Data science is an interdisciplinary field consisting of traditional mathematics fundamentals, computer science, and knowledge of the specific area that you are analyzing. For example, you need to have some expertise in finances if you want to use data science for stock market analysis.
Data mining, analyzing, and modeling are the main actions of data scientists. Those concepts often mix because it doesn’t describe some action strictly.
Data mining is mainly extracting essential data in some big data set. Also data mining can find some insights or patterns in data structures.
Data analyzing can be used in business intelligence as it finds most important KPI’s in data.
Data modeling helps develop most reliable methods for finding essential information inside the data.
You can compare these data science actions with analytical chemistry. Data mining is like the sampling of materials. Data analytics is like using methods of analytical chemistry to analyze taken samples. And data modeling is like experimental chemistry in which you find best ways for examining the materials.