If you’re looking for a single, detailed, and correct answer, this is a challenging question to answer and one that we can debate for hours.
Instead, I’ll give you a very high-level perspective I don’t believe (or hope) that many people will disagree with.
Finally, this “syllabus” will not be what you would discover in a single university course, but rather what I believe you should know.
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Simple programming: Since you’ll be working with a machine, learn programming principles, most likely in Python.
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Data loading, data cleansing, simple logical statements, loops, and data saving are excellent places to start.
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Inference, sampling, distributions, and how to validate a model are all covered in introductory statistics.
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Unsupervised Machine Learning : PCA, t-SNE. Supervised Machine Learning: (deep) neural networks, including convolutional nets, random forest (therefore also decision trees).
The first is for dimensionality reduction, and the second is for visualization (if you haven’t heard of t-SNE, look it up; it’s a fantastic piece of work).