I've stopped studying mathematics ever since graduating high school four years ago...

I've stopped studying mathematics ever since graduating high school four years ago, so my current knowledge is limited to derivatives and whatnot.
I've recently taken an interest in learning about math, and more specifically, computer science and quantitative finance.
I'm not exactly sure where I should start and what I should aim for, given how low my current level is and how broad those subjects are.
Could I get some suggestions?

Also, I've never been particularly gifted at math, and unlike some people here, I don't have a natural, intuitive understanding of mathematical concepts.
Will this give me trouble at some point if I plan to study financial math and CS?

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Stay outta pure math. No real analysis, no topology. The areas of math you should look at are Applied Linear Algebra and Statistics. Go find some textbooks and start doing some problems

If you are talking about that book, they use a lot of examples that require some basic knowledge of math. For example in the first chapter one of the examples they give is a program for finding roots using Newton's method, which requires some basic knowledge of calculus.

In general though, you don't need to know any math to study CS.

>Applied Linear Algebra and Statistics
Are those basic enough that I can dive right in?
I just remembered I own a book about basic math, with explanations and exercises about the fundamentals of trigonometry, algebra, calculus etc. Is that not necessary?
No, I'm not talking about SICP in particular.
>you don't need to know any math to study CS
I'm interested in the more theoretical parts like algorithms, ML, and cryptography. Not much about the practical aspect, I already know how to program.

He should at least do some calculus as well.


CS in my university requires these things
- Discrete mathematics I & 2
- Linear Algebra
- Statistics & Probability
- Calculus
- Algorithms and Data structures 1, 2 & 3 (not sure if this qualifies as math)

If you want to review high school level mathematics first before diving into the college/uni level stuff try doing Khanacademy + a Precalculus book

Are there any good textbooks you'd recommend for those subjects?
"Introduction to Algorithms" seems like the reference for algorithms and data structures, I'm not sure about the rest.
I might use Khanacademy, thanks.

Currently reading the book. I'm at the second chapter and it doesn't require anything other than basic knowledge of calculus, algebra and linear algebra.

Out of my way, Veeky Forumsfags. Leave the education of this newcomer to me and my meme list .

-- -- -- -- -- -- -- --

0. Remedial Mathematics
Khan Academy

-- -- -- --

>1. The Prerequisites of University Mathematics
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
How to Prove It - D. J. Velleman

-- -- -- --

Pick One Path:

>2a. Introduction to Applied Mathematics (Some Proofs)
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross


>2b. Introduction to Pure Mathematics (Proof-Based)
Calculus Vol. I & II - T. M. Apostol
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter


>2c. The Mixed Approach
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter


-- -- -- --

>3. Foundations for Advanced Pure Mathematics
Linear Algebra - K. M. Hoffman & Ray Kunze
Analysis I & II - Terence Tao
Visual Complex Analysis - Tristan Needham
Algebra - Michael Artin


-- -- -- -- -- -- -- --

The problem with quantitative finance is that you're definitely going to need to be able to handle some degree of pure mathematics, in addition to being skilled in the linear algebra, probability, and programming skills necessary for machine learning. If you're looking less towards improving your general ability and more towards shooting for a specific niche, then let me know and we can work with something different after any 2. track.

That's great, thank you.
>you're definitely going to need to be able to handle some degree of pure mathematics
What specializations of pure math are used in quant finance?
>programming skills necessary for machine learning
I know how to program, but I have no knowledge of machine learning.
From what I've seen though, C++ seems to be very popular in that field (and in finance in general), and I have some experience with that.
>shooting for a specific niche
Right now I don't know much about the technicalities of the models used for computational finance.
I'm assuming that there isn't a lot of difference in the skill sets required to do HFT, algorithmic trading and quantitative investing, which seem to be the three big fields of quant finance.
Aren't new models coming from unrelated fields of science being constantly discovered, though?

>C++
ooo boi, among mainstream programming languages C++ has the seepest learning curve. It takes several years of real job experience to start writing C++ code that is not complete shit.

At least I'm not a complete novice then.

I would definitely say linear algebra for CS and I suggest doing all the calculus you can. I am a CS major and I've done way more math than I should but I think it's helpful for me to keep taking math while studying CS. CS can get a bit boring and math keeps me interested for the term.

>Will this give me trouble at some point?
I'd like to know this
Is it possible to git gud if you're not naturally gud?

Cryptography is just mathematics(mostly number theory), if you don't mean applied cryptography.
Algorithms are considered mostly math too but idk what you mean by theoretical parts.
ML is applied math, mostly calc and statistics.

>ML is applied math, mostly calc and statistics.
Is Norvig's book a good introduction to it?

Veeky Forums-science.wikia.com/wiki/Computer_Science_and_Engineering

dunno about finance

>computer science
ctrl+f "graph theory" no results. What the fuck Veeky Forums?

Basic graph theory will go along way in terms of understanding common programming problems and data structures. I mean, one of the most common data structures is a tree or variant thereof. Basic set theory is also something you should study.

>Also, I've never been particularly gifted at math, and unlike some people here, I don't have a natural, intuitive understanding of mathematical concepts.
Will this give me trouble at some point if I plan to study financial math and CS?
I can only speak for CS, but it depends. You can study CS at a university without needing to do too much math, but you can also link CS and math extensively if you so chose to, especially if you're interested in going the academic route and doing research instead of working.

