R. Cooke – författare

This book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn some­ thing of value about Kovalevskaya herself and about the mathematical world she inhabited. Having been trained as a mathematician, I also hoped to learn something about the proper approach to the history of the subject. The decision to begin the study with Kovalevskaya, apart from the intrinsic interest of Kovalevskaya herself, was primarily based upon the fact that the writing on her in English had been done by people who were interested in sociological and psychological aspects of her life. None of these writings discussed her mathematical work in much detail. This omission seemed to me a serious one in biographical studies of a woman whose primary significance was her mathematical work. In regard to both the content of nineteenth century mathematics and the nature of the history of mathematics I learned a great deal from writing this book. The attempt to put Kovalevskaya's work in historical context involved reading dozens of significant papers by great mathematicians. In many cases, I fear, the purport of these papers is better known to many of my readers than to me. If I persevered despite misgivings, my excuse is that this book is, after all, primarily about Kovalevskaya. If specialists in Euler, Cauchy, etc.

The First Conference on Engineering Probability in Flood Defense was orga­ nized by the Department of Mathematics and Informatics of the Delft U niver­ sity of Technology and the Department of Industrial Engineering and Opera­ tions Research of the University of California at Berkeley, and was held on June 1,2 1995 in Delft. Groups at Berkeley and Delft were both deeply engaged in modeling deterioration in civil structures, particularly flood defense structures. The plans for the conference were well under way when the dramatic floods in The Netherlands and California in the winter of 1994-1995 focused world attention on these problems. The design of civil engineering structures and systems is essentially an example of decision making under uncertainty. Although the decision making part of the process is generally acknowledged, the uncertainty in variables and param­ eters in the design problem is less frequently recognized. In many practical design procedures the uncertainty is concealed behind sharp probabilistic de­ sign targets like 'once in a thousand years' combined with a standardized use of safety factors. The choice of these probabilistic design targets, however, is based on an assessment of the uncertainty of the variable under consideration, and on its assessed importance. The value of the safety factor is governed by similar considerations. Standard practice is simply accu~ulated experience and engineering judgment. In light of the great number of civil engineering structures that function suc-. cessfully, one may say that this standard practice has proven itself broadly satisfactory.

This book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn some­ thing of value about Kovalevskaya herself and about the mathematical world she inhabited. Having been trained as a mathematician, I also hoped to learn something about the proper approach to the history of the subject. The decision to begin the study with Kovalevskaya, apart from the intrinsic interest of Kovalevskaya herself, was primarily based upon the fact that the writing on her in English had been done by people who were interested in sociological and psychological aspects of her life. None of these writings discussed her mathematical work in much detail. This omission seemed to me a serious one in biographical studies of a woman whose primary significance was her mathematical work. In regard to both the content of nineteenth century mathematics and the nature of the history of mathematics I learned a great deal from writing this book. The attempt to put Kovalevskaya''s work in historical context involved reading dozens of significant papers by great mathematicians. In many cases, I fear, the purport of these papers is better known to many of my readers than to me. If I persevered despite misgivings, my excuse is that this book is, after all, primarily about Kovalevskaya. If specialists in Euler, Cauchy, etc.

This book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn some­ thing of value about Kovalevskaya herself and about the mathematical world she inhabited. Having been trained as a mathematician, I also hoped to learn something about the proper approach to the history of the subject. The decision to begin the study with Kovalevskaya, apart from the intrinsic interest of Kovalevskaya herself, was primarily based upon the fact that the writing on her in English had been done by people who were interested in sociological and psychological aspects of her life. None of these writings discussed her mathematical work in much detail. This omission seemed to me a serious one in biographical studies of a woman whose primary significance was her mathematical work. In regard to both the content of nineteenth century mathematics and the nature of the history of mathematics I learned a great deal from writing this book. The attempt to put Kovalevskaya's work in historical context involved reading dozens of significant papers by great mathematicians. In many cases, I fear, the purport of these papers is better known to many of my readers than to me. If I persevered despite misgivings, my excuse is that this book is, after all, primarily about Kovalevskaya. If specialists in Euler, Cauchy, etc.

The First Conference on Engineering Probability in Flood Defense was orga­ nized by the Department of Mathematics and Informatics of the Delft U niver­ sity of Technology and the Department of Industrial Engineering and Opera­ tions Research of the University of California at Berkeley, and was held on June 1,2 1995 in Delft. Groups at Berkeley and Delft were both deeply engaged in modeling deterioration in civil structures, particularly flood defense structures. The plans for the conference were well under way when the dramatic floods in The Netherlands and California in the winter of 1994-1995 focused world attention on these problems. The design of civil engineering structures and systems is essentially an example of decision making under uncertainty. Although the decision making part of the process is generally acknowledged, the uncertainty in variables and param­ eters in the design problem is less frequently recognized. In many practical design procedures the uncertainty is concealed behind sharp probabilistic de­ sign targets like ''once in a thousand years'' combined with a standardized use of safety factors. The choice of these probabilistic design targets, however, is based on an assessment of the uncertainty of the variable under consideration, and on its assessed importance. The value of the safety factor is governed by similar considerations. Standard practice is simply accu~ulated experience and engineering judgment. In light of the great number of civil engineering structures that function suc-. cessfully, one may say that this standard practice has proven itself broadly satisfactory.

The First Conference on Engineering Probability in Flood Defense was orga­ nized by the Department of Mathematics and Informatics of the Delft U niver­ sity of Technology and the Department of Industrial Engineering and Opera­ tions Research of the University of California at Berkeley, and was held on June 1,2 1995 in Delft. Groups at Berkeley and Delft were both deeply engaged in modeling deterioration in civil structures, particularly flood defense structures. The plans for the conference were well under way when the dramatic floods in The Netherlands and California in the winter of 1994-1995 focused world attention on these problems. The design of civil engineering structures and systems is essentially an example of decision making under uncertainty. Although the decision making part of the process is generally acknowledged, the uncertainty in variables and param­ eters in the design problem is less frequently recognized. In many practical design procedures the uncertainty is concealed behind sharp probabilistic de­ sign targets like 'once in a thousand years' combined with a standardized use of safety factors. The choice of these probabilistic design targets, however, is based on an assessment of the uncertainty of the variable under consideration, and on its assessed importance. The value of the safety factor is governed by similar considerations. Standard practice is simply accu~ulated experience and engineering judgment. In light of the great number of civil engineering structures that function suc-. cessfully, one may say that this standard practice has proven itself broadly satisfactory.

An inference may be defined as a passage of thought according to some method. In the theory of knowledge it is customary to distinguish deductive and non-deductive inferences. Deductive inferences are truth preserving, that is, the truth of the premises is preserved in the con­ clusion. As a result, the conclusion of a deductive inference is already ''contained'' in the premises, although we may not know this fact until the inference is performed. Standard examples of deductive inferences are taken from logic and mathematics. Non-deductive inferences need not preserve truth, that is, ''thought may pass'' from true premises to false conclusions. Such inferences can be expansive, or, ampliative in the sense that the performances of such inferences actually increases our putative knowledge. Standard non-deductive inferences do not really exist, but one may think of elementary inductive inferences in which conclusions regarding the future are drawn from knowledge of the past. Since the body of scientific knowledge is increasing, it is obvious that the method of science must allow non-deductive as well as deductive inferences. Indeed, the explosive growth of science in recent times points to a prominent role for the former. Philosophers of science have long tried to isolate and study the non-deductive inferences in science. The inevitability of such inferences one the one hand, juxtaposed with the poverty of all efforts to identify them, constitutes one of the major cognitive embarrassments of our time.