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>Speaking of math, you should have some familiarity with calculus, probability and linear algebra Curious to know if anyone has had success learning/re-learnin

by xor1 10y ago

>Speaking of math, you should have some familiarity with calculus, probability and linear algebra Curious to know if anyone has had success learning/re-learning these as a mid-20s or older adult who works fulltime, and if you could potentially provide a list of books/courses to go through. I personally never learned anything past geometry (in high school). The most advanced math class I took in college was College Algebra. That means I never learned trig or anything past it (so no calc, linear algebra, or probability), and I'm sure most people on HN surpassed me math-wise sometime in high school :) I've been able to skate by with my embarrassing lack of math knowledge/skills as a developer, but I feel like it's only a matter of time until the mathematical steamroller becomes a serious threat career-wise and I get crushed.

mliker 10y ago
While I did take courses in probability, linear algebra, and lots of calculus, until recently, I forgot most of the probability and all of the linear algebra I learned in school. As for calculus, I only remembered how to take basic derivatives. In any case, I've been spending the past month brushing up on my linear algebra and probability, and it's been a struggle, but now that I'm motivated and under no time pressure to relearn the material, I find it way more fascinating than I did in college. In fact, I skipped tons of my linear algebra classes because I thought the subject was dry and dull. I also rushed through my probability and stats homework just so I could get a good grade on them. I think if you're motivated, and you can do basic math, you should be able to educate yourself in calculus, probability, and linear algebra. It'll be a struggle, but with motivation, you'll be able to pick up the concepts. for probability and stats: https://www.amazon.com/Introduction-Probability-2nd-Dimitri-Bertsekas/dp/188652923X https://www.amazon.com/Introduction-Probability-2nd-Dimitri-... for linear algebra: https://www.amazon.com/Coding-Matrix-Algebra-Applications-Computer/dp/0615880991 https://www.amazon.com/Coding-Matrix-Algebra-Applications-Co... this was my college calculus textbook: https://www.amazon.com/Calculus-7th-James-Stewart/dp/0538497815 https://www.amazon.com/Calculus-7th-James-Stewart/dp/0538497.... I can't comment if it was good or not because by college, I had taken calculus twice so it was all a refresher best of luck! You sound educated enough (yes, I'm judging from the couple sentences you wrote) that I think you won't have any problems acquiring math knowledge with persistence.
WhitneyLand 10y ago
Yes, you can easily catch up on the math if you put in the time and it's so much easier now with the resources out there. You say didn't take trig? Check this out as one example: https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/intro-to-the-trig-ratios/v/basic-trigonometry https://www.khanacademy.org/math/trigonometry/trigonometry-r...
YeGoblynQueenne 10y ago
My maths level was probably worse than yours: I too only paid any attention to geometry at school, plus trigonometry and the single chapter we did on logic. I think I hid under the desk when we were learning calculus. I graduated from CompSci in 2011 and worked as a proud code monkey since then. Last year I took up a Master's course in AI (well, "Intelligent Systems") which was chock-full of machine learning modules, as expected [1]. I finished just a few weeks ago. I struggled a lot, particularly because I did the course part-time and I was only offered an (optional) maths course in the second year after the machine learning and image processing modules- and concurrently with an NLP module. The maths module helped a great deal and it cleared up a hell of a lot to do with differentiation and linear algebra. I still struggled with the maths module itself and to be honest I got a lot of help on the homework from my roommate who is a maths wiz, but in the end I managed to feel comfortable with the material and to get a good mark (75%) in the maths module. I think I impressed my maths lecturer even -but that was my coding skillz, haha. Teach was amazed I managed to implement an LSTM RNN in Python [2] (we went over optimisation and had to code a hill-climb/gradient ascent algo, plus a RNN). In truth once you get the maths down pat the coding is nothing, but I guess mathematicians are crap as coders :P Anyway, what I mean to say is: yes, totally. You can totally get at the very least comfortable with the material required for deep (or standard machine) learning. And if you've built a good level of coding skill from work you'll find it gives you a big boost, and can even help you clarify some of the maths. Frex, I feel I got a good intuition about optimisation in general from implementing hill climb/ gradient ascent, especially because I spent hours watching it trying to get over a ridge in a datascape and getting stuck every. single. time. the dumb thing XD I think you'll find linear algebra in particular the easiest to learn because it's almost just array manipulation and you've done that in spades. Differentiation is a bit harder, but at some point it clicks ("it's like stepping on a break pedal" or some such analogy) and it goes swimmingly from there. Probabilities are not hard either, it's just a form of logic. Other stuff- ymmv, but it's all doable. As to books- I don't have any recommendations. I think any popular textbook is going to be good enough to get you started :) [1] How I ended up doing that course- I got into AI via logic programming, that I learned during my degree. Many Prolog textbooks are also AI and particularly NLP textbooks so I thought it would be a shame to let all that kewl stuff I learned by reading them go to waste. At the time I had no idea how hot machine learning is in the industry. [2] Plug: https://github.com/stassa/lstm_rnn https://github.com/stassa/lstm_rnn
Noseshine 10y ago
edX has quite a few good and very good courses on the subject. For example, right now "MITx: 6.008.1x Computational Probability and Inference" is being offered (other courses are available in archived mode), as well as Caltech's "Learning from Data" (theory heavy) course. There also is a lot on Coursera, but the more theoretical university courses on probability theory are on edX. Everything is free - if you ignore the certificates (if you really need to prove you took a course take a screenshot of the progress page).
conjectures 10y ago
It's totally possible. Which isn't to say that it's easy. If you go down that road, be prepared to sacrifice your social life for several years. The most frustrating thing will be going through basics that don't seem connected to your eventual goal of ML; this is potentially a long phase. I'd recommend Khan Academy for the math basics. Schaum's Outlines series for lots of worked problems. I'd recommend Strang's MIT OCW videos and books for Linear Algebra. I first learned calculus from an economics book, probably best not repeated ;). Bishop's PRML book is a good source on probability, Bayesian stats and machine learning. I did a part time MSc in applied stats while working full time. Even in the MOOC era, there's nothing like real exams to focus your efforts.
- RandomInteger4 10y ago
  Khan Academy is a great place to start. I second that recommendation. Although I was pretty confident in my maths up through basic calculus, I began fresh earlier this year starting from pre-algebra on their videos and problem sets. I took the approach of looking at the mind as a muscle and if I had taken a long break from lifting, I wouldn't jump right back in lifting the same weights. The analogy isn't perfect, but I feel like it helped to reinforce the old basic neural pathways in order to prime my mind for more difficult topics. EDIT: Also the achievement points aspect helped as a learning tool as well.
ivan_ah 10y ago
Check out my math and physics textbook, it sounds like it would be perfect for you: https://minireference.com/ https://minireference.com/ I also have one on linear algebra: https://gum.co/noBSLA https://gum.co/noBSLA Piece of advice: don't skip the exercises. It's great to learn and understand math, but you don't really learn the material until you have to solve problems and make use of the math. Since you're a developer, you'll probably also enjoy this short tutorial on basic math using SymPy: https://minireference.com/static/tutorials/sympy_tutorial.pdf https://minireference.com/static/tutorials/sympy_tutorial.pd...

