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Chances are you actually suck at algebra. I went through this issue when I started electrical engineering as part of an overly elaborate midlife crisis. I got t
by upofadown 5y ago
Chances are you actually suck at algebra. I went through this issue when I started electrical engineering as part of an overly elaborate midlife crisis. I got the book in the bookstore that was supposed to bring you up to high school level and just did all of the exercises. Then I did a whole lot of exercises for the introductory university math courses.
Basically it is something you have to grind at. Once you do enough problems all algebra will seem easy and you are done.
I am not sure that you actually need math for programming. Code is its own algebra.
- amelius 5y ago> I went through this issue when I started electrical engineering as part of an overly elaborate midlife crisis. Did it ease your midlife crisis? Would you do it again?
- sho_hn 5y agoAs someone with a "Watch Later" queue recently filled up with oscilloscope and variable power bench PSU reviews - I'd also love to know.
- dls2016 5y agoI second the grind. There's not really a shortcut... like lifting weights or practicing scales/rudiments. I returned to grad school at 27 for math and had trouble passing qualifying exams. I ended up using spaced-repetition to memorize large sections of books and old questions. I had previously shunned memorization... but coupled with focused practice it is a powerful tool. Memorizing forces you to distill the material and patterns to their essence and allows you to recognize the patterns in new situations.
- 300bps 5y agoThere's not really a shortcut... like lifting weights And just like lifting weights, you will lose it when you stop doing it. I remember doing the CFA program which is math and formula heavy. I had hundreds of formulas memorized. I couldn’t tell you the formula to calculate the standard deviation of a portfolio of three assets now if my life depended on it.
- solaxun 5y agoThis is my main qualm with testing as a means of validating understanding. If you truly understand a topic, you will probably pass a test on it. However passing a test most definitely does not guarantee understanding. I remember very, very little from the CFA exams (passed L3 about 10 yrs ago), because it tested surface level knowledge of an incredibly broad array of subjects. Far too broad to allow a deep-dive in any one thing. At the time, I could fit a bunch of formulas in my head and regurgitate them on command, but it was like filling up a leaky bucket. I had to load that sucker up and run into the exam center before it poured out. IMO testing well is it's own skill, and has little to do with understanding a topic. Understanding is when you've forgotten all the stuff you've memorized, but you can work your way back to a solution from first principles. I think the only way to get to that point is genuine interest and sustained study.
- wyclif 5y agoAnd just like lifting weights, you will lose it when you stop doing it While this is 100% true, I hate putting it that way because it makes weight training (and mathematics) sound like drudgery. The way I like to think about it is that if you want to stay strong, you have to push against resistance on a constant basis. It's the same thing with math. You have to exercise that part of your brain with algebraic resistance.
- HumanReadable 5y agoI agree there are no shortcuts, but just like the scales will come much more easily to someone naturally gifted at music, so will algebraic operations to someone gifted at math. We can all improve our abilities, but those not gifted has a much steeper hill to climb.
- Py-o7 5y agoI am a big fan of the working out analogy. In all cases you need to have a decent plan then execute-- basically this means showing up and putting in the work. If you do it right it should be a bit painful at times. And just like working out some people will progress more rapidly than you and have an easier time at it. So what? As long as your goal isn't to 'place' at the elite level, this is irrelevant. You really just need to show up and embrace the struggle. (For elite level tasks including grad school, its a bit more involved.)
- melenaboija 5y ago3Blue1Brown series on linear algebra is an amazing resource as a starting point. https://youtube.com/playlist?list=PL0-GT3co4r2y2YErbmuJw2L5tW4Ew2O5B https://youtube.com/playlist?list=PL0-GT3co4r2y2YErbmuJw2L5t...
- inetknght 5y agoI was going to add my own post recommending 3Blue1Brown. I'm glad you've already recommended it :)
- animal_spirits 5y agoLinear algebra is _much_ more complicated than normal algebra
- threatofrain 5y ago3B1B has stated that the series is mostly useful for summarizing or augmenting existing knowledge after taking the class; it's not for learning Linear Algebra fresh. If you sum all the minutes in the 3B1B videos it's basically the length of one video from a university course.
- melenaboija 5y agoAgree, I said starting point assuming that he has some basic knowledge as he is struggling so he must know something. For more advanced linear algebra I would recommend the class from Prof. Gilbert at MIT. https://youtube.com/playlist?list=PLE7DDD91010BC51F8 https://youtube.com/playlist?list=PLE7DDD91010BC51F8 https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra... What is your recommendation?
