7 ms·

I really hope this doesn't come across as brash. I don't mean it to, but I must disagree with your assertions (In my case at least). Learning advanced mathemati

by mungoid 10y ago

I really hope this doesn't come across as brash. I don't mean it to, but I must disagree with your assertions (In my case at least). Learning advanced mathematics without university is completely possible. Because it is at your own learning pace. Not one of a University. I graduated several years ago with a BS in Computer Science, with a Focus on Networking. And during that time, I held 3 part time jobs while also being a math tutor. Almost none of the math I use today as a physics developer was learned from schools. I also never had that piece of mind you mentioned, because I was constantly juggling several things at once while going to school. My knowledge of advanced mathematics at the time of my graduation was pretty non existent. I think the most advanced math I had was Algebra 2 or something like that, and the Professors just basically read verbatim from the book. A few years after Uni, I started teaching myself Calc, Trig, Vector maths, Diff Eq and Physics strictly from what I have found on various sites, software and books. Because of that, I ended up getting a physics simulation developer position at a software company. Because in my companies view, being able to teach yourself all that math is much more impressive than being taught from a University. I hated math during High School and College, but since then, I have found that I absolutely love math, and I will never stop trying to learn or do new things. My degree was two small lines on my CV, while about 50% of what I had on my CV was all learned on my free time, by myself. So learning math without a College or University is totally possible, and in my situation, worked way better. Sites like Khan Academy, Wolfram, Youtube, etc. all give you the resources and leave it up to you to progress at your own pace, for free.

