Liu Jia's Lecture Notes on Probability will let us know what probability theory is with the most basic theory, the most comprehensive analysis and the most popular narration. We can understand probability theory from its four cornerstones, calculation rules, frequency theory, probability distribution and Bess rule, and then we can use it correctly.
In the inherent cognition of the public, probability theory is closely related to abstract formulas and complex calculations. Throughout the history of human science and technology development, all fields including big data, artificial intelligence, biomedicine and gene editing are inseparable from probability theory. What we need to recognize is that randomness and probability are the normal state of this world and the background color of this world. Probability theory will certainly be used when making choices and decisions.
In life, probability theory can be said to be everywhere, just because our consciousness has not attributed these things to probability problems and has not systematically sorted them out. In the book, the example given by the author tells us a basic problem that has long been superficial, that is, many problems in life can be improved by probability theory. As long as we are good at finding problems and know how to use probability theory to solve them.
This book is divided into seven chapters. In these seven chapters, Liu Jia will use easy-to-understand explanations to complete the cognition, understanding and application of probability theory. In the last two chapters, he will discuss the difference between probability school and Bayesian method, which will help you build a probabilistic knowledge framework and effectively improve probabilistic thinking in your life.
In the preface of this book, Liu Jia stated her purpose of writing this book: to make abstract mathematics lively and interesting, so that you can understand it and get some inspiration. I'm good at this. I am your bridge to probability theory, and cultivate probabilistic thinking.
The basis of each subject comes from the understanding of Chinese knowledge, which is mainly manifested in whether each step can be successfully completed and whether the accuracy can be improved in the process of examining, judging and solving problems.
The basis of probability theory is also the understanding of Chinese knowledge, which determines your reading comprehension ability, further determines your judgment ability and directly affects your calculation ability.
"There are three realms in life. Seeing a mountain is a mountain, seeing a mountain is not a mountain, and seeing a mountain is a mountain. " Liu Jia compared this sentence to his mathematical knowledge. What he did was to let us have a glimpse from a more general angle, understand probability theory in the shortest time, and then use it better.
In this book, Liu Jiajun puts forward "the problem to be considered in this section" under each section. These topics are very interesting, such as a question after a random plate: we have all played WeChat red envelopes. Is the amount of red envelopes we grabbed random?
Another example is the question behind the probability section: What is the probability that Lao Wang has three children and only 1 girl? ()
A. There are three children, among whom 1 is a girl, so the probability is one third.
B. According to the birth order, three children have eight situations, and only 1 girl has three situations, so the probability is three out of eight.
C. Lao Wang's family can have 0, 1, 2, 3 girls and 1 girl, so the probability is one in four.
Through these questions, we can see that probability theory is closely related to our human life, and all aspects of life will involve probability problems, and we only need to understand the whole picture of probability theory through this book and enjoy the fun from the mathematical field from the author's vivid and interesting discussions and examples.
What I realized after reading this book is that probability theory may have been an unattainable peak in our eyes, but when you really appreciate its interest through this book, probability theory is no longer an unreachable flower. Anyone can easily pick it up through Liu Jia's lecture notes on probability theory, ignore it and classify it into his own knowledge system.