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The ramified type (τ 1,...,τ m |σ 1,...,σ n) can be modeled as the product of the type (τ 1,...,τ m,σ 1,...,σ n) with the set of sequences of n quantifiers (∀ or ∃) indicating which quantifier should be applied to each variable σ i. (One can vary this slightly by allowing the σs to be quantified in any order, or allowing them to ...
Likewise, reviewing the book for the Mathematical Association of America, Allen Stenger noted that while the book only presumed knowledge of high-school algebra and trigonometry, it also in places demanded a "high level of mathematical reasoning". Stenger expected that many readers would be unable to follow all of the explanations unaided. [2]
The term antonym (and the related antonymy) is commonly taken to be synonymous with opposite, but antonym also has other more restricted meanings. Graded (or gradable) antonyms are word pairs whose meanings are opposite and which lie on a continuous spectrum (hot, cold).
A Mathematician's Lament, often referred to informally as Lockhart's Lament, is a short book on mathematics education by Paul Lockhart, originally a research mathematician at Brown University and U.C. Santa Cruz, and subsequently a math teacher at Saint Ann's School in Brooklyn, New York City for many years.
This is not sharp; the gap between the functions is everywhere at least 1. Among the exponential functions of the form α x, setting α = e 2/e = 2.0870652... results in a sharp upper bound; the slightly smaller choice α = 2 fails to produce an upper bound, since then α 3 = 8 < 3 2. In applied fields the word "tight" is often used with the ...
The book has consistently received good reviews. [1] [2] The book has been praised by Martin Gardner. [3] The book is the winner of the Neumann Prize. [4] The book has been praised by Boing Boing. [5]
A History of Greek Mathematics; An Account of the Rotula Arithmetica; Adventures Among the Toroids; The Algebraic Eigenvalue Problem; Algorithmic Combinatorics on Partial Words; The Analyst; Analytic Combinatorics (book) The Annotated Turing; Antifragile (book) Antiquarian science books; The Applicability of Mathematics in Science ...
The branch of mathematics deals with the properties and relationships of numbers, especially positive integers. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory ...