Required background in math

What background knowledge would be helpful to know as a datascientist? Know of any good (and free) resources? The following list is not complete, so please consider contributing via a pull request or sending me an email with suggestions or edits.

In the previous lesson on What is Data Science? we learnt that it is multifacted and requiers strong scientific analysis to create meaningful results. For this reason, to be a good data scientist, one requires a strong background in math: statistics and computer science as well as linear algebra and multivariable caluclus. Why? Not understanding the fundamentals will lead to incorrect analysis and result is poor decision making.

Most people give more emphasis on statistics (or computer science) over linear algebra and calculus since many of the machine learning algorithms are already implemented (so why learn the math?). While it is true that it is recommended to use already implemented algorithms, it is important to have a fundamental undestranding of how the algorithms are implemented. This way you understand the assumptions in using the algorithm both quickly and correctly.

The required knowledge is broken down into the following sections:

Precalculus and Mathematical Thinking
Statistics
Linear Algebra
Calculus

Precalculus and Mathematical Thinking

Data is fundamentally represented by numbers, so having a strong foundation in mathematics is very important. The following are links to good resources to provide a background:

Precalculus Mathematical Thinking Introductiuon to Logic Better Explained Math Concepts

When I am learning a new math concept, I usually search it on BetterExplained first to get a more intuitive explanation.

Statistics

Stats is arguably the most important background knowledge required since machine learning is applied statistics. I highly recommend reading StatsBookOnline and going through all the modules. It will provide a very comprehensive foundation the the frequentist approach to statistics. After reading the modules you should have a good understanding of the following topics:

Data basics:

Nominal, ordinal, interval, ratio scales and how to compare

Discriptive Statistics

mean, median, range, standard deviation, variance, and exploratory data analysis

Inferenial Statistics

Probability Theory Random variables Distribution functions (normal, poisson, gaussian) Percentiles and Outliers Skewness Analysis of Variance Prob Desnsity Function Central Limit theorem Monte carlo Hypothesis testing p-value chi^2 estimation confidence interval maximum-likelihood estimation Kernel density estimate regression co-variance corellation pearson coeff causation least squares Factor analysis

Bayesian vs Frequentist Approach

In addition, a data scientist should know the bayesian vs Frequentist approach to statistics and should be familiary with bayes theory and Bayesian Statistics. The notes go into Bayes Theorem.

Linear Algebra

What concepts are important?

From here

A lot of machine learning (ML) or applied statistics concepts are tied to linear algebra concepts. Some basic examples, PCA - eigenvalue, regression - matrix multiplication… As most ML techniques deal with high dimensional data, they are often times represented as matrices. Concepts such as singular value decomposition, projections, principal components, eigenvalue, eigenvectors, regression, matrix multiplication, matrix operations, matrix, inverse, solving differential equations using matrices are all important.

For Mathematical Modeling: for example, if you want to capture behaviors (sales, engagement, etc.) in a mathematical model, you can use matrix to breakdown the samples into their own subgroups, and each has its own parameter instead of using a global value. This requires some basic matrix manipulation. Matrix inversion, derivation, solving partial differential or first order differential equations with matrices, for example.For Understanding High Dimensional Distribution: multinomial as the basic example and there are many more.

Good resources:

Matrix Cookbook Khan Academy’s Linear Algebra Videos If you are really having difficulty, you can buy Linear Algebra Done Right which is both a comprehensive guide and provides great intuition. Hands on Linear Algebra for Data Scientists

Calculus

Khan Academy provides a great overview of many of the necessary concepts:

Calculus Integral Calculus MultiVariable Calculus Differential Equations

Calculus and differential equations is very important for methematic modeling of systems and used in optimization.

Once you feel you have the required mathematrical background, you can move onto the other parts of the required background