As an IT technology involving multidisciplinary knowledge, big data technology has different research directions, and the amount of mathematical knowledge involved in different directions is also different. But in many cases, when learning big data, the basic knowledge of mathematics is not directly required, but big data involves a certain mathematical foundation, which makes it easier to understand the knowledge to be learned by big data. The mathematical knowledge involved in big data learning generally includes probability theory, mathematical statistics, linear algebra, optimization theory, discrete mathematics and so on. First of all, probability theory

1, why learn probability theory?

Probability theory is a branch that studies the quantitative laws of random phenomena. The purpose of data analysis in big data processing technology can not be separated from analyzing the current situation or predicting the future, but neither of these two aspects can draw absolute conclusions, only various possibilities can be drawn, and the occurrence of these possibilities needs probability to explain.

2. Learning content of probability theory

Definition: traditional probability and conditional probability.

Theorems: complementary rule, zero probability of impossible events, mutual exclusion rule, difference set relation, multiplication rule, multiplication rule of irrelevant events, complete probability, Bayes theorem.

Second, mathematical statistics

1, why learn mathematical statistics?

Mathematical statistics is a branch of mathematics, which is divided into descriptive statistics and inferential statistics. Based on probability theory, it studies a large number of random phenomena and statistical laws. In big data analysis, the description of the size, deviation and distribution characteristics of random variables and the description of the relationship between two or more random variables are often involved. Mathematical statistics is a mathematical tool to quantitatively describe the relationship between random variables and random variables.

2, data statistics learning content

Parameter estimation, hypothesis testing, correlation analysis, experimental participation, nonparametric statistics, process statistics, etc.

Third, linear algebra

1, why study linear algebra?

Linear algebra is a branch of mathematics, and its research objects are vectors, vector spaces (linear spaces), linear transformations and linear equations with finite dimensions. In big data, the analysis objects of many application scenarios can represent the dimension matrix abstractly. For example, a large number of web pages and their relationships, and Weibo users and their relationships can all be represented by a matrix.

2. Learning content of linear algebra

Eigenvalue and eigenvector, determinant, matrix, linear equation.

Fourth, the optimization method

1, why do you want to learn optimization methods?

Optimization method refers to the method to solve the optimization problem. The so-called optimization problem refers to the problem of determining the values of some optional variables under certain constraints, so that the selected objective function can achieve the best. That is, the latest scientific and technological means and processing methods are adopted to realize the overall optimization of the system, so as to put forward the optimization scheme of system design, construction, management and operation. Model learning training is a method to analyze and mine the parameters of many models. In model learning and training, function is used to find the optimal method.

2. Optimize theoretical learning content.

Seeking extreme value in differential calculus, unconstrained optimization problems, common differential formulas, convex sets and convex functions, equality constrained optimization problems, inequality constrained optimization problems, and seeking extreme value in variational methods.