yodsanklai 10y ago
Congratulations, and I'm glad you proved me wrong :)
- mungoid 10y ago
  Thank you! I will admit that it was by no means quick or easy and there were many, many times I wish I could have had an actual person with me to explain it. Not to mention the frequent of wanting to give up when something wasn't 'clicking' and i felt i couldn't do it.
heimatau 10y ago
I'm glad you had success but...let's not measure your outlier experience with the rest of the world. Especially in Adv Mathematics. I'd point you and other HNs to Srinivasa Ramanujan. He is self taught but...he was wrong [1]. He had a brilliant mind but...due to being self taught, he made some critical mistakes. Being self taught can easily lead the learner to some critical mistakes. Eventually, they may be corrected (and at what 'cost' does this mistake cause an organization or business or those involved) but it's more efficient of someone's time to just learn from another. I'm not saying everyone needs a University Degree. I'm saying that everyone needs a teacher. Everyone. Why? Because instead of 'the blind leading the blind' (you as a 'blind' teacher, leading you as a 'blind' learner). You have the efficiency of being led by a mentor of some kind that can steer you away from faulty concepts that may come in. It's great that we now have more free/cheap materials than ever before at our disposal but without a mentor or some kind of peer-review, we could be misapplying concepts. Also, to comment on something you specifically said: > Because in my companies view, being able to teach yourself all that math is much more impressive than being taught from a University. Yes, it's 'impressive' but...most don't learn this way. Which is way it's 'impressive'. Also, being self-taught, how do you truly verify what you understand mathematically is accurate and solid? [2] You might be and I'm not going to fault you but learning concepts is one thing but applying them is even more challenging. It's one thing to be 'impressive', it's a whole other thing to have mastery over a topic. And I'm a firm believer mastery is mostly achieved with peer/mentor feedback. I applaud you but let's not steer others to just teach themselves, without help from others. Let's encourage self taught and peer feedback. It's not one or the other, it's both. [1] - https://www.youtube.com/watch?v=jcKRGpMiVTw https://www.youtube.com/watch?v=jcKRGpMiVTw [2] - I searched for 30 minutes to find this article, that I read, that stated the current environment of Mathematical Research [3]. Namely, it stated that a lot of research is being published that is NOT peer-reviewed because there isn't enough skilled* Mathematicians to review the work. That it's a 'dirty little secret' in the industry that "known" Mathematicians would get a pass (published w/o review) but many others trying new groundbreaking ideas couldn't get their research peer-reviewed. And with the given University culture to publish NEW research and not review, it's understandable how this environment was created. Namely, Einstein gets the fame but it took numerous people to peer-review his work before it was accepted. [3] - I know this article exists. It's one of the reasons why I'm becoming a Mathematician. I read it in the past 2-3 years. It was a major site (NewScientist or something that focuses on emerging research). If you can find it, I'd be very grateful. I'm now* using Zotero to save all my findings, so hopefully when I quote something I'll have a source. ;) *(edited) - original said 'not'. I meant 'now I'm using Zotero'. ;). original said 'skill', I meant 'skilled'
aluhut 10y ago
I wish I could make the jump again. When I was a kid, I loved Math. I even got one of this badges that were so popular in my east block country, for being the best kid in Math for my whole year group. Then we moved to Germany. Math level was far below mine, I got bored, started to do other stuff and lost it when they overtook me. Growing up and work did the rest. I lost it. When I had/have to do some math I'm doing what is needed but this creative spark you need is gone. Now I find it very complicated to get even into the syntax...I fix most of my problem through the net. It's like losing a friend whose face you've already forgotten.
- mungoid 10y ago
  Yeah it becomes increasingly difficult as you get older. I really wish I would have gotten into it sooner. DIY math is great, but it taught me to be more of a loner than I'd like.
deleted 10y ago
[deleted]
visarga 10y ago
The web is full of videos and PDFs with learning materials. But what is needed for learning to actually work is to have exercises to practice on. What I mean is fine gradation of difficulty and tracking prerequisites (notions needed in order to tackle a problem) so as to give students problems that are not too easy or too difficult, but just at the right level. I seldom find such problems/examples tuned to slightly above my level of understanding. Same problem in programming and machine learning - people need a little hand holding in the form of a sequence of problems to solve that would never be either too difficult or too easy. Examples usually jump from Todo MVC to full apps, in one step, or in ML, from a simple MNIST example (or even the minuscule Iris dataset) to double LSTM with memory and attention. Where are the intermediary nice problems to learn on? When I was learning math in school and high school there were loads gradual problems to solve, but at university suddenly there was just theory and almost no useful problems to practice on.
gjulianm 10y ago
