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I pretty much followed the same route as OP re-studying mathematics seriously after 10 years in industry after initially doing a CS degree and doing mostly soft

I pretty much followed the same route as OP re-studying mathematics seriously after 10 years in industry after initially doing a CS degree and doing mostly software engineering but transitioning into Data Science the last 3 years. When I saw Book of Proof then Spivak then Apostol on his list I chuckled because that’s exactly the route I ended up following as well. Studying from 04:30 to 06:30 in the week and about 8 hours split up over the weekend, Spivak took 8 months to complete (excluding some of the appendix chapters) but if you can force yourself to truly master the exercises - and Spivak’s value is the exercises - then you’re close to having that weird state called “mathematical maturity” or at least an intuition as to what that means. You can forget about doing the starred exercises, unless you’re gifted. Spend a lot of time on the first few chapters (again, the exercises), it will pay off later in the book. It was a very frustrating experience and I had so much self doubt working through it, it’s an absolutely brutal book. Some exercises will take you literally hours to try and figure out. If you do Book of Proof first you will find Spivak much easier, since Spivak is very light on using set theoretic definitions of things. Even the way he defines a function pretty much avoids using set terminology. Book of Proof on the other hand slowly builds up everything through set theory. It was like learning assembly language, then going to a high level language (Spivak) and I could reason about what’s going on “under the hood”. Book of Proof is such a beautiful book, I wish I had something like it in high school, mathematics would have just made sense if I had that one book. I read a quote somewhere, think it was Von Neumann that said, you never really understand mathematics, you just get used to it. Keep that in mind.

nsainsbury 7y ago
Heh, nice to find someone who walked a similar path! :-) Ah Spivak...yes, I absolutely agree it's one of the best books to build up that mathematical maturity everyone talks about. For me Spivak took about 6 months and I managed to do almost all of the starred exercises - Gifted? No. Brutally determined: yes. And I was quite fortunate to be in a place in life where I could put serious hours in to it at the time. After that, I learned to relax a bit more as I realised I had pushed myself way too hard and was close to burning out. I still love looking back at that damn book though. There's just something that's so special about it...the way the exercises build upon each other and connect together. It's really unique.
p1esk 7y ago
So, you've made all that effort, how does it help you in your new role as a data scientist? Is there anything you do now that requires "mathematical maturity"? Or is it something that can be learned much quicker on as needed basis?
- laichzeit0 7y ago
  There are a lot of charlatans in the Data Science space who lack the necessary mathematical background for their roles. For me it was necessary to get a rigorous understanding of probability theory, and applied probability theory is basically what mathematical statistics is about. My background was CS and software so R, Python, data visualisation and ML operationalization is by and large the easy part of Data Science to me. If you pick up any book like Bishop's or ESL you will be extremely frustrated if your mathematical background is not there. I didn't feel comfortable creating predictive models for production use that I didn't completely understand what was going on "under the hood", the assumptions being made and how they could fail. It's the only ethical thing for any engineer to do.
  - p1esk 7y ago
    I do deep learning research for a living. I've taken graduate classes in probability, stochastic processes, optimization algorithms, and signal analysis (ECE PhD). I almost never completely understand what's going on under the hood of my models as soon as they get larger than a single neuron XOR mapper. That does not prevent me from finding ways to improve the performance of very large models (millions of parameters and dozens of layers). I agree that there are some papers (or the two books you mentioned) that can be quite dense and heavy on math, but I can't say I've ever felt like I needed any math other than basic calculus, linear algebra, and prob/stats 101 to understand almost all ML methods that people actually use in real world. Obviously if you want to make breakthroughs in theoretical ML, then sure, you do need the mathematical maturity (mostly because you will need to be formally proving things), but if you're a regular data scientist? Can you give some example what kind of math is involved in your predictive models?

nsainsbury 7y ago

Heh, nice to find someone who walked a similar path! :-) Ah Spivak...yes, I absolutely agree it's one of the best books to build up that mathematical maturity everyone talks about. For me Spivak took about 6 months and I managed to do almost all of the starred exercises - Gifted? No. Brutally determined: yes. And I was quite fortunate to be in a place in life where I could put serious hours in to it at the time. After that, I learned to relax a bit more as I realised I had pushed myself way too hard and was close to burning out. I still love looking back at that damn book though. There's just something that's so special about it...the way the exercises build upon each other and connect together. It's really unique.

p1esk 7y ago

So, you've made all that effort, how does it help you in your new role as a data scientist? Is there anything you do now that requires "mathematical maturity"? Or is it something that can be learned much quicker on as needed basis?

laichzeit0 7y ago
There are a lot of charlatans in the Data Science space who lack the necessary mathematical background for their roles. For me it was necessary to get a rigorous understanding of probability theory, and applied probability theory is basically what mathematical statistics is about. My background was CS and software so R, Python, data visualisation and ML operationalization is by and large the easy part of Data Science to me. If you pick up any book like Bishop's or ESL you will be extremely frustrated if your mathematical background is not there. I didn't feel comfortable creating predictive models for production use that I didn't completely understand what was going on "under the hood", the assumptions being made and how they could fail. It's the only ethical thing for any engineer to do.
- p1esk 7y ago
  I do deep learning research for a living. I've taken graduate classes in probability, stochastic processes, optimization algorithms, and signal analysis (ECE PhD). I almost never completely understand what's going on under the hood of my models as soon as they get larger than a single neuron XOR mapper. That does not prevent me from finding ways to improve the performance of very large models (millions of parameters and dozens of layers). I agree that there are some papers (or the two books you mentioned) that can be quite dense and heavy on math, but I can't say I've ever felt like I needed any math other than basic calculus, linear algebra, and prob/stats 101 to understand almost all ML methods that people actually use in real world. Obviously if you want to make breakthroughs in theoretical ML, then sure, you do need the mathematical maturity (mostly because you will need to be formally proving things), but if you're a regular data scientist? Can you give some example what kind of math is involved in your predictive models?