983 B—2 1983 B-4 Group theory 1968 B—2 1969 B—2 1972 B-3 1975 B—1 1976 B—2 1977 B-6 Hamiltonian circuits 1968 A—3 Heron’s formula 1982 B—6 Higher plane curves, cycloids, etc 1971 B—5 Hyperbolic functions 1979 B—1 1980 B-1 Incidence matrices 1965 A—4 Inequalities, arithmetic mean-geometric mean 1968 A—6 1975 B-6 Inequalities, Cauchy — Schwarz 1966 B—3 1977 B-5 1979 B—6 Inequalities, functional considerations 1967 A-1 1967 B—6 1973 B—4 1973 B—6 1974 B—5 1978 A—5 1980 A-6 Inequalities, geometric (triangle, polygon, etc.) 1966 A—2 1966 B—1 1971 A—3 1973 A-1 1982 B—6 Inequalities, miscellaneous 1968 A—2 1978 B—6 1979 A—6 1980 A—4 1982 A-5 Inequalities, series 1966 B—3 1974 B—5 1980 B-1 Infinite products 1969 B—3 1970 B—1 1977 B-1 Infinite sequences 1965 A—3 1966 A-1 1966 A—3 1969 A—6 1969 B—3 1969 B—5 1970 A—4 1972 A—3 1978 B—3 1979 A—3 1980 B—3 1982 B—5 1983 A—5 1983 B-4 1983 B-5 Infinite series 1967 A—2 1967 B—5 1969 A-4 1970 A-1 1972 B—1 1972 B—6 1973 A-2 1975 B—5 1976 B—1 1977 A—4 1978 B-2 1979 A—6 1980 B—1 1981 B—5 1982 A—6 1984 A-2 Infinite series, convergence and divergence 1966 B—3 1969 B—5 Integral calculus 1980 A—5 Integral calculus, definite integrals 1965 B—1 1967 B-3 1968 A-1 1969 A—4 1970 B—1 1970 B—2 1970 B—4 1972 A—6 1973 B-4 1976 B—1 1979 B—2 1980 A—3 1980 A—6 1982 A—3 1983 B-5 Integral calculus, double integrals 1981 A—3 1981 B-6 1982 B—2 1983 A-6 Integral calculus, improper integrals 1968 B—4 1976 A-5 1982 A—3 Integral calculus, triple integrals 1984 A—5 Integral equations 1967 A—4 1980 A-5 Irrational numbers 1974 B—3 1977 B—3 1980 A-4 Isoperimetric problems 1972 A—4 L'Hopital’s rule 1979 B—2 1983 A-6 Lattice points 1981 A—6 Law of Cosines 1972 B—5 1983 A-2 Limits 1965 B—4 1966 A—3 1966 A—6 1967 B—3 1969 B—5 1970 A—4 1972 A—3 1974 B—2 1976 B—1 1978 B—3 1979 B-2 1981 A-1 1981 A—3 1981 B—1 1982 B—3 1983 B-5 Linear algebra, determinants 1969 A—2 1978 A-2 Linear algebra, incidence matrices 1965 A—4 Linear algebra, matrices 1968 B—5 1969 B—6 1981 B-4 Linear algebra, permutation matrices 1967 A—2 Linear algebra, symmetric matrices 1967 A—2 Linear functions 1980 B—2 Linear programming 1980 B—2 Locker room problem 1967 B—4 Mappings 1966 A—5 Mappings, binary operations 1978 A—4 Mathematical induction 1978 B—3 1978 B-6 Matrices 1967 A—2 1968 B—5 1969 B-6 1981 B—4 1984 A-3 Maxima 1983 A—2 Maximum & minimum problems 1975 A—3 1978 B—5 1979 A-1 1981 B—2 1984 A-4 1984 B—2 Multivariable calculus 1975 A—3 Normal lines 1979 B—1 Number theory 1966 A—4 1974 A—3 1976 A-3 Number theory, arithmetic 1975 A—1 Number theory, congruences 1968 B—5 1969 B—1 1973 B—1 1977 A—5 1983 A-3 Number theory, Diophantine equations 1971 A—5 1978 B—4 1979 A-1 Number theory, divisibility 1966 B—2 1966 B—4 1971 B—1 1971 B—6 1972 A—5 1973 B-3 1981 A-1 1981 B—3 1982 B—4 1983 A-1 1983 A—3 Number theory, Euler phi-function 1968 B—3 1972 A-5 Number theory, Fermat’s theorem 1983 A—3 Number theory, irrational numbers 1974 B—3 1977 B-3 1980 A—4 Number theory, least common multiple 1980 A—2 Number theory, multiplicative functions 1967 B—4 Number theory, Pythagorean