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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
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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: William Lowell Putnam Mathematical Competition: Problems and Solutions 1965-1984

: Alexanderson G.L. (ed.), Klosinski L.F. (ed.), Larson L.C. (ed.)

:

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.


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Abstract algebra, binary operations      1971 B1 1972 A-2 1978 A4
Abstract algebra, extension fields      1968 B3 1980 A-4
Abstract algebra, finite fields      1979 B3
Abstract algebra, group theory      1968 B2 1969 B2 1972 B3 1975 B1 1976 B2 1977 B-6
Abstract algebra, mappings      1966 A5
Area      1978 B1 1979 B5 1981 B6 1984 A4 1984 B-6
Arithmetic geometric mean inequality      1968 A6 1975 B6 1978 A-3
Arithmetic progressions      1972 A-1 1978 1979 A3
Balanced triples      1977 B3
Bernoulli polynomials      1981 B1 1982 A-2
Binary operations      1971 B1 1972 A2 1978 A4 1984 B-3
Binary representation      1981 B5 1973 B1 1984 B-5
Binomial coefficients      1965 B4 1967 B5 1971 A4 1972 A-1 1974 A4 1974 B-6 1977 A5 1983 A-4
Calculus      see Differential calculus Integral Real
Cauchy Schwarz inequality      1977 B5 1978 A6 1979 B6 1982 B-6
Centroids      1982 A-1 1984 B4
Chessboard      1981 A2
clocks      1983 A2
Coloring problems      1979 A4
Combinatorial identities      1965 A2 1974 A-4
Combinatorics      1965 A5 1965 B5 1967 A6 1973 A6 1974 A-1 1980 B4
Combinatorics, inequalities      1978 A6
Combinatorics, optimization      1974 B1
complex numbers      1967 B1 1973 B2 1979 B-6
Complex numbers, algebra      1975 A4
Complex numbers, graphing      1975 A2
Complex variables      1972 B6
Continuous functions      1966 A5 1978 B-5 1982 B5
Convex sets      1967 A5 1969 B4 1979 B-5
Decimal representation      1984 A6
Determinants      1969 A2 1978 A2 1984 A-3
Difference equations      1980 B3
Differences      1971 A6 1974 A6 1976 B-5 1983 A4
Differential calculus, differentiation      1967 A1
Differential calculus, maxima & minima      1970 A2 1973 B-6 1981 B2
Differential calculus, partial derivatives      1967 B6
Differential calculus, rates      1970 B4 1972 B-2
Differential equations      1975 A5 1983 B-3
Differential equations, higher order      1966 B6
Differential equations, homogeneous linear      1979 B4
Differential equations, nonhomogeneous linear      1979 B4
Differential equations, systems      1969 A5 1971 B5 1973 A-5 1982 A4
Diophantine equations      1971 A5 1978 B-4 1979 A5
Dissections      1982 B1
Equations, functional      1971 B2 1979 A-2
Equations, systems      1967 A6 1977 A2 1980 A-5
Eulers formula for polyhedra      1969 A3
Extension fields      1968 B3 1980 A-4
Factorials      1984 A6 1984 B-1
Fermats theorem      1983 A3
Fields, characteristic      1979 B3
Finite fields      1979 B3
Functions      1977 A3
Functions, continuous      1966 A5 1982 B-5
Functions, convex      1980 B5
Functions, linear      1980 B2
Games      1971 A5
Gamma function      1984 A5
Geometry      see Plane geometry Plane Solid
graphs      1965 A4
Graphs, coloring      1979 A4
Graphs, Hamiltonian circuits      1968 A3
Graphs, incidence matrices      1965 A4
