What role does math actually play in data science?
Blending coding skills with math skills is the core of data science. The algorithms that we use in data science are all worded in mathematics. Whether its an optimization problem, probability problem, or scoring metrics – all of those things are going to require math skills to understand what's going on.
So what specific math do you need to know to become a Data Scientist?
Linear Algebra, Calculus, Probability, and Statistics are the four core math concepts for Data Science. The math that you need to know might depend on what area of data science that you specialize in, but these four areas will be important for any data scientist.
Linear Algebra might be the most important because so many of our algorithms are based in Linear Algebra. You should be comfortable with matrices and vectors. Eventually, we start talking about higher dimensional spaces like vectors and matrices and understanding how those computations work.
What is Calculus?
Calculus is a study of the instantaneous rate of change. Any time you are taking derivatives and trying to understand how a function is changing, that's the first part of the Calculus. The other part of Calculus is integrals – how a quantity accumulates. Integrals and derivatives make up the bulk of Calculus. Those two happen to be intimately linked through the fundamental theorem of Calculus.
What concepts in data science would Calculus show up in?
Some of the algorithms we use are solved with optimization routines and that is going to involve derivatives and rates of change.
Stochastic gradient descent is definitely something data science students should know. It is basically a numerical method to come up with a minimum for a function. We end up using optimization functions and minimizing things often in data science.
What is Probability?
Probability is the study of how likely some outcome is. There are some algorithms that are strictly probabilistic in nature. Having a good, strong grasp of what these things mean is important to any Data Scientist.
What kind of Probability concepts should someone know for data science?
The first Probability concept that data science students should brush up on is the random variable. It can get tricky, but ultimately all you need to understand is that a random variable is a variable where some properties of the variable are known but the quantity is not because that variable depends on some random phenomenon. We might know its mean or variance but we're still recognizing that there's some kind of randomness going on.
What is Statistics?
Statistics is essentially what we did with data before there was big data or data science. Statistics concepts developed before we had machine learning and algorithms. We were talking about smaller amounts of data at that time. The mean and variance and those statistical summaries are still important here.
Data distribution is important. This means thinking about what distribution your data comes from and understanding probability mass/density functions and cumulative distribution functions. Once you know a bit about the distribution of your data, you can use that to form a hypothesis test, understand P values.
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