What are the most important math courses for data science majors?

I'm thinking about majoring in data science when I get to college. What math courses should I focus on to be well-prepared for this major? Is there a specific order I should take them?

Typically, the most essential courses for data science at the collegiate level involve a strong foundation in statistics and calculus. Here's a recommended order in which you could tackle these subjects:

1. Principles of Data Science: This would be an introductory course that provides a basic understanding of topics such as data inspection, exploration, sampling, quantification, visualization, and cleaning.

2. Discrete Mathematics: This primarily involves studying mathematical structures that are fundamentally discrete rather than continuous. This would come in handy especially when you're dealing with specific, separated values.

3. Linear Algebra: Understanding vectors, matrices, linear transformations, eigenvalues and eigenvectors is crucial as this forms the basis for a lot of machine learning methodologies.

4. Calculus: You'll usually start with Calculus I (Differential Calculus) followed by Calculus II (Integral Calculus). They involve studying rates of change and accumulation of quantities respectively. These are integral to understanding how algorithms work, especially in fields such as machine learning and artificial intelligence.

5. Statistics and Probability: This is perhaps the most important field you need to master for data science, as these form the backbone of data analysis. These might include courses like Probability Theory, Inferential Statistics, Statistical Modeling, Multivariate Statistics, and Bayesian Statistics.

6. Advanced Courses: After you've got the basics covered, there are advanced math courses like Numerical Analysis, Multivariable Calculus, and Optimization that could come in handy, especially in complex data modeling and algorithm building.

7. Machine Learning: Though not a pure math course, it's a direct application of your mathematical skills. It would be great to get a head start on machine learning as it is an integral part of data science.

It's essential to note that proper course sequencing can vary depending on the specific college and the chosen curriculum, so it's important to consult with an academic advisor to determine the best plan for your specific case. It's also beneficial to know how to use mathematical software such as MATLAB or Mathematica, or programming languages often used in data science like Python or R, that will directly apply these mathematical principles.