概率论与数理统计

Probability is the study of the likelihood an event will happen, and statistics is the analysis of large datasets, usually with the goal of either usefully describing this data or inferring conclusions about a larger dataset based on a representative sample. These two branches of mathematics can be considered two sides of a coin: statistics help you to understand the past, and probability helps you use that knowledge to predict the future!

Statistics and probability are essential tools for data science. These skills enable you to determine whether your data collection methods are sound, derive relevant insights from massive datasets, build analytic models that produce usable results, and much more. Important concepts and skills in the data science context include sampling distributions, statistical significance, hypothesis testing, and regression analysis.

As a branch of mathematics, statistics requires high-level numeracy and quantitative skills as a foundation. However, that’s only the beginning. Being a statistician is a bit like being a detective - you need superb analytical skills to determine whether your data is statistically significant, properly interpret it, and test whether your resulting findings are meaningful.

While the core theories of statistics aren’t new, today’s statisticians rely on the power of sophisticated computer programs to deliver more powerful insights with these principles than ever before. Thus, computer literacy is also an essential skill for statisticians, and particularly familiarity with programs like Stata and SAS as well as the programming languages R and Python.\n\nFinally, all of that statistical analysis becomes much more useful for problem-solving if you are able to convey it effectively. Thus, compelling data visualization capabilities as well as strong written and oral communication skills are essential to putting your insights into action.

Working in statistics and probability isn’t just about becoming a statistician or theoretical mathematician (although it can be). Like data science, these skills open the door to an incredibly wide range of career choices. After all, what company doesn’t need to either predict the future or understand the past?

If you’re interested in going into the business world, statistics and probability are essential for business analysts, market research analysts, risk analysts, and economists to understand global markets and identify likely business opportunities. If you want to work in tech, an understanding of these fields can be invaluable for data scientists, software engineers, machine learning engineers, and many other jobs.

Statistical expertise is also a core skill for understanding risk, and is central to the work of public health researchers, environmental scientists, criminologists, meteorologists, pharmaceutical engineers, and countless other roles that seek to protect clients or the general public. So whether your career goals are about doing well financially, doing good for the world, or both, statistics and probability skills can take you where you want to go.

Like many other branches of math, computer science, and data science, there are more opportunities than ever to learn probability and statistics online. You can brush up on your theoretical foundations with courses in basic statistics, statistical inference, Bayesian statistics, and regression models; build your computer skills with courses in R programming, statistics with Python, and data visualization; and put your statistics and probability know-how to work with courses in business statistics, econometrics, or even biostatistics in public health.

No matter what your goals in statistics and probability are, Coursera offers Professional Certificates, MasterTrack certificates, Specializations, Guided Projects and courses in probability and statistics from top universities like Johns Hopkins University, University of Michigan and Duke University. You can also learn about statistics and probability in the context of computer science and data science degrees from top-ranked colleges like University of Illinois, Imperial College London, University of Michigan, University of Colorado Boulder, and University of Pennsylvania.