As a mathematician, and seeing what's on the article (and with no intention to downplay your achievements, which are impressive), that's not what I think of when I hear "advanced mathematics". Vectorial calculus and differential equations (ordinary, not partial) are basic courses in math degrees. For the things that the article explains, such as topology, group/ring theory, measure theory, functional analysis, etc (which are still nothing fancy that doesn't get reviewed in a degree, so not yet "advanced"), I think that self-learning is almost impossible unless you're near to a Terence Tao-level genius. Here I talk from experience. I remember reading books on some of these subjects and understanding few things, without really getting a grasp of what they're talking about. A lot of times, the problem is that you don't know what is missing in your knowledge. You need a clear roadmap, you need relationships, you need to solve a lot of questions, you need to do exams and, most importantly, you need to test your knowledge. I cannot even count how many time I thought I understood some theorem only to do some exercise and see that I had absolutely no idea. Sometimes you notice yourself, sometimes you do it so bad that you don't even notice it is incorrect. And, for these subjects, the material on the Internet starts to diminish and be less accessible (more oriented to professional mathematicians than to learners). Khan Academy does not have advanced courses, the definitions on Wolfram or Wikipedia are only useful if you have already a grasp of the subject (see for example https://en.wikipedia.org/wiki/Measure_(mathematics)#Definition https://en.wikipedia.org/wiki/Measure_(mathematics)#Definiti... - What is important? What are the critical aspects? Which are the subtle parts of the definition that you must read carefully?) and in Youtube you may find lectures, but usually they're like the books: you will be lucky if it's not a succession of theorems and definitions, and you still lack the possibility of checking and testing your knowledge. So, while some parts of math can be learned independently, I don't think that advanced mathematics can be done. Myself, only after 5 years of mathematics I'm somehow comfortable to study subjects by myself, and it's still hard.
- wnewman 10y ago
  (responding not to what is in the article, but only to your comment on how difficult it is to study what is more nearly "advanced mathematics") I got 800 on the 1980s-era math SATs, came in third in the Portland OR area in a math contest in high school, and did OK at Caltech (not in a math major), but I'm no Terry Tao, and I very much doubt I'd've been anything very special in a good math undergrad program. Some years after graduation, I found it challenging but doable to get my mind around a fair fraction of an abstract-algebra-for-math-sophomores textbook, including a reasonable amount of group theory (enough to formalize a significant amount of the proof of Solow theorem as an exercise in HOL Light, and also various parts of the basics of how to get to the famous result on impossibility of a closed-form solution for roots of a quintic). From what I've seen of real analysis and measure theory (a real analysis course in grad school motivated by practical path integral Monte Carlo calculations, plus various skimming of texts over the years), it'd be similarly manageable to self-learn it. One problem is that some math topics tend to be poorly treated for self-learning, not because they are insanely difficult but because the author seems never to have stepped back and carefully figured out how to express what is going on in a precise self-contained way, just relying (I guess) on a lot of informal backup from a teaching assistant explaining things behind the scenes. On a small scale, some important bit of notation or terminology can be left undefined, which is usually not too bad with modern search engines but was a potential PITA before that. On a larger scale, I found the treatment of basic category theory in several introductory abstract algebra texts seemed prone to this kind of sloppiness, not taking adequate care to ground definitions and concepts in terms of definitions and concepts that a self-studying student could be expected to know, and that's harder to solve with a search engine, tending to lead into a tangle of much more category theory and abstraction than one needs to know for the purpose at hand. My impression is that mathematicians are worse at this than they need to be, in particular worse than physicists: various things in quantum mechanics seem as nontrivial and slippery as category theory to me, but the physicists seem to be better at introducing it and grounding it. (Admittedly, though, physicists can ground it in a series of motivating concrete experiments, which is an aid to keeping their arguments straight which the mathematicians have to do without.) I have been much more motivated to study CS-related and machine-learning-related stuff than pure math, and I have been about as motivated to self-study other things (like electronics and history) as pure math, so I have probably put only a handful of man-months into math over the years. If I had put several man-years into it, it seems possible that I could have made progress at a useful fraction of the speed of progress I'd expect from taking college math courses in the usual way. I think it would be particularly manageable to get up to speed on particular applications by self-study: not an overview of group theory in the abstract, but learning the part of group theory needed to understand the famous proof about roots of the quintic, or something hairier like (some manageable-size fraction of) the proof of the classification of finite simple groups. Still not easy, likely a level harder than teaching oneself programming, but not an incredible intellectual tour de force. "Myself, only after 5 years of mathematics I'm somehow comfortable to study subjects by myself, and it's still hard." Serious math seems to be reasonably difficult, self-study or not. Even people taking college courses in the ordinary way are seldom able to coast, right?
