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William Lowell Putnam Mathematical Competition results; William Lowell Putnam Competition problems, solutions, and results archive; Archive of Problems 1938–2003; Searchable data base for information about careers of Putnam Fellows; A comprehensive history of the Putnam competition An electronic update of Gallian's 2004 paper (PDF)
Theorem (Calvin Richard Putnam) [1] Let T, M, N be linear operators on a complex Hilbert space, and suppose that M and N are normal, T is bounded and MT = TN. Then M * T = TN *. First proof (Marvin Rosenblum) : By induction, the hypothesis implies that M k T = TN k for all k .
For example, Gödel–Dummett logic has a simple semantic characterization in terms of total orders. Specific intermediate logics may be given by semantical description. Others are often given by adding one or more axioms to Intuitionistic logic (usually denoted as intuitionistic propositional calculus IPC, but also Int, IL or H) Examples include:
In logic and computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.
Matiyasevich's theorem, also called the Matiyasevich–Robinson–Davis–Putnam or MRDP theorem, says: . Every computably enumerable set is Diophantine, and the converse.. A set S of integers is computably enumerable if there is an algorithm such that: For each integer input n, if n is a member of S, then the algorithm eventually halts; otherwise it runs forever.
For Goodman they illustrate the problem of projectible predicates and ultimately, which empirical generalizations are law-like and which are not. [1] [2] Goodman's construction and use of grue and bleen illustrates how philosophers use simple examples in conceptual analysis.
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In computer science, Putnam is known for the Davis–Putnam algorithm for the Boolean satisfiability problem (SAT), developed with Martin Davis in 1960. [5] The algorithm finds whether there is a set of true or false values that satisfies a given Boolean expression so that the entire expression becomes true.