Mathematical theories and methods and effective computational algorithms are crucial
in coping with the challenges arising in the sciences and in many areas of their
application. New concepts and approaches are necessary in order to overcome the
complexity barriers particularly created by nonlinearity, high-dimensionality, multiple
scales and uncertainty. Combining advanced mathematical and computational
methods and computer technology is an essential key to achieving progress, often
even in purely theoretical research.
Math is an integral part of our increasingly complex daily life. Calculus for the
Managerial, Life, and Social Sciences, Seventh Edition, attempts to illustrate this
point with its applied approach to mathematics. Our objective for this Seventh
Edition is twofold: (1) to write an applied text that motivates students and (2) to
make the book a useful teaching tool for instructors. We hope that with the present
edition we have come one step closer to realizing our goal.
We prove that the existence of an automorphism of ﬁnite order on a Q-variety X implies the existence of algebraic linear relations between the logarithm of certain periods of X and the logarithm of special values of the Γ-function. This implies that a slight variation of results by Anderson, Colmez and Gross on the periods of CM abelian varieties is valid for a larger class of CM motives. In particular, we prove a weak form of the period conjecture of Gross-Deligne [11, p. 205]1 .