sixo 10y ago
I don't mean to be rude by saying this, but the truly-difficult advanced math - the stuff that's really hard to build an understanding of by yourself, because it's fairly distantly separated from any obvious applications or anything you'd readily have experience with, and heavily obfuscated (to newcomers) by the notation and pedantic proof-focused thoroughness (appropriate for academic math, less so for applications) - starts a few courses after Diff eq.
- tprice7 10y ago
  If you don't consider the topics mungoid mentioned to be advanced math, perhaps you'll still consider this to be: http://arxiv.org/abs/1509.05797 http://arxiv.org/abs/1509.05797 It was accepted to Algebraic Geometry in May, (the Foundation Compositio Mathematica journal, not JAG), so it will probably appear online sometime around December. So far I've received three invitations to visit two different universities as a result of this paper. (search for "Price" on these pages: http://www2.math.binghamton.edu/p/seminars/arit http://www2.math.binghamton.edu/p/seminars/arit http://www2.math.binghamton.edu/p/seminars/arit/spring2016 http://www2.math.binghamton.edu/p/seminars/arit/spring2016 , I will also be travelling to a German university in October but unfortunately I have no evidence to show for this currently). I say this as someone who left undergrad after four terms and is mostly self-taught, from such resources as books, online papers, and wikipedia.
  - gone35 10y ago
    Impressive. Congratulations on your achievement!
- mungoid 10y ago
  Nah, not rude =-) I consider the math I do at work to be somewhat advanced. Statics, dynamics, a touch of thermo dynamics, etc. But if you are talking like quantum mechanics or NASA JPL level math, then yeah I totally agree those topics would definitely be better learned in a proper environment.
- santaclaus 10y ago
  > because it's fairly distantly separated from any obvious applications or anything you'd readily have experience with Right, but the math tagged as 'advanced' in the article is fairly applied.
p1esk 10y ago
* the most advanced math I had was Algebra 2* How could you get a BS in CS without taking calculus courses? Which school did you go to?
- kragen 10y ago
  It's kind of a shame that so many schools push you to study calculus in order to study CS; digital computers are algebraic machines, not analytical ones, pace Babbage. Combinatorics and graph theory would be far more useful. (Although maybe this will change with machine learning.)
  - tzs 10y ago
    Richard Feynman spent some time working at Thinking Machines, working on the router for the Connection Machine. From Danny Hillis' account of this [1]: By the end of that summer of 1983, Richard had completed his analysis of the behavior of the router, and much to our surprise and amusement, he presented his answer in the form of a set of partial differential equations. To a physicist this may seem natural, but to a computer designer, treating a set of boolean circuits as a continuous, differentiable system is a bit strange. Feynman's router equations were in terms of variables representing continuous quantities such as "the average number of 1 bits in a message address." I was much more accustomed to seeing analysis in terms of inductive proof and case analysis than taking the derivative of "the number of 1's" with respect to time. Our discrete analysis said we needed seven buffers per chip; Feynman's equations suggested that we only needed five. We decided to play it safe and ignore Feynman. The decision to ignore Feynman's analysis was made in September, but by next spring we were up against a wall. The chips that we had designed were slightly too big to manufacture and the only way to solve the problem was to cut the number of buffers per chip back to five. Since Feynman's equations claimed we could do this safely, his unconventional methods of analysis started looking better and better to us. We decided to go ahead and make the chips with the smaller number of buffers. Fortunately, he was right. When we put together the chips the machine worked. [1] http://longnow.org/essays/richard-feynman-connection-machine/ http://longnow.org/essays/richard-feynman-connection-machine...
ElysianEagle 10y ago
> A few years after Uni, I started teaching myself Calc, Trig, Vector maths, Diff Eq and Physics strictly from what I have found on various sites, software and books. Most unis I know of (I'm in the US) require those courses to be taken as part of your undergrad before you can attain the CS degree. Furthermore, with the prevalence of AP courses at the high school level, many students enter college already having taken some, possibly all of those courses.
- mungoid 10y ago
  Yeah unfortunately mine was a private, non-profit university (US) and I think because of that private status, they can change curriculum to suit their needs. I wouldnt have went to them if I had known that. Whats confusing is that they are an actual University but can mess with curriculum that much. And for almost 50k in tuition..