by xor1 10y ago

mliker 10y ago

While I did take courses in probability, linear algebra, and lots of calculus, until recently, I forgot most of the probability and all of the linear algebra I learned in school. As for calculus, I only remembered how to take basic derivatives. In any case, I've been spending the past month brushing up on my linear algebra and probability, and it's been a struggle, but now that I'm motivated and under no time pressure to relearn the material, I find it way more fascinating than I did in college. In fact, I skipped tons of my linear algebra classes because I thought the subject was dry and dull. I also rushed through my probability and stats homework just so I could get a good grade on them. I think if you're motivated, and you can do basic math, you should be able to educate yourself in calculus, probability, and linear algebra. It'll be a struggle, but with motivation, you'll be able to pick up the concepts. for probability and stats: https://www.amazon.com/Introduction-Probability-2nd-Dimitri-Bertsekas/dp/188652923X https://www.amazon.com/Introduction-Probability-2nd-Dimitri-... for linear algebra: https://www.amazon.com/Coding-Matrix-Algebra-Applications-Computer/dp/0615880991 https://www.amazon.com/Coding-Matrix-Algebra-Applications-Co... this was my college calculus textbook: https://www.amazon.com/Calculus-7th-James-Stewart/dp/0538497815 https://www.amazon.com/Calculus-7th-James-Stewart/dp/0538497.... I can't comment if it was good or not because by college, I had taken calculus twice so it was all a refresher best of luck! You sound educated enough (yes, I'm judging from the couple sentences you wrote) that I think you won't have any problems acquiring math knowledge with persistence.

WhitneyLand 10y ago

Yes, you can easily catch up on the math if you put in the time and it's so much easier now with the resources out there. You say didn't take trig? Check this out as one example: https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/intro-to-the-trig-ratios/v/basic-trigonometry https://www.khanacademy.org/math/trigonometry/trigonometry-r...

