Greetings,
I just completed the first of three courses for the mathematics for machine learning specialization.
This was my first exposure to linear algebra. Overall, I felt the course was produced well, with great instruction and great supporting content.
What I learned:
- Solving systems of linear equations
- Vectors and linear transformations
- Determinant and eigenvectors
- Matrix multiplication with NumPy
The math is quite useful to demystify a lot of the algos and interpret them with confidence.
However, I did leave feeling there was something missing. All the exercises show you how to do the math for functions that are available in common Python packages.
Im still very curious about the expectations for a data scientist to apply math in the field.
Or have we reached a point where everything has been abstracted through a python package?
Either way, these skills are a hard requirement for any data scientist role. Glad I got through the first one 
Cheers!
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@dan_herman unfortunately I have not reached the ‘professional’ stage yet, but IMHO the math is useful for:
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Perhaps developing your own custom models and methods of abstraction.
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Noticing when, even using libraries, something is ‘going wrong’. Even having simply a general sense of the inner workings of a model and how it is constructed will provide a sense if your analysis is producing expected results. Without this knowledge you will have no idea where/what to debug.
I do though hope a present practioner can fill you (and me, for that matter) in with more answers.
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I just look at it as an investment of time. There is so much to learn and I only have a limited amount of time.
How much more time can I spend on this topic? I would love to do the entire course again. But it’s not practical.
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@dan_herman I understand.
I mean personally the further I go into this topic I realize just how dense it is and how much there is to learn.
Personally, I haven’t taken the maths course on here so I’m not sure how direct it is in terms of ‘motivating cases’ (i.e. did you learn to do PCA ?).
In the end I think a lot also depends on the level of employment you are looking for (say, data analyst vs data scientist).
I mean, at the end of the day one also has to consider, at least in the US there is a reason being a Data Scientist is a really well paying job. You have to know a lot of stuff.
It is not like working at McDonalds (which I have the right to say because before the dawn of time one of my first jobs was the grill guy at Burger King).
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Just trying to hit the sweet spot and move on.
Will go through a few tutorials for regression, clustering and recommender systems. I feel those are the main algos to start with. Will be interesting to see how hard they are to build from scratch.
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@dan_herman Once you hit recommender systems on sparse matrices you will see what all that linear algebra was for (i.e. your SVD).
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Hello,
I think one ultimate end use of maths is to deduce/invent new methods. Maths provides a language to reason this world that common spoken language can’t easily do. For example, with matrix algebra, you can deduce the so-called closed-form solution for a linear regression problem. With that solution, you have a new method.
Of course, then we could say, why care while some python library can do that for me?
I think we should care because it is an example for the power of deducing new approach with basic maths. If we focused on how unnecessary learning maths is to use the closed-form solution, then we might be unintentionally burying this creative-power side of the maths.
How far we can use the maths depends on us. If we want to implement some paper’s algorithms for our organization, we would need to be able to understand the maths because the paper may not be prepared to guide us through. There might be gaps everywhere for us to fill in ourselves. What do we use to fill those gaps? We need some of that creative power to make something and fill the gaps, don’t we?
If we want to be the creative guy for our organizations, we might need to read even more and discuss with like-minded people. Do we speak the language of maths when it is required? Or do we always need a translator sitting next to us?
If we want to just know how to best carry out some other duties with algorithms, then, I think the second point of @Nevermnd’s first reply has explained that.
Therefore, I think we will find our maths skills to be helping when we decide to use them. Demystifying, as @dan_herman exemplified, is a good way. Maybe implementing some paper’s algorithms, as inspired by @Nevermnd, will be another good way, and probably will be the way that we will discover what kind of maths we are lacking, instead of wondering what maths can do for us. 
Cheers,
Raymond
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