by mungoid 10y ago

yodsanklai 10y ago

Congratulations, and I'm glad you proved me wrong :)

mungoid 10y ago
Thank you! I will admit that it was by no means quick or easy and there were many, many times I wish I could have had an actual person with me to explain it. Not to mention the frequent of wanting to give up when something wasn't 'clicking' and i felt i couldn't do it.

heimatau 10y ago

I'm glad you had success but...let's not measure your outlier experience with the rest of the world. Especially in Adv Mathematics. I'd point you and other HNs to Srinivasa Ramanujan. He is self taught but...he was wrong [1]. He had a brilliant mind but...due to being self taught, he made some critical mistakes. Being self taught can easily lead the learner to some critical mistakes. Eventually, they may be corrected (and at what 'cost' does this mistake cause an organization or business or those involved) but it's more efficient of someone's time to just learn from another. I'm not saying everyone needs a University Degree. I'm saying that everyone needs a teacher. Everyone. Why? Because instead of 'the blind leading the blind' (you as a 'blind' teacher, leading you as a 'blind' learner). You have the efficiency of being led by a mentor of some kind that can steer you away from faulty concepts that may come in. It's great that we now have more free/cheap materials than ever before at our disposal but without a mentor or some kind of peer-review, we could be misapplying concepts. Also, to comment on something you specifically said: > Because in my companies view, being able to teach yourself all that math is much more impressive than being taught from a University. Yes, it's 'impressive' but...most don't learn this way. Which is way it's 'impressive'. Also, being self-taught, how do you truly verify what you understand mathematically is accurate and solid? [2] You might be and I'm not going to fault you but learning concepts is one thing but applying them is even more challenging. It's one thing to be 'impressive', it's a whole other thing to have mastery over a topic. And I'm a firm believer mastery is mostly achieved with peer/mentor feedback. I applaud you but let's not steer others to just teach themselves, without help from others. Let's encourage self taught and peer feedback. It's not one or the other, it's both. [1] - https://www.youtube.com/watch?v=jcKRGpMiVTw https://www.youtube.com/watch?v=jcKRGpMiVTw [2] - I searched for 30 minutes to find this article, that I read, that stated the current environment of Mathematical Research [3]. Namely, it stated that a lot of research is being published that is NOT peer-reviewed because there isn't enough skilled* Mathematicians to review the work. That it's a 'dirty little secret' in the industry that "known" Mathematicians would get a pass (published w/o review) but many others trying new groundbreaking ideas couldn't get their research peer-reviewed. And with the given University culture to publish NEW research and not review, it's understandable how this environment was created. Namely, Einstein gets the fame but it took numerous people to peer-review his work before it was accepted. [3] - I know this article exists. It's one of the reasons why I'm becoming a Mathematician. I read it in the past 2-3 years. It was a major site (NewScientist or something that focuses on emerging research). If you can find it, I'd be very grateful. I'm now* using Zotero to save all my findings, so hopefully when I quote something I'll have a source. ;) *(edited) - original said 'not'. I meant 'now I'm using Zotero'. ;). original said 'skill', I meant 'skilled'

aluhut 10y ago

I wish I could make the jump again. When I was a kid, I loved Math. I even got one of this badges that were so popular in my east block country, for being the best kid in Math for my whole year group. Then we moved to Germany. Math level was far below mine, I got bored, started to do other stuff and lost it when they overtook me. Growing up and work did the rest. I lost it. When I had/have to do some math I'm doing what is needed but this creative spark you need is gone. Now I find it very complicated to get even into the syntax...I fix most of my problem through the net. It's like losing a friend whose face you've already forgotten.

mungoid 10y ago
Yeah it becomes increasingly difficult as you get older. I really wish I would have gotten into it sooner. DIY math is great, but it taught me to be more of a loner than I'd like.

deleted 10y ago

[deleted]

visarga 10y ago

The web is full of videos and PDFs with learning materials. But what is needed for learning to actually work is to have exercises to practice on. What I mean is fine gradation of difficulty and tracking prerequisites (notions needed in order to tackle a problem) so as to give students problems that are not too easy or too difficult, but just at the right level. I seldom find such problems/examples tuned to slightly above my level of understanding. Same problem in programming and machine learning - people need a little hand holding in the form of a sequence of problems to solve that would never be either too difficult or too easy. Examples usually jump from Todo MVC to full apps, in one step, or in ML, from a simple MNIST example (or even the minuscule Iris dataset) to double LSTM with memory and attention. Where are the intermediary nice problems to learn on? When I was learning math in school and high school there were loads gradual problems to solve, but at university suddenly there was just theory and almost no useful problems to practice on.