Greatest integer function      1973 A3 1979 A5 1983 A5 1983 B2 1983 B-4
Group theory      1968 B2 1969 B2 1972 B-3 1975 B1 1976 B2 1977 B-6
Hamiltonian circuits      1968 A3
Herons formula      1982 B6
Higher plane curves, cycloids, etc      1971 B5
Hyperbolic functions      1979 B1 1980 B-1
Incidence matrices      1965 A4
Inequalities, arithmetic mean-geometric mean      1968 A6 1975 B-6
Inequalities, Cauchy Schwarz      1966 B3 1977 B-5 1979 B6
Inequalities, functional considerations      1967 A-1 1967 B6 1973 B4 1973 B6 1974 B5 1978 A5 1980 A-6
Inequalities, geometric (triangle, polygon, etc.)      1966 A2 1966 B1 1971 A3 1973 A-1 1982 B6
Inequalities, miscellaneous      1968 A2 1978 B6 1979 A6 1980 A4 1982 A-5
Inequalities, series      1966 B3 1974 B5 1980 B-1
Infinite products      1969 B3 1970 B1 1977 B-1
Infinite sequences      1965 A3 1966 A-1 1966 A3 1969 A6 1969 B3 1969 B5 1970 A4 1972 A3 1978 B3 1979 A3 1980 B3 1982 B5 1983 A5 1983 B-4 1983 B-5
Infinite series      1967 A2 1967 B5 1969 A-4 1970 A-1 1972 B1 1972 B6 1973 A-2 1975 B5 1976 B1 1977 A4 1978 B-2 1979 A6 1980 B1 1981 B5 1982 A6 1984 A-2
Infinite series, convergence and divergence      1966 B3 1969 B5
Integral calculus      1980 A5
Integral calculus, definite integrals      1965 B1 1967 B-3 1968 A-1 1969 A4 1970 B1 1970 B2 1970 B4 1972 A6 1973 B-4 1976 B1 1979 B2 1980 A3 1980 A6 1982 A3 1983 B-5
Integral calculus, double integrals      1981 A3 1981 B-6 1982 B2 1983 A-6
Integral calculus, improper integrals      1968 B4 1976 A-5 1982 A3
Integral calculus, triple integrals      1984 A5
Integral equations      1967 A4 1980 A-5
Irrational numbers      1974 B3 1977 B3 1980 A-4
Isoperimetric problems      1972 A4
L'Hopitals rule      1979 B2 1983 A-6
Lattice points      1981 A6
Law of Cosines      1972 B5 1983 A-2
Limits      1965 B4 1966 A3 1966 A6 1967 B3 1969 B5 1970 A4 1972 A3 1974 B2 1976 B1 1978 B3 1979 B-2 1981 A-1 1981 A3 1981 B1 1982 B3 1983 B-5
Linear algebra, determinants      1969 A2 1978 A-2
Linear algebra, incidence matrices      1965 A4
Linear algebra, matrices      1968 B5 1969 B6 1981 B-4
Linear algebra, permutation matrices      1967 A2
Linear algebra, symmetric matrices      1967 A2
Linear functions      1980 B2
Linear programming      1980 B2
Locker room problem      1967 B4
Mappings      1966 A5
Mappings, binary operations      1978 A4
Mathematical induction      1978 B3 1978 B-6
Matrices      1967 A2 1968 B5 1969 B-6 1981 B4 1984 A-3
Maxima      1983 A2
Maximum & minimum problems      1975 A3 1978 B5 1979 A-1 1981 B2 1984 A-4 1984 B2
Multivariable calculus      1975 A3
Normal lines      1979 B1
Number theory      1966 A4 1974 A3 1976 A-3
Number theory, arithmetic      1975 A1
Number theory, congruences      1968 B5 1969 B1 1973 B1 1977 A5 1983 A-3
Number theory, Diophantine equations      1971 A5 1978 B4 1979 A-1
Number theory, divisibility      1966 B2 1966 B4 1971 B1 1971 B6 1972 A5 1973 B-3 1981 A-1 1981 B3 1982 B4 1983 A-1 1983 A3
Number theory, Euler phi-function      1968 B3 1972 A-5
Number theory, Fermats theorem      1983 A3
Number theory, irrational numbers      1974 B3 1977 B-3 1980 A4
Number theory, least common multiple      1980 A2
Number theory, multiplicative functions      1967 B4
Number theory, Pythagorean triples      1965 B3