triples 1965 B—3 Number theory, relatively prime integers 1974 A—1 Number theory, representation of integers 1970 A—3 1973 B—1 1981 B—5 1983 B-2 Number theory, sums of divisors 1969 B—1 1976 B-6 Partial derivatives 1967 B—6 Permutation matrices 1967 A—2 permutations 1982 A—6 Pick’s Theorem 1971 A—3 Pigeonhole Principle 1971 A-1 1978 A-1 1980 A—4 Plane analytic geometry 1965 A—6 1972 A-4 1977 A-1 Plane analytic geometry, ellipses 1976 B—4 Plane analytic geometry, higher plane curves 1971 B—5 Plane analytic geometry, hyperbolas 1967 B—2 Plane analytic geometry, parabolas 1974 A—5 1980 A-1 Plane geometry and mechanics 1974 A—2 Plane geometry, circles 1965 B—6 Plane geometry, impossible constructions 1968 B—3 Plane geometry, lattices 1971 A—3 Plane geometry, minimum problem 1976 A—1 Plane geometry, octagons 1978 B—1 Plane geometry, pentagons 1984 A—4 Plane geometry, polygons 1966 B—1 1966 B—5 1967 B—1 1969 A—3 1978 B—1 1981 B—6 1984 B-6 Plane geometry, quadrilaterals 1970 B—6 1972 B-5 Plane geometry, triangles 1965 A-1 1965 B—3 1966 A-2 1971 A—3 1973 A—1 1981 A—6 1982 B—1 1982 B-6 Points, collinear 1979 A—4 POLYGONS 1984 B—1 Polyhedra 1980 B—2 Polynomials 1967 A—3 1968 A—5 1968 A-6 1970 B—2 1971 A—2 1971 A—4 1972 B—4 1973 B—5 1974 A—6 1975 A—4 1976 B-5 1978 B—3 1978 B—5 1979 A—5 1980 A-1 1981 A—5 1983 B-6 Polynomials, irreducible 1979 B—3 Polynomials, two variables 1969 A-1 1970 B—2 1976 A-2 probability 1968 B—1 1970 A—6 1976 B-3 1982 B—3 Progressions 1972 A-1 1978 A-1 1979 A—3 Quickest descent problem 1974 A—2 Rational numbers 1973 B—2 1978 B—2 1980 B—6 1981 B-5 Real analysis 1970 B—3 1971 A—6 1972 B-2 1976 A—6 1978 A—5 1983 A—5 1984 B-4 Real analysis, compact sets 1968 B—6 Real analysis, continuity 1970 B—5 1972 A—3 1973 A—4 1974 B—4 1977 A—6 1979 A-2 Real analysis, limits 1974 B—2 Real analysis, measure theory 1972 A—6 Real analysis, minimizing an integral 1978 A—3 Real analysis, Taylor’s remainder theorem 1974 B—5 Recurrence relations 1966 A—3 1967 A-2 1969 A—6 1971 B—6 1973 B—5 1975 B-5 1979 A—3 1980 B—3 1980 B—6 1982 B-5 1983 B—2 1983 B-4 Reflection 1981 A—4 Representation of Integers 1983 B—2 Rolle’s Theorem 1973 A—4 1980 A—5 1981 A-5 Sequences see Infinite sequences Series see Infinite series Sets 1968 A—3 1975 B—1 1980 B-4 Solid analytic geometry 1970 A—5 1971 B-4 Solid geometry, covering problems 1975 B—2 Solid geometry, cubes 1983 B—1 Solid geometry, lattices 1971 A—1 Solid geometry, polyhedra 1980 B—2 Solid geometry, quadrilaterals 1977 B—2 Solid geometry, spheres 1968 A—4 1983 B-1 Solid geometry, triangles 1975 A—6 Symmetric functions, polynomials in several variables 1975 B—3 tangents 1980 A—1 Theory of equations, roots 1968 A—6 1976 A—4 1977 A-1 Topology, closed curve in the plane 1977 B—4 Topology, connectedness 1975 B—4 Triangle inequality 1979 A—4 Triangular numbers 1975 A—1 Trigonometric functions 1967 A—1 Trigonometry 1974 B—3 Trigonometry, Law of Cosines 1983 A—2 Vectors 1968 A—4 1975 A—6 1983 A-2 volumes 1983 B—1 1984 A-1 Wallis product 1969 B—3 1983 B-5
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