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Mathematics for the Adventurous Self-Learner

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Re: Mathematics for the Adventurous Self-Learner

#71

Post by OJFord »

injb wrote: post #30
gavinray wrote: post #6

I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make: I have yet to find a guide that does not start with the assumption that you graduated highschool. That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to…

I won't repeat the good suggestions already made, but I'll add this: find a set of the Open University MST124 text books. The OU publishes their own maths books, which are specially written for self-study (since that's your only option with the OU) and their courses generally assume very little or no previous knowledge. There's an even more basic course (MST123 I think) if that one is too advanced. These are serious…

I have no direct experience of the OU, but I did have a mathematics teacher (head or deputy head I think of the department at a large school, and taught the more advanced courses) who used it.

Not taught courses, took its courses himself, in mathematics.

It went up in my estimations then for sure, because he was already a great teacher, intelligent and knowledgeable in the subject (certainly more than enough for up to 'Further Additional' at A level) and studying for his own interest (or I suppose a career change or further study for all I know).

Re: Mathematics for the Adventurous Self-Learner

#72

Post by gherkinnn »

ivansavz wrote: post #16
look_lookatme wrote: post #12

Earlier quoted context omitted.

The No Bullshit Guide To Math And Physics https://minireference.com/ I bought the Math and Physics copy because it has an ebook option and the first chapter is the Math guide. I’m going through a few pages a day and it’s crisp and straightforward. There is a sample of the first chapter on the site, I suggest you check it out to see if this is what you are looking for. Found via an HN thread from last year on this top…

Ha, I came here to shamelessly self-promote, but I see my book has already been mentioned! Here is a direct link to the preview: https://minireference.com/static/excerpts/noBSguide_v5_previ... I won't claim that Chapter 1 is complete and detailed review of all of high school math, but I did my best to cover all the essential topics needed for mechanics and calculus so that the book will be self-contained.

Great work. I read the sample and bought a copy myself.

Re: Mathematics for the Adventurous Self-Learner

#73

Post by mark259 »

OJFord wrote: post #66
gavinray wrote: post #6

I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make: I have yet to find a guide that does not start with the assumption that you graduated highschool. That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to…

> (Also, curse the Greeks for not using more idiomatic variables. ∑ would never pass code review, what an entirely unreadable identifier) S for Sum, T for Total, N for Number, I for Index, etc. might though.

At least in stats, the use of greek letters is helpful. Usually, the upper cases are kept for function like T(x) or to denote random variables. The lower cases for observed values. So when we see a greek letter, we know right away it's constant or a parameter.

Re: Mathematics for the Adventurous Self-Learner

#74

Post by speedplane »

rustybolt wrote: post #70
puritanicdev wrote: post #67

Earlier quoted context omitted.

I'm in the same shoes, and as ridiculous as it sounds but I've been in programming (self-taught) for 10 years now without an especially good knowledge of math. I've been slacking in HS on math classes, despite the fact that I loved math and was really good once I sat to listen, practice and understand the material. Also, I'm painfully aware of the fact that my math is really bad and that I'm missing on utilizing it i…

What is an example where you missed mathematical knowledge to do your job? Honestly curious, I never needed any math during programming for my job.

> What is an example where you missed mathematical knowledge to do your job? Honestly curious, I never needed any math during programming for my job.

Basic arithmetic comes up all the time: pro-rating a monthly plan, figuring out how much to scale up or down a system in response to changes in data, figuring out when your system will run out of memory/disk.

Statistics and probability are also pretty common. I'm often calculating standard deviations and finding expected values of non uniform random variables. For example, how fast does a queue have to be to handle 1 second tasks 90% of the time, but 30 second tasks 10% of the time?

Derivatives comes with many graphics tasks, such as 3D graphics or animations.

Re: Mathematics for the Adventurous Self-Learner

#75

Post by aidos »

rustybolt wrote: post #70
puritanicdev wrote: post #67

Earlier quoted context omitted.

I'm in the same shoes, and as ridiculous as it sounds but I've been in programming (self-taught) for 10 years now without an especially good knowledge of math. I've been slacking in HS on math classes, despite the fact that I loved math and was really good once I sat to listen, practice and understand the material. Also, I'm painfully aware of the fact that my math is really bad and that I'm missing on utilizing it i…

What is an example where you missed mathematical knowledge to do your job? Honestly curious, I never needed any math during programming for my job.

I guess the thing is that for any bit of reasoning, “there’s math for that”. So whether it feels like you’re using maths or not, you are.

Restructuring code, for example, often needs a good grasp of negation in logic.

Do you need formal training to do it? Not really. It’s advantageous to have a good math grounding though. My colleagues that have a good math education can often reason and communicate using graph theory, especially when it comes to architecture. Set theory is also super useful - I’ll often see people writing crappy algorithms because they don’t know about using sets (again, understanding computability and complexity would have helped here).

Maths is all around us, it is really just the study of patterns after all. That applies more so in software, even if it’s not immediately apparent.

Re: Mathematics for the Adventurous Self-Learner

#76

Post by thorn »

I am always astonished to learn that there are such self-learners in the world. I wonder how it is even possible to have a family and spend whole day building a startup - I cannot imagine that startup work is less than 8 hours a day - and then at evening they learn math or other complicated branch of science. What time and more especially how much energy they have for the family? Are these guys superhumans? I never was able to achieve such level of daily energy spent without trapping in burn out. I am not critiquing or being jealous here, just having genuine interest. How is it possible to be sustainable across so many years?

Re: Mathematics for the Adventurous Self-Learner

#78

Post by OJFord »

mark259 wrote: post #73
OJFord wrote: post #66

Earlier quoted context omitted.

> (Also, curse the Greeks for not using more idiomatic variables. ∑ would never pass code review, what an entirely unreadable identifier) S for Sum, T for Total, N for Number, I for Index, etc. might though.

At least in stats, the use of greek letters is helpful. Usually, the upper cases are kept for function like T(x) or to denote random variables. The lower cases for observed values. So when we see a greek letter, we know right away it's constant or a parameter.

I agree completely, and would emphasise 'at least', or change it to 'for example' even.

I only meant that criticising anyone for using them in the first place is unfair/hypocritical, because we'd quite readily do the same with the Latin alphabet.

Re: Mathematics for the Adventurous Self-Learner

#79

Post by marzell »

gavinray wrote: post #6

I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make: I have yet to find a guide that does not start with the assumption that you graduated highschool. That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to…

I'm in a similar situation - been programming for 25 years (off and on) since I started in middle school on my own. But in school we had 'Algebra I' and 'Geometry I' and I never went beyond that. Struggled with quadratic equations and factoring, never heard anything about trigonometry (which I now realize starts in basic geometry), calculus, and never heard the words 'function' or 'intuition' in regards to maths in school. Tried to do the classic Andrew Ng course on data science and I was completely lost every step of the way because of new language and the fact that his class was nothing like the way I had been taught so long ago.

Re: Mathematics for the Adventurous Self-Learner

#80

Post by angry_octet »

polyphonicist wrote: post #24

I am going to suggest something that might go against this idea of self-studying math. Do not do it alone. I mean, it is okay to self-learn mathematics as much as possible but don't let that be the only way to learn. Find a self-study group where you can discuss what you are learning with others. I think the social-effect can be profound in learning. I realized this when I used to learn calculus on my own. My progres…

Agree. And if one is a well paid software engineer, one can definitely afford to pay a maths grad student for an hour week, preferably a bit more than whatever pittance the local univeristy pays them for being a tutor. You will progress far quicker and with fewer wrong turns. It is also far cheaper than enrolling at a university. A personal trainer for the brain.
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