Education has always been one of the main concerns of human societies, but in different periods and different communities educational goals have varied. Nowadays, and especially here in Iran, the main goal of education is to prepare children for real life and its problem. More specifically, the goal in mathematics education is help students with solving real life problems using their acquired m...

in the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{kim} and textit{lee} [w.k. kim and k.h. lee, generalized fuzzy games and fuzzy equilibria, fuzzy sets and systems, 122 (2001), 293-301] and textit{tarafdar} [e. tarafdar, fixed point theorems i...

The goal of this first major report from the Western Reserve Reading Project Math component is to explore the etiology of the relationship among tester-administered measures of mathematics ability, reading ability, and general cognitive ability. Data are available on 314 pairs of monozygotic and same-sex dizygotic twins analyzed across 5 waves of assessment. Univariate analyses provide a range ...

(4.1) Let P : R → R be a polynomial which does not vanish identically. Use Fubini’s Theorem to show, by induction on the dimension n, that Z(P ) = {x ∈ R|P (x) = 0} has Lebesgue measure equal to zero. proof By induction on n. For n = 1, consider a polynomial P ∈ R[X], and let d = degP . Then P has at most d roots, and Z(P ) = {x ∈ R|P (x) = 0} is finite, thus has measure 0. Now let n ≥ 1, and a...

And hence d(x, 0) ≥ lim inf d(0, xn)− lim sup d(xn, x) = 1 Thus x ∈ S. Hence S is closed. Clearly S is bounded since it is contained in B2(0). Define en = (0, 0, . . . , 0, 1, 0, . . . ) be the sequence with all 0’s except a 1 in the nth place. Notice that en ∈ S (for `, `∞, c0). However, notice also that since, in every case, d(en, em) ≥ 1 whenever n 6= m, then the sequence en has no convergen...

Recent work across several AI subdisciplines has focused on automatically solving math word problems. In this paper we introduce MAWPS, an online repository of Math Word Problems, to provide a unified testbed to evaluate different algorithms. MAWPS allows for the automatic construction of datasets with particular characteristics, providing tools for tuning the lexical and template overlap of a ...

Rudin, Chapter 4, Problem #3. The space L(T ) is separable since the trigonometric polynomials with complex coefficients whose real and imaginary parts are rational form a countable dense subset. (Denseness follows from Theorem 3.14 and Theorem 4.25; countability is clear since {e | n ∈ Z} is a countable basis of the trigonometric polynomials.) Meanwhile the space L(T ) is not separable. To see...

we have by construction μ(En) = an. An important observation is that a subset of consecutive intervals En, En+1, . . . , En+k are either pairwise disjoint, or they cover the whole interval [0, 1]. Now for all n, let fn = 1En . Then we have • ‖fn‖1 = ∫ X |1En |dμ = μ(En) = an. • for all x ∈ [0, 1], (fn(x))n does not converge. Indeed, if we suppose by contradiction that (fn(x))n converges for som...

(10.1) Let k ∈ N, and let X = C k ([0, 1] d) to be the set of all functions f ∈ C 0 ([0, 1] d) such that for all α ∈ ∆ k , f (α) = ∂f ∂x α 1 1 ...∂x α d d exists and is continuous on (0, 1) d , and extends continuously on [0, 1] d. Here