Quantitative trading was about manufacturing clean mathematical formulas to price products. Data science is about learning what the data tells you in all its complexity. There are no formulas. It is a pure technology-driven application of Machine Learning.
Data science is a subject that deals with large amounts of data and makes use of machine learning techniques to make new predictions. If you are a beginner and want to know more about Python and R programming language then do refer the following video tutorials:
You can get a hands-on project by referring to Data Science online courses which will teach you Data Science from scratch to advance.
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If you want a detailed explanation of Data Science then do check out Data Science tutorial which will help you in understanding Data Science.