Once you decide to get started with Data Science (in a serious way), the first few months (if not year) can seem pretty difficult. At times, maybe even hopeless, especially if you do not have the necessary academic background or it has been a while since you have been in an academic setting. In my judgment, you should not let that stop you from your pursuit. There are so many resources online/offline to help you start to fill in your gaps.

Below are some of the key areas that you should have mastery over for you to go further with data science/machine learning:

**Calculus**

- Functions
- Continuity
- Differentiability
- Integration (single and multi-variables)
- Optimization
- Convexity/Concavity

**Linear Algebra**

- Vectors
- Matrices
- Eigenvalue
- Vector
- Singular Value Decomposition
- Least Squares Estimation and Matrix Algebra

**Statistics/Probability**

- Basic probability
- Sample spaces
- Conditional probabilities and independence
- Random variables
- Moments
- Distributions
- Chi-Squared
- F-Test
- T-Test
- Bayes’ Theorem
- Marginalization
- Bayesian Inference
- Likelihood
- Estimation
- Regression
- Analysis of Variance

**Stochastic Processes and Dynamical Systems**

- Dirichlet Processes
- Gaussian Processes for Machine Learning

What else do you think is necessary?

I thought it was worth mentioning this site http://www.societyofdatascientists.com.