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Probability is one of the great achievements of this century. Like geometry, it is a way of looking at nature. There are many ways of approaching natural problems, many points of view. The geometrical point of view has been with us for thousands of years. The probabilistic point of view is another way of focusing on problems that has been successful in many instances. The purpose of this course is to learn to think probabilistically. Unfortunately the only way to learn to think probabilistically is to learn the theorems of probability. Only later, as one has mastered the theorems, does the probabilistic point of view begin to emerge while the specific theorems fade in one's memory: much as the grin on the Cheshire cat.
We begin by giving a bird's-eye view of probability by examining some of the great unsolved problems of probability theory. It's only by seeing what the unsolved problems are that one gets a feeling for the field.
Probability is one of the great achievements of this century. Like geometry, it is a way of looking at nature. There are many ways of approaching natural problems, many points of view. The geometrical point of view has been with us for thousands of years. The probabilistic point of view is another way of focusing on problems that has been successful in many instances. The purpose of this course is to learn to think probabilistically. Unfortunately the only way to learn to think probabilistically is to learn the theorems of probability. Only later, as one has mastered the theorems, does the probabilistic point of view begin to emerge while the specific theorems fade in one's memory: much as the grin on the Cheshire cat.
We begin by giving a bird's-eye view of probability by examining some of the great unsolved problems of probability theory. It's only by seeing what the unsolved problems are that one gets a feeling for the field.
