概率论学习中几个值得注意的问题探究

【摘要】 概率论是随机数学的基础，学好概率论对于金融数学，统计学等学科有着重要的意义。在多年的概率论教学中，以下三点是值得注意的。首先将概率论的历史发展融入概率论教学，这对于学生的理解是有价值的；另外通过比较的方法来学习有助于学生的理解。如比较不同的极限理论可以使得大数定律，中心极限定理更加容易理解；最后，在概率论与随机过程的学习中经常会遇到一些概念性的错误。我们以更新过程中的Feller初等更新定理的证明为例。指出同学们容易产生一些概念性的错误，并将这些错误的原因做出解释，以便让学生对概念的理解更加清晰，避免在概率论与随机过程的学习中犯类似的错误。更多还原

【Abstract】 Theory of Probability is basic course of stochastic mathematics, especially for financial mathematics and statistics etc.In years of teaching Theory of Probability, I found that it is important to study the history of probability, which can help the students learn the concepts of probability. It can be also helpful to learn by comparison. For example, the Law of Large Numbers and central limit theorem can be easily studied by comparing the limit theory. Finally, In the proof of the Feller renewal theorem, there are several problems that students always make mistake. Theses mistakes are often made in the study of probability and stochastic processes. We will give the explanation to clean the concept and avoid similar mistakes.更多还原