1, calculus. Calculus, a mathematical concept, is a branch of higher mathematics that studies the differential and integral of functions and related concepts and applications.
It is a basic subject of mathematics, including limit, differential calculus, integral calculus and its application. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change.
It makes the function, velocity, acceleration and curve slope can be discussed with a set of universal symbols. Integral calculus, including the calculation of integral, provides a general method to define and calculate area and volume.
2. Linear algebra. Linear algebra is a branch of mathematics, and its research objects are vectors, vector spaces (or linear spaces), linear transformations and linear equations with finite dimensions.
Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis; Through analytic geometry, linear algebra can be expressed concretely.
The theory of linear algebra has been extended to operator theory. Because the nonlinear model in scientific research can usually be approximated as a linear model, linear algebra is widely used in natural science and social science.
3. Probability theory. The main contents of this book include events and probability, conditional probability and independence, random variables and their distributions, random vectors and their distributions, numerical characteristics and characteristic functions, laws of large numbers and central limit theorems. Each chapter is equipped with appropriate exercises with different difficulties, and the answers or tips of the exercises are attached at the end of the book for readers' reference.
This book is readable, and can be used as a teaching book for independent colleges or students with a considerable level, and also as a reference book for students of other majors. In order to meet the needs of students at different levels, the contents of this book are divided into compulsory parts and elective parts (plus * parts), and the exercises are divided into two groups (A) and (B), with Group B being slightly more difficult.
4. Mathematical statistics. Mathematical statistics is a branch of mathematics, which is divided into descriptive statistics and inferential statistics. Based on probability theory, it studies the statistical laws of a large number of random phenomena.
The task of descriptive statistics is to collect data, sort out and group them, compile a frequency distribution table, draw a frequency distribution curve and calculate various characteristic indexes to describe the concentration trend, deviation trend and skewness of data frequency distribution.