- threatofrain 5y agoI'm not sure about recommending video courses because... there are so few people who have taken up the burden of producing a full Linear Algebra video course. It's sad. But I would at least say that whether you're following Gilbert Strang or someone else, you should be following with a book as well. There's another guy, Jim Hefferon of St Michael's College, who has written a full book for his own class and produced a full video course on Linear Algebra (all free). https://hefferon.net/linearalgebra/ https://hefferon.net/linearalgebra/ https://www.youtube.com/watch?v=JnTa9XtvmfI https://www.youtube.com/watch?v=JnTa9XtvmfI https://www.youtube.com/watch?v=DJ6YwBN7Ya8 https://www.youtube.com/watch?v=DJ6YwBN7Ya8
- Tutanota1 5y agoThis is so true. I sucked at arithmetic but was quite good at Higher secondary maths.
- munchbunny 5y ago100% agree this is something you grind at. Calculus, even multivariate, and even the stuff beyond that, still grind. I used to be really good at it, definitely not the best but among the higher scores in my college math classes. But 10+ years later, when I go and look at stuff that would have barely fazed me then, I go cross eyed now. I remember the concepts, vaguely, but following the math and linking together the various theorems and transformations feels like wading through syrup. It’s a problem for me as I’m trying to dig into data science stuff, and it feels like getting back into marathon shape after 10 years of not running. There’s absolutely a component of learning the concepts, but a huge part of being good at the math is just building up the mental muscle memory for symbolic manipulation. Sure there’s innately talented people out there, but the consistent application of incremental effort will get you very far regardless of talent.
- jordanpg 5y agoAgree with this and would also add: in addition to being able to do algebra fast and have it be second-nature, at higher levels it helps if you are able to do it 100% accurately. 5 nines isn't enough. I didn't appreciate this until I was a graduate physics student and was frequently frustrated by minor algebra errors in long, complex problems.
- bigbillheck 5y agoI've known a lot of mathematicians, some of whom were really good, and five nines (one-in-one hundred thousand) is an implausibly high standard for humans to reach. I'm certainly nowhere near there. What's worked for me is to develop an intuition about how things 'should' look, so that if I do make a mistake I'll get a 'hey, that's not right' feeling a couple steps later.
- qsmi 5y agoJust to expand on this, when I worked as a grader in college I noted on engineering test keys the professor's answers were always roughly three short lines of handwritten equation. But the student's answer section were often totally darken with pencil they wrote so much. The heuristic was definitely the longer the answer the more wrong it was. This is something I've taken to heart professionally too. If the equations are getting out of hand it's either wrong or I need some simplifying assumptions (like that cow needs to be spherical). Otherwise one just can't keep track of it and reason about it. If I need a more precise answer, that's what computer numerics is for.
- sdenton4 5y agoWhat's important isn't being able to do it right quickly the first time. It's having a strong habit of checking your work as you go, both at a low level and a high level. (Kinda like unit testing and integration testing...) Fast arithmetic and algebra are fairly particular skills. As one progresses into new world of math, the calculations and operations may be completely different from what's been practiced, making the fast math less useful. But a good habit for careful progress is completely general!
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- redman25 5y agoI‘ve enjoyed revisiting topics I learned in school through the Kahn Academy[1]. You can pick any topic you want to start with and follow it through as far as you want. [1] https://www.khanacademy.org https://www.khanacademy.org
- web007 5y agoSeconding this. I went through precalc in school, then promptly forgot most of it once I started working. All of the bits I had learned felt rushed, so a lot of them fell out of my brain even while in school. I only had a basic understanding of most of what I "learned". About a year ago I decided to go back to basics, and start over from zero on Khan Academy. I've been v.e.r.y slow, maybe a lesson a month on average, but have been grinding through the lowest level math to really understand and remember it. Down to addition, subtraction and multiplication even - I've relearned how to multiply small numbers in my head, and gotten much better at quick mental addition and subtraction. I have scheduled and dedicated more time for it this year, so I hope to catch up to my original math basis. This time, hopefully, remembering all of it instead of skimming. That should set me up well for linear algebra, and then calculus next year and beyond. One thing that may help regardless of how you choose to learn: pick a problem you want to tackle that needs Fancy Maths. It doesn't need to be anything useful, or anything difficult like "prove this unproven theorem". It will motivate you as long as it keeps your brain engaged. For me it's factoring and primality proving, where I can't even read the equations / algorithms because I don't have the basic tools. As I get further along I keep looking back to those problems and seeing how the bits I'm learning apply around the edges or to simpler factoring algorithms. It keeps me motivated to learn more to be able to dive deeper into the juicy parts.
