The book treats two approaches to decision theory: (1) the normative, purporting to determine how a 'perfectly rational' actor ought to choose among available alternatives; (2) the descriptive, based on observations of how people actually choose in real life and in laboratory experiments. The mathematical tools used in the normative approach range from elementary algebra to matrix and differential equations. Sections on different levels can be studied independently. Special emphasis is made on 'offshoots' of both theories to cognitive psychology, theoretical biology, and philosophy.

Rapid advances in the physical and biological sciences and in related technologies have brought about equally farreaching changes in mathematical research. Focusing on control theory, invariant imbedding, dynamic programming, and quasilinearization, Mr. Bellman explores with ease and clarity the mathematical research problems arising from scientific questions in engineering, physics, biology, and medicine. Special attention is paid in these essays to the use of the digital computer in obtaining the numerical solution of numerical problems, its influence in the formulation of new and old scientific problems in new terms, and to some of the effects of the computer revolution on educational and social systems. The new opportunities for mathematical research presage, Bellman concludes, a renaissance of mathematics in human affairs by involving it closely in the problems of society.

Lyapunov methods and equations of parabolic type.- Multiple solutions of nonlinear partial differential equations.- Fading memory and functional-differential equations.- Singular perturbation by a quasilinear operator.- Remarks on branching from multiple eigenvalues.- Asymptotic analysis of a class of nonlinear integral equations.- Remarks about bifurcation and stability of quasi-periodic solutions which bifurcate from periodic solutions of the Navier Stokes equations.- Bifurcation of periodic solutions into invariant tori: The work of Ruelle and Takens.- Ergodic theory and statistical mechanics of non-equilibrium processes.- Mathematical problems in theoretical biology.- On predator-prey equations simulating an immune response.- Bifurcation theory for gradient systems.- Six lectures on the transition to instability.- Groundwater flow as a singular perturbation problem and remarks about numerical methods.- Nonlinear problems in nuclear reactor analysis.- Some non-linear problems in statistical mechanics and biology.- Stability properties and periodic behavior of controlled biochemical systems.

Mental Chronometry (MC) comprises a variety of techniques for measuring the speed with which the brain processes information. First developed in mid-1800, MC was subsequently eclipsed by more complex and practically useful types of psychometric tests stemming from Alfred Binet. This class of mental tests, however, has no true metric relating the test scores to any specific properties of the brain per se. The scores merely represent an ordinal scale, only ranking individuals according to their overall performance on a variety of complex mental tasks. The resulting scores represent no more than ranks rather than being a true metrical scale of any specific dimension of brain function. Such an ordinal scale, which merely ranks individuals in some defined population, possesses no true scale properties, possessing neither a true zero or equal intervals throughout the scale. This deficiency obstructs the development of a true natural science of mental ability. The present burgeoning interest in understanding individual differences in mental abilities in terms of the natural sciences, biology and the brain sciences in particular, demands direct measures that functionally link brain and behavior. One such natural ratio scale is time itself - the time it takes the brain to perform some elementary cognitive task, measured in milliseconds. After more than 25 years researching MC, Jensen here presents results on an absolute scale showing times for intake of visual and auditory information, for accessing short-term and long-term memory, and other cognitive skills, as a function of age, at yearly intervals from 3 to 80 years. The possible uses of MC in neurological diagnosis and the monitoring of drug effects on cognition, the chronometric study of special time-sensitive talents such as musical performance, and presents a theory of general intelligence, or g, as a function of the rate of oscillation of neural action potentials as

This milestone extensive work combines the essentials of history – biography, chronology, political and economic background – with the observations, theories, principles, laws and equations that constitute the specifics of science. The 5800-page Encyclopedia arises from the conviction that the optimal perspective on science is through the lens of history, setting aside traditional divisions of discipline and specialty, and rising above geopolitical boundaries. Reaching from 4,200 BCE to the 21st century CE, the Encyclopedia tells (as the author himself puts it) "not only who did it and when it was done but also precisely what was done." The author, Ari Ben-Menahem, surveys 100 generations of great thinkers, offering 2070 detailed biographies of scientists, engineers, explorers and inventors, who left their mark on the history of science and technology. The span of coverage is all-encompassing: mathematics, philosophy, logic, physical and environmental sciences (including physics, chemistry, astronomy, earth and space sciences and cosmology), life sciences (biology, medicine, physiology, botany, zoology and biochemistry), associated engineering disciplines, and the social sciences (among them economics, psychology, sociology, anthropology, linguistics and more). The six-volume Encyclopedia also includes 380 articles summarizing the time-line of ideas in the leading fields of science, technology, mathematics and philosophy, plus useful tables, figures and photos, and 20 ‘Science Progress Reports’ detailing scientific setbacks. Interspersed throughout are quotations, gathered from the wit and wisdom of sages, savants and scholars throughout the ages from antiquity to modern times.

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