gjulianm 10y ago

As a mathematician, and seeing what's on the article (and with no intention to downplay your achievements, which are impressive), that's not what I think of when I hear "advanced mathematics". Vectorial calculus and differential equations (ordinary, not partial) are basic courses in math degrees. For the things that the article explains, such as topology, group/ring theory, measure theory, functional analysis, etc (which are still nothing fancy that doesn't get reviewed in a degree, so not yet "advanced"), I think that self-learning is almost impossible unless you're near to a Terence Tao-level genius. Here I talk from experience. I remember reading books on some of these subjects and understanding few things, without really getting a grasp of what they're talking about. A lot of times, the problem is that you don't know what is missing in your knowledge. You need a clear roadmap, you need relationships, you need to solve a lot of questions, you need to do exams and, most importantly, you need to test your knowledge. I cannot even count how many time I thought I understood some theorem only to do some exercise and see that I had absolutely no idea. Sometimes you notice yourself, sometimes you do it so bad that you don't even notice it is incorrect. And, for these subjects, the material on the Internet starts to diminish and be less accessible (more oriented to professional mathematicians than to learners). Khan Academy does not have advanced courses, the definitions on Wolfram or Wikipedia are only useful if you have already a grasp of the subject (see for example https://en.wikipedia.org/wiki/Measure_(mathematics)#Definition https://en.wikipedia.org/wiki/Measure_(mathematics)#Definiti... - What is important? What are the critical aspects? Which are the subtle parts of the definition that you must read carefully?) and in Youtube you may find lectures, but usually they're like the books: you will be lucky if it's not a succession of theorems and definitions, and you still lack the possibility of checking and testing your knowledge. So, while some parts of math can be learned independently, I don't think that advanced mathematics can be done. Myself, only after 5 years of mathematics I'm somehow comfortable to study subjects by myself, and it's still hard.

wnewman 10y ago
(responding not to what is in the article, but only to your comment on how difficult it is to study what is more nearly "advanced mathematics") I got 800 on the 1980s-era math SATs, came in third in the Portland OR area in a math contest in high school, and did OK at Caltech (not in a math major), but I'm no Terry Tao, and I very much doubt I'd've been anything very special in a good math undergrad program. Some years after graduation, I found it challenging but doable to get my mind around a fair fraction of an abstract-algebra-for-math-sophomores textbook, including a reasonable amount of group theory (enough to formalize a significant amount of the proof of Solow theorem as an exercise in HOL Light, and also various parts of the basics of how to get to the famous result on impossibility of a closed-form solution for roots of a quintic). From what I've seen of real analysis and measure theory (a real analysis course in grad school motivated by practical path integral Monte Carlo calculations, plus various skimming of texts over the years), it'd be similarly manageable to self-learn it. One problem is that some math topics tend to be poorly treated for self-learning, not because they are insanely difficult but because the author seems never to have stepped back and carefully figured out how to express what is going on in a precise self-contained way, just relying (I guess) on a lot of informal backup from a teaching assistant explaining things behind the scenes. On a small scale, some important bit of notation or terminology can be left undefined, which is usually not too bad with modern search engines but was a potential PITA before that. On a larger scale, I found the treatment of basic category theory in several introductory abstract algebra texts seemed prone to this kind of sloppiness, not taking adequate care to ground definitions and concepts in terms of definitions and concepts that a self-studying student could be expected to know, and that's harder to solve with a search engine, tending to lead into a tangle of much more category theory and abstraction than one needs to know for the purpose at hand. My impression is that mathematicians are worse at this than they need to be, in particular worse than physicists: various things in quantum mechanics seem as nontrivial and slippery as category theory to me, but the physicists seem to be better at introducing it and grounding it. (Admittedly, though, physicists can ground it in a series of motivating concrete experiments, which is an aid to keeping their arguments straight which the mathematicians have to do without.) I have been much more motivated to study CS-related and machine-learning-related stuff than pure math, and I have been about as motivated to self-study other things (like electronics and history) as pure math, so I have probably put only a handful of man-months into math over the years. If I had put several man-years into it, it seems possible that I could have made progress at a useful fraction of the speed of progress I'd expect from taking college math courses in the usual way. I think it would be particularly manageable to get up to speed on particular applications by self-study: not an overview of group theory in the abstract, but learning the part of group theory needed to understand the famous proof about roots of the quintic, or something hairier like (some manageable-size fraction of) the proof of the classification of finite simple groups. Still not easy, likely a level harder than teaching oneself programming, but not an incredible intellectual tour de force. "Myself, only after 5 years of mathematics I'm somehow comfortable to study subjects by myself, and it's still hard." Serious math seems to be reasonably difficult, self-study or not. Even people taking college courses in the ordinary way are seldom able to coast, right?