- badactor 5y agoThe problem for me is identifying where exactly in my mathematical fundamentals things fall apart (like with prime numbers, some basic arithmetic, geometry) that makes higher-level math a struggle conceptually. It's always felt like there were holes in my fundamentals. I suspect the only way to figure this out is to go back and do everything again either through Khan Academy or books. Does anyone else have this issue? When it comes to math, I try to avoid self-diagnosing with dyscalculia or with poor working memory. Instead, I think I've gone so long with math being an anxiety-inducing subject that any time I need to solve math under the tiniest amounts of pressure, I fall apart. Mind naming what book you used?
- Kye 5y agohttps://www.amazon.com/Schaums-Outline-Elementary-Mathematics-Outlines/dp/007176254X https://www.amazon.com/Schaums-Outline-Elementary-Mathematic... Schaum's Outlines are like that "Learn X in Y Minutes" site for school subjects. They give the clearest, most bare bones explanation so you can quickly identify gaps. I had the college algebra book for the required math class in technical school. Between that and YouTube, I was able to pass the class.
- pthread_t 5y agoTry Khan Academy. The exercises (especially with how they focus on mastery), coupled with the videos will help you root out your weak points and even master them. Do not be ashamed in starting with the kindergarten math topics and moving upwards from there. If you are able to power through it, good on you. If you get stuck on something, even better -- now is your chance to master it. KA helped me go from hating math in high school to double majoring in Math & CS in college, and graduating with honors. I donate to KA now.
- ambrozk 5y ago"Mathematical fundamentals" is a sliding scale. You have to define your end goal. What do you want to understand, that you are currently unable to understand due to your incapacity with mathematics? If you want to understand computational complexity theory, for instance, you need a different set of "fundamentals" than you do if you want to understand high-school physics. It'll be a different thing if you want to read econ papers, and a different thing if you want to study machine learning. Within the intersection of all these fundamentals is probably basic arithmetic and algebra. Those tools are basic requirements for everything else. Beyond that, you need to define your goal before you decide what math to learn.
- bigbillheck 5y agoI used to teach college calculus, and can confirm: if you're not comfortable with algebra, you're going to have a bad time of it.
- ransom1538 5y agoIF!! You have kids learning math is right there with a full program. I forgot all my math so I keep up with my kids and help at least 15 minutes per day. I have been tripped up with 5th grade word problems - it is fun. Follow along with your kids math - it will move quicker than you think. I remember my last math class: Number theory. I got through the final, shook the professors hand and told him, "this is the end of intellectual ability". I have never seen a professor laugh that hard. Once you get past abstract math classes thin out fast and it just gets weird.
- corysama 5y agoAnyone who sucks at algebra and has a low grind tolerance should try https://dragonbox.com/products/algebra-12 https://dragonbox.com/products/algebra-12 It’s very well made. And, it’s designed for 12 year olds. So, adults can usually manage to keep up.
- RegBarclay 5y agoI hadn't thought about it that way. I was good at algebra, but can't get through calculus to save my life. I've mostly found that coding is more about logic than math. When math has come up in my work, it's generally a formula or calculation that's already defined and I just have to code it into a system, which has never been a problem for me.
- commandlinefan 5y ago> I did a whole lot of exercises Same happened to me. I completed a BS in CS and learned just enough algebra, trig & calculus to pass the classes and then forgot almost everything. Many years after graduation, I came across an interesting post in comp.lang.java - somebody was asking how to create a java applet that could draw a 3D block arrow that could orient itself in any direction. I'm pretty sure somebody was asking for help with his homework, but I thought it was an interesting problem so I started looking at it and the first issue I ran into was drawing a line perpendicular to another. I vaguely remembered that there was a formula for computing the slope of a line perpendicular to another and when I looked it up - in context to a problem I was trying to solve - it just kind of "clicked" and I found it interesting. From there I fell down the rabbit hole of re-learning everything up to differential equations that I was supposed to be learning when I was an undergraduate.
- ThinkBeat 5y agoAlgebra is a wide topic. My second year of university is where i fell off math. Several people have told me that once they reached post graduate level at university that math made sense to them. They saw the perspective of unified math. How it all fits together. Sadly, all I did know I have forgotten.
- randmeerkat 5y agoI’m curious, was getting the EE degree as part of a midlife crisis worth it? Or would you have done things differently looking back?
- znpy 5y agoI'm no math genius however I just want to add this tiny bits: - you don't really "learn" math, you just get used to it - math is really mental gymnastics, and "learning math" actually is doing a lot of math exercises
- maxgiraldo 5y agoIf anyone is looking to brush up on their Algebra fundamentals, I built an app for that and it's free to use: https://apps.apple.com/us/app/pensend/id1571322730 https://apps.apple.com/us/app/pensend/id1571322730. I had a similar problem where I didn't understand where my fundamental knowledge gaps were so I ended up starting from the beginning (pre-algebra). I hope this is helpful for people! (sorry for the shameless plug)