Math 318 Exam #1 Solutions

MATH 127 Solutions to Final Exam

Meromorphic Solutions of First - Order Algebraic Differential Equations

i. P. Deligne, Usp. Mat. Nauk, 30, No. 5, 159-190 (1975). 2. H. Jacquet andR. P. Langlands, Automorphic Formson GL(2), Springer-Verlag (1970). 3. S. Banach,.Oeuvres, Vol. i, Warsawa (1967), pp. 318-322. 4. G. A. Margulis, Monatsh. Mmth., 9__0, No. 3, 233-235 (1980), 5. D. Sullivan, Bull. Am. Math. Soc., ~, No. i, 121-123 (1981). 6. R. A. Rank_in, Proc. Cambridge Philos. Soc., 35, 351-372 (1939)...

Solutions to Take-Home Part of Math 317 Exam #1

where the first inequality is an application of the triangle inequality, the second follows from (1) and (2), and the third from the choice of m. Therefore, since our choice of > 0 was arbitrary, we conclude that the subsequence (xnm)→ b. A similar argument using the sequence (zm) given by zm = inf{xm, xm+1, . . .} and the version of Lemma 1.3.7 suitable for infima (see Exercise 1.3.2, which yo...

Math 51 Final Exam Review Solutions

Recall some basic facts about eigenspaces — we say that Eα is an eigenspace of a matrixM of dimension d if the dimension of the nullspace of αI −M has dimension d. Moreover, by the theory covered in class, we must have that the polynomial (λ− α) divides the characteristic polynomial of M , which is defined to be det(λI −M). We first calculate the eigenspaces of Bn. Observe that if α = 1, then w...

Cytokine responses andmath performance: The role of stereotype threat and anxiety reappraisals

• Female college students take a math exam described as gender-fair or gender-biased. • In one condition, participants directed to reappraise physiological arousal. • Performance on math exam and post-exam levels of the cytokine IL-6 were measured. • Reappraisal of physiological arousal buffers inflammatory responses to exam across conditions. • Reappraisal of arousal especially effective buffe...