Math 172: Practice Final Solutions

Math anxiety differentially affects WAIS-IV arithmetic performance in undergraduates.

Previous research has shown that math anxiety can influence the math performance level; however, to date, it is unknown whether math anxiety influences performance on working memory tasks during neuropsychological evaluation. In the present study, 172 undergraduate students completed measures of math achievement (the Math Computation subtest from the Wide Range Achievement Test-IV), math anxiet...

MATH 127 Solutions to Final Exam

Warmstarting the homogeneous and self-dual interior point method for linear and conic quadratic problems

We present two strategies for warmstarting primal-dual interior point methods for the homogeneous self-dual model when applied to mixed linear and quadratic conic optimization problems. Common to both strategies is their use of only the final (optimal) iterate of the initial problem and their negligible computational cost. This is a major advantage when compared to previously suggested strategi...

Stat 310A/Math 230A Theory of Probability Practice Final Solutions

Solution : Assume, without loss of generality |x2 − x1| ≥ 2−n+1. Then there exists an integer k ∈ {1, . . . , 2 − 1}, such that x1 < k · 2−n < (k + 1)2−n < x2. Of course PX((x1, x2)) ≥ P(k · 2−n ≤ X(ω) ≤ (k + 1)2−n) . (4) The integer k admits the unique binary expansion k = ∑n i=1 ki2 n−i. Then P(k · 2−n ≤ X(ω) ≤ (k + 1)2−n) = P(Cn,(k1...,kn)) = p 1(1− p)0 , (5) with n0(k) and n1(k) the number ...

Math 110: Linear Algebra Practice Final Solutions

Question 1. (1) Write f(x) = amx m + am−1xm−1 + · · ·+ a0. Then F = f(T ) = amT + am−1Tm−1 + · · ·+a0I. Since T is upper triangular, (T )ii = T k ii for all positive k and i ∈ {1, . . . , n}. Hence Fii = amT m ii + am−1T m−1 ii + · · ·+ a0 = f(Tii). (2) TF = Tf(T ) = T (amT m+am−1Tm−1+ · · ·+a0I) = amT+am−1T+ · · ·+a0T = (amT m + am−1Tm−1 + · · ·+ a0I)T = f(T )T = FT . (3) Since T is upper tria...