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How and what mathematics must be taught for training engineering students with the mathematics required for Machine Learning?

How can one conduct training of mathematics required for application-based topics like ML? The students are basically engineering students having covered basic Engineering Mathematics.

Can anyone please give any tips for an intuitive way of teaching ML Maths? Also, recommendations on any good books that the students will find easy to comprehend are welcome...

Edit- the scope of the course is to make the students industry-ready with principles of mathematics used in ML topics. It is not as deep as research Mathematics but certainly more rigorous and focused than the general Engineering Mathematics.

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  • $\begingroup$ Could you be more precise about what basic engineering mathematics is? I would guess single and multivariable calculus, linear algebra and ordinary differential equations. But might also include probability, statistics, partial differential equations and/or complex analysis. $\endgroup$
    – J W
    Commented Jun 17, 2021 at 9:46
  • $\begingroup$ Yes, multivariable calculus, linear algebra and ordinary differential equations, probability, statistics, partial differential equations, complex analysis are included. But the depth and application orientation required for ML lacks in the course. $\endgroup$
    – Aatmaj
    Commented Jun 17, 2021 at 10:57
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    $\begingroup$ Machine Learning is such a broad topic. It could definitely be all of those listed by @Aatmaj, or it could be none of those(!), depending on the purpose of the course. There are plenty of examples in online courses of both math-oriented and concept-oriented courses along with the material they cover. Several platforms exist that remove the requirement of math and focus on pipeline processes of ML. But again, what's the purpose of the course? That would largely answer your question. $\endgroup$
    – Carser
    Commented Jun 17, 2021 at 11:44
  • $\begingroup$ Thanks. edited accordingly $\endgroup$
    – Aatmaj
    Commented Jun 17, 2021 at 12:24

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This may help, the labs and associated materials for a course CSC 294: Computational Machine Learning: github link. See course-materials/Labs/, Jupyter Notebooks:

  • k-means
  • PCA
  • SVD
  • k-NN
  • Gradient descent
  • SVM
  • Decision trees
  • Deep learning
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Dustin Mixon at The Ohio State University has written rigorous notes on the Mathematics of Data Science that cover both "fundamentals" (matrix analysis, convex optimization, probability) and "applications" (dimensionality reduction, clustering, compressed sensing).

These notes are pitched at a reasonably high graduate level, but they contain plenty of approachable material worth sharing with an undergraduate audience.

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I am sure you will enjoy this Mathematics for Machine Learning specialization by UCL

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If you are talking about a short exposure (hard to tell but guessing), I think running an in class lab on multiple regression, would be good. There's a lot of hype around "machine learning" and "AI", but in practice, it often has elements of regressions, DOE, etc. In any case, those tools are very close and have uses of their own. Plus if you do an in class lab with Stata or R, where they can play around with degrees of freedom, fitting, second order effects (squared terms and interactions), it will not feel like "math class", but something sort of computer-ish and useful. And stats IS math. (Not) sorry, Rudin luvverz!

It's very hard to answer this, because we don't know the context. Are you talking about all the foundational mathematics for these students (so basic calculus and the like)? Or sooper high level research? (Doubt that, think you are talking bachelor's students trying to cash in on the buzzword. But of course, some MIT Ph.D. might be using some hairy stuff and doing theory papers, needing all the high end gadgets of optimization.)

If we take for granted, these are CS BS students, and they will get the normal slew of math courses for CS (calculus, linear algebra). They are not going to want to be forced through a bunch of hairy stuff that doesn't directly apply. There is a reason why (most of) these students are doing CS instead of physics. ;-)

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