221–230 of 231 posts
A Programmer's Introduction to Mathematics by Dr. Jeremy Kun
I've only just started it, but so far it does a great job of introducing math while assuming just the right amount of programming knowledge to make math approachable.
Earlier quoted context omitted.
This is terrible advice. Apart from the last sentence. A better advice would be to specify which subject to learn. For example, (since I don't really have much time) 1. Topology (book by Munkres) 2. Real Analysis and Measure Theory (book series by Stein Shakarchi) 3. Algebra (book by Aluffi) 4. Linear Algebra (book by Friedberg Insel) 5. Measure Theoretic Probability (book by Cinlar) 6. Differential Geometry (book Sm…
The advice I gave is not exclusive to working through the typical undergraduate books. I was questioning why the OP wants to self-study an undergrad math curriculum to begin with. It's probably not to become a pure mathematician. So I suggested, instead of creating a massive goal of getting through a collection of books just for the sake of being a completionist, to have a concrete personal goal. Otherwise, people ca…
But your advice has a point, just going through books mindlessly is not motivation enough/ can lead to wandering. And it is always good to have specific tasks at hand. Like, solving a particular ordinary differential equations numerically.
Here's my personal opinion about how you should approach this. It's all well and good to want to cover undergraduate math courses. When you are actually enrolled in a university, you will have enough inertia and motivation to complete the courses. However, when you are self-studying you are doing it all on your own. It's hard to be as thorough and cover everything. And so I ask, what really is your goal here? You don…
This is terrible advice. Apart from the last sentence. A better advice would be to specify which subject to learn. For example, (since I don't really have much time) 1. Topology (book by Munkres) 2. Real Analysis and Measure Theory (book series by Stein Shakarchi) 3. Algebra (book by Aluffi) 4. Linear Algebra (book by Friedberg Insel) 5. Measure Theoretic Probability (book by Cinlar) 6. Differential Geometry (book Sm…
Earlier quoted context omitted.
This is terrible advice. Apart from the last sentence. A better advice would be to specify which subject to learn. For example, (since I don't really have much time) 1. Topology (book by Munkres) 2. Real Analysis and Measure Theory (book series by Stein Shakarchi) 3. Algebra (book by Aluffi) 4. Linear Algebra (book by Friedberg Insel) 5. Measure Theoretic Probability (book by Cinlar) 6. Differential Geometry (book Sm…
Is this the recommended order to read/learn them in? If I was primarily concerned with getting up to par with math for the sake of being able to actually understand everyone's favorite algorithms textbooks, would you still suggest working through all of these, or could you recommend an abridged list?
Also, unfortunately, its not the recommended order to learn them in.
Here's my personal opinion about how you should approach this. It's all well and good to want to cover undergraduate math courses. When you are actually enrolled in a university, you will have enough inertia and motivation to complete the courses. However, when you are self-studying you are doing it all on your own. It's hard to be as thorough and cover everything. And so I ask, what really is your goal here? You don…
My oldest brother had a real love of mathematics and got a masters degree but never even applied to a PhD program. When I asked him about it he just said he was tired of working on other people's problems. He had a quiet programming position in a large company that gave him time to work on personal projects. Among other things he volunteered at the local schools teaching "fun" math. I guess I'm just agreeing with you…
While I appreciate your brother's personal choice, to each their own after all. There is quite a lot of merit in your PhD advisor helping you in choosing a problem. That being said, good advisors provide students with an array of good problems out of which the student can choose one they are the most passionate about. This is what happened with me, I was provided with around 7 different choices to make. In the end, I chose 2 of them even though I wanted to chose 3 more but couldn't because of lack of time.
"Ask HN: How to self-learn math?" https://news.ycombinator.com/item?id=16562173
If we are talking about content you can find plenty of advice here or elsewhere. But do yourself a favor and pay a tutor and/or find a study group. As in writing, dancing, etc. you cannot evaluate your own work good enough. You will not improve your math watching youtube videos and reading books. You need to produce stuff that pass the "sniff test" to your colleagues.
Let me add to that. It you don’t have somebody challenging you and checking your work, you will likely plateau very quickly unless you are especially gifted. You will Hit walls of concrete and walls of glass. You will misunderstand concepts and not notice it. Your proofs will have logical gaps and you won’t notice it.
Earlier quoted context omitted.
As someone who did study both math and CS at university I disagree. I think there are numerous courses that can more easily be self-taught[1], mostly what one would encounter in their first ~2 years in a math degree. After that things get conceptually a lot more difficult. For me personally I didn't really need an instructor for most of my calculus courses, or ordinary differential equations, or most of the linear al…
The reality is that having a great mentor is a privilege, not a given. I don't think anyone is arguing that having a genius and brilliant teacher wouldn't help, rather that it is possible to reach an "advanced" (grad/undergrad level) understanding of mathematics without the luxury of having someone who is far more knowledgeable to turn to for help.
Of course you can learn a ton on your own by reading and working exercises and doing research, but there is no substitute for collaboration.
Mathematics is inherently a social activity, even if the bulk of it can (counter-intuitively) be done in relative solitude.
There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…
Basic topology is also important.
There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…
Most engineers I know have not learned set theory or groups/rings/lattices. They still seem to be doing pretty well.