Number theory, relatively prime integers      1974 A1
Number theory, representation of integers      1970 A3 1973 B1 1981 B5 1983 B-2
Number theory, sums of divisors      1969 B1 1976 B-6
Partial derivatives      1967 B6
Permutation matrices      1967 A2
permutations      1982 A6
Picks Theorem      1971 A3
Pigeonhole Principle      1971 A-1 1978 A-1 1980 A4
Plane analytic geometry      1965 A6 1972 A-4 1977 A-1
Plane analytic geometry, ellipses      1976 B4
Plane analytic geometry, higher plane curves      1971 B5
Plane analytic geometry, hyperbolas      1967 B2
Plane analytic geometry, parabolas      1974 A5 1980 A-1
Plane geometry and mechanics      1974 A2
Plane geometry, circles      1965 B6
Plane geometry, impossible constructions      1968 B3
Plane geometry, lattices      1971 A3
Plane geometry, minimum problem      1976 A1
Plane geometry, octagons      1978 B1
Plane geometry, pentagons      1984 A4
Plane geometry, polygons      1966 B1 1966 B5 1967 B1 1969 A3 1978 B1 1981 B6 1984 B-6
Plane geometry, quadrilaterals      1970 B6 1972 B-5
Plane geometry, triangles      1965 A-1 1965 B3 1966 A-2 1971 A3 1973 A1 1981 A6 1982 B1 1982 B-6
Points, collinear      1979 A4
POLYGONS      1984 B1
Polyhedra      1980 B2
Polynomials      1967 A3 1968 A5 1968 A-6 1970 B2 1971 A2 1971 A4 1972 B4 1973 B5 1974 A6 1975 A4 1976 B-5 1978 B3 1978 B5 1979 A5 1980 A-1 1981 A5 1983 B-6
Polynomials, irreducible      1979 B3
Polynomials, two variables      1969 A-1 1970 B2 1976 A-2
probability      1968 B1 1970 A6 1976 B-3 1982 B3
Progressions      1972 A-1 1978 A-1 1979 A3
Quickest descent problem      1974 A2
Rational numbers      1973 B2 1978 B2 1980 B6 1981 B-5
Real analysis      1970 B3 1971 A6 1972 B-2 1976 A6 1978 A5 1983 A5 1984 B-4
Real analysis, compact sets      1968 B6
Real analysis, continuity      1970 B5 1972 A3 1973 A4 1974 B4 1977 A6 1979 A-2
Real analysis, limits      1974 B2
Real analysis, measure theory      1972 A6
Real analysis, minimizing an integral      1978 A3
Real analysis, Taylors remainder theorem      1974 B5
Recurrence relations      1966 A3 1967 A-2 1969 A6 1971 B6 1973 B5 1975 B-5 1979 A3 1980 B3 1980 B6 1982 B-5 1983 B2 1983 B-4
Reflection      1981 A4
Representation of Integers      1983 B2
Rolles Theorem      1973 A4 1980 A5 1981 A-5
Sequences      see Infinite sequences
Series      see Infinite series
Sets      1968 A3 1975 B1 1980 B-4
Solid analytic geometry      1970 A5 1971 B-4
Solid geometry, covering problems      1975 B2
Solid geometry, cubes      1983 B1
Solid geometry, lattices      1971 A1
Solid geometry, polyhedra      1980 B2
Solid geometry, quadrilaterals      1977 B2
Solid geometry, spheres      1968 A4 1983 B-1
Solid geometry, triangles      1975 A6
Symmetric functions, polynomials in several variables      1975 B3
tangents      1980 A1
Theory of equations, roots      1968 A6 1976 A4 1977 A-1
Topology, closed curve in the plane      1977 B4
Topology, connectedness      1975 B4
Triangle inequality      1979 A4
Triangular numbers      1975 A1
Trigonometric functions      1967 A1
Trigonometry      1974 B3
Trigonometry, Law of Cosines      1983 A2
Vectors      1968 A4 1975 A6 1983 A-2
volumes      1983 B1 1984 A-1
Wallis product      1969 B3 1983 B-5
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