sixo 10y ago

I don't mean to be rude by saying this, but the truly-difficult advanced math - the stuff that's really hard to build an understanding of by yourself, because it's fairly distantly separated from any obvious applications or anything you'd readily have experience with, and heavily obfuscated (to newcomers) by the notation and pedantic proof-focused thoroughness (appropriate for academic math, less so for applications) - starts a few courses after Diff eq.

tprice7 10y ago
If you don't consider the topics mungoid mentioned to be advanced math, perhaps you'll still consider this to be: http://arxiv.org/abs/1509.05797 http://arxiv.org/abs/1509.05797 It was accepted to Algebraic Geometry in May, (the Foundation Compositio Mathematica journal, not JAG), so it will probably appear online sometime around December. So far I've received three invitations to visit two different universities as a result of this paper. (search for "Price" on these pages: http://www2.math.binghamton.edu/p/seminars/arit http://www2.math.binghamton.edu/p/seminars/arit http://www2.math.binghamton.edu/p/seminars/arit/spring2016 http://www2.math.binghamton.edu/p/seminars/arit/spring2016 , I will also be travelling to a German university in October but unfortunately I have no evidence to show for this currently). I say this as someone who left undergrad after four terms and is mostly self-taught, from such resources as books, online papers, and wikipedia.
- gone35 10y ago
  Impressive. Congratulations on your achievement!
mungoid 10y ago
Nah, not rude =-) I consider the math I do at work to be somewhat advanced. Statics, dynamics, a touch of thermo dynamics, etc. But if you are talking like quantum mechanics or NASA JPL level math, then yeah I totally agree those topics would definitely be better learned in a proper environment.
santaclaus 10y ago
> because it's fairly distantly separated from any obvious applications or anything you'd readily have experience with Right, but the math tagged as 'advanced' in the article is fairly applied.

p1esk 10y ago

* the most advanced math I had was Algebra 2* How could you get a BS in CS without taking calculus courses? Which school did you go to?

kragen 10y ago
It's kind of a shame that so many schools push you to study calculus in order to study CS; digital computers are algebraic machines, not analytical ones, pace Babbage. Combinatorics and graph theory would be far more useful. (Although maybe this will change with machine learning.)
- tzs 10y ago
  Richard Feynman spent some time working at Thinking Machines, working on the router for the Connection Machine. From Danny Hillis' account of this [1]: By the end of that summer of 1983, Richard had completed his analysis of the behavior of the router, and much to our surprise and amusement, he presented his answer in the form of a set of partial differential equations. To a physicist this may seem natural, but to a computer designer, treating a set of boolean circuits as a continuous, differentiable system is a bit strange. Feynman's router equations were in terms of variables representing continuous quantities such as "the average number of 1 bits in a message address." I was much more accustomed to seeing analysis in terms of inductive proof and case analysis than taking the derivative of "the number of 1's" with respect to time. Our discrete analysis said we needed seven buffers per chip; Feynman's equations suggested that we only needed five. We decided to play it safe and ignore Feynman. The decision to ignore Feynman's analysis was made in September, but by next spring we were up against a wall. The chips that we had designed were slightly too big to manufacture and the only way to solve the problem was to cut the number of buffers per chip back to five. Since Feynman's equations claimed we could do this safely, his unconventional methods of analysis started looking better and better to us. We decided to go ahead and make the chips with the smaller number of buffers. Fortunately, he was right. When we put together the chips the machine worked. [1] http://longnow.org/essays/richard-feynman-connection-machine/ http://longnow.org/essays/richard-feynman-connection-machine...

ElysianEagle 10y ago

> A few years after Uni, I started teaching myself Calc, Trig, Vector maths, Diff Eq and Physics strictly from what I have found on various sites, software and books. Most unis I know of (I'm in the US) require those courses to be taken as part of your undergrad before you can attain the CS degree. Furthermore, with the prevalence of AP courses at the high school level, many students enter college already having taken some, possibly all of those courses.

mungoid 10y ago
Yeah unfortunately mine was a private, non-profit university (US) and I think because of that private status, they can change curriculum to suit their needs. I wouldnt have went to them if I had known that. Whats confusing is that they are an actual University but can mess with curriculum that much. And for almost 50k in tuition..