YeGoblynQueenne 10y ago

My maths level was probably worse than yours: I too only paid any attention to geometry at school, plus trigonometry and the single chapter we did on logic. I think I hid under the desk when we were learning calculus. I graduated from CompSci in 2011 and worked as a proud code monkey since then. Last year I took up a Master's course in AI (well, "Intelligent Systems") which was chock-full of machine learning modules, as expected [1]. I finished just a few weeks ago. I struggled a lot, particularly because I did the course part-time and I was only offered an (optional) maths course in the second year after the machine learning and image processing modules- and concurrently with an NLP module. The maths module helped a great deal and it cleared up a hell of a lot to do with differentiation and linear algebra. I still struggled with the maths module itself and to be honest I got a lot of help on the homework from my roommate who is a maths wiz, but in the end I managed to feel comfortable with the material and to get a good mark (75%) in the maths module. I think I impressed my maths lecturer even -but that was my coding skillz, haha. Teach was amazed I managed to implement an LSTM RNN in Python [2] (we went over optimisation and had to code a hill-climb/gradient ascent algo, plus a RNN). In truth once you get the maths down pat the coding is nothing, but I guess mathematicians are crap as coders :P Anyway, what I mean to say is: yes, totally. You can totally get at the very least comfortable with the material required for deep (or standard machine) learning. And if you've built a good level of coding skill from work you'll find it gives you a big boost, and can even help you clarify some of the maths. Frex, I feel I got a good intuition about optimisation in general from implementing hill climb/ gradient ascent, especially because I spent hours watching it trying to get over a ridge in a datascape and getting stuck every. single. time. the dumb thing XD I think you'll find linear algebra in particular the easiest to learn because it's almost just array manipulation and you've done that in spades. Differentiation is a bit harder, but at some point it clicks ("it's like stepping on a break pedal" or some such analogy) and it goes swimmingly from there. Probabilities are not hard either, it's just a form of logic. Other stuff- ymmv, but it's all doable. As to books- I don't have any recommendations. I think any popular textbook is going to be good enough to get you started :) [1] How I ended up doing that course- I got into AI via logic programming, that I learned during my degree. Many Prolog textbooks are also AI and particularly NLP textbooks so I thought it would be a shame to let all that kewl stuff I learned by reading them go to waste. At the time I had no idea how hot machine learning is in the industry. [2] Plug: https://github.com/stassa/lstm_rnn https://github.com/stassa/lstm_rnn

Noseshine 10y ago

edX has quite a few good and very good courses on the subject. For example, right now "MITx: 6.008.1x Computational Probability and Inference" is being offered (other courses are available in archived mode), as well as Caltech's "Learning from Data" (theory heavy) course. There also is a lot on Coursera, but the more theoretical university courses on probability theory are on edX. Everything is free - if you ignore the certificates (if you really need to prove you took a course take a screenshot of the progress page).

conjectures 10y ago

It's totally possible. Which isn't to say that it's easy. If you go down that road, be prepared to sacrifice your social life for several years. The most frustrating thing will be going through basics that don't seem connected to your eventual goal of ML; this is potentially a long phase. I'd recommend Khan Academy for the math basics. Schaum's Outlines series for lots of worked problems. I'd recommend Strang's MIT OCW videos and books for Linear Algebra. I first learned calculus from an economics book, probably best not repeated ;). Bishop's PRML book is a good source on probability, Bayesian stats and machine learning. I did a part time MSc in applied stats while working full time. Even in the MOOC era, there's nothing like real exams to focus your efforts.

RandomInteger4 10y ago
Khan Academy is a great place to start. I second that recommendation. Although I was pretty confident in my maths up through basic calculus, I began fresh earlier this year starting from pre-algebra on their videos and problem sets. I took the approach of looking at the mind as a muscle and if I had taken a long break from lifting, I wouldn't jump right back in lifting the same weights. The analogy isn't perfect, but I feel like it helped to reinforce the old basic neural pathways in order to prime my mind for more difficult topics. EDIT: Also the achievement points aspect helped as a learning tool as well.

ivan_ah 10y ago

Check out my math and physics textbook, it sounds like it would be perfect for you: https://minireference.com/ https://minireference.com/ I also have one on linear algebra: https://gum.co/noBSLA https://gum.co/noBSLA Piece of advice: don't skip the exercises. It's great to learn and understand math, but you don't really learn the material until you have to solve problems and make use of the math. Since you're a developer, you'll probably also enjoy this short tutorial on basic math using SymPy: https://minireference.com/static/tutorials/sympy_tutorial.pdf https://minireference.com/static/tutorials/sympy_tutorial.pd...