Like some people have said, there is also certain math that's applicable to certain areas of computer science, e.g. statistics, stochastic modeling, and cryptography, though if you've not got an interest in those fields, you can forego them.

Yes it's still used in most classes.

functionalcs.github.io/curriculum do the core fundamentals and apply to Jane St Capital or Two Sigma as a developer they will teach you finance

SICP some of the exercises have you doing proofs you would've learned in a first year Calc course, as all students doing 6.001 at MIT originally already had 2 semesters of calculus.

OP should just start as an algorithmic trader or 'quant developer' for above mentioned companies, then take math p/t at any school if he/she wants to get into real Quant trading. You can teach yourself, but it's much, much better to get this done correctly with TAs and professors around to challenge your logic/correct it

>apply to Jane St Capital or Two Sigma as a developer
>OP should just start as an algorithmic trader or 'quant developer'
Isn't the barrier to entry for those companies extremely high? Why would they hire someone who doesn't have at the very least a master's degree in a relevant field?

I think what he meant is "if I'm not naturally good at math, can I ever become really good".

The minimum requirement for jane street is a phd from a world top 100, at least in the UK.

Even as a developer?

Presumably as everything needs to be peak performance but there might be more wiggle room

Not for development, for being a mathematician/trader yes the barrier is high but you can start as a dev working with the traders and use the large bonuses these kinds of fintech corps pay out to put yourself through math grad school, then go back as a trader as you know everyone doing the hiring.

Alright. World top 100 according to which rankings? Things become less clear as you get past the top 25-30.
>start as a dev working with the traders and use the large bonuses these kinds of fintech corps pay out to put yourself through math grad school
Is that something people do frequently?
What does the barrier to entry look like for development, compared to researchers and traders?

blogs.janestreet.com/interviewing-at-jane-street/

Im just being vague but the sort of university should be clear. A phd from say leeds and a phd from cambridge are going to be different quality in general but both still high quality at both places - both would have some chance of getting in. A phd in math from south flyover state university on the other hand is not going to work.

Thats not to say MMaths dont get in but then we are looking at a much smaller list of 4-5 universities in the UK.

For quantitative finance you need linear algebra, calculus 1-3, ordinary Differential Equations, partial Differential Equations, Probability, and analysis.

There are some books that go over all the math you will need to study finance along with the finance itself. It honestly gets pretty op, finance is the only field I've ever seen Stochastic Integro-Partial Differential Equations applied to.

Thank you, that was informative. They do state that they're looking for competent people, not necessarily PhDs, and the required knowledge is fairly straightforward.
What if the university is neither from North America nor from the UK?
Also, do math/statistics PhD programs that aren't shit and don't require a BSc/MSc in the related subject exist? Assuming I have the required knowledge to pursue the degree of course.
The problem is that I have no formal education in math, meaning that I'd have to go through a bachelor's first otherwise.

It just needs to be good basically. Toronto, Leuven, IIT etc. engineering physics comp sci are also fine amongst others - it is not math exclusively.

I think Krakow is also a target campus

Yeah. As for my other question, do you know of any university departments that don't have formal education requirements for their STEM PhD programs?
I checked with famous ones like Oxford and a few others, but they seem to require an accredited MSc in the relevant field of study, which means I'm fucked (or that I have to start with a bachelor's, which is a huge waste of time).
The most convenient would be to find a program either in Germany or France, thankfully both have renowned research universities, I think.

Yes the major ones in Germany,France,Switzerland are all good to go and probably Coimbra in Portugal as well but I am just guessing that. I think you need STEM MSc minimum in a relevant field in general and id go further to say economics is insufficient. It is possible to shift from engineering to other STEM etc however

>I think you need STEM MSc minimum
Thanks for the info, I'm in trouble then but I'll see what can be done.

If you like financial mathematics in general a decent back up plan is actuarial or risk work which has a much lower barrier - a math heavy bsc is usually sufficient, and uses similar fields just lower level.

Yeah, I guess. I'll still look around, since the problem isn't with my degree itself, but rather its lack of accreditation, even though it's technically the equivalent of a BSc in software engineering.
There must be a good research department willing to accept that, even if it's for a master's program instead of a PhD, I hope so at least.

Masters program first for sure - good luck!

Yep, now that I think about it it's probably an easier, albeit slower path.
Thanks for your advice, user.

You should start with C first, then move onto C++

Are there any poor souls who actually start with C++ with no prior programming experience?

I liked your old memelist more

Which memelist is better? These, or the one in ?

>Differential Equations - Shepley Ross

The one published in the 80s? Is it really good?

Jacob Appellbaum from Tor is at TU/e in NL getting a PhD in Cryptography and he dropped out of college. It's possible in Germany too I'm pretty sure but you have to take a 2 semester prep to qualify/get into a graduate program. Then as postdoc transfer wherever

>The one published in the 80s? Is it really good?
The most recent edition, 3rd, was published in 200. And yes, it is very good compared to most other books on the market, only lacking in extensive applications & computational approaches... which isn't really that important since you'll learn that in whatever specialization you choose if you need it. And the best part? You can find it on libgen.

The new list is better because it doesn't waste your time with repetitive and extraneous stuff, plus some of those books like that "Dobrushkin" isn't even available online. The Art & Craft of Problem-Solving, How to Think Like a Mathematician, Mathematics, Its Content etc., and Apostol is unnecessary given the path. This wasn't my meme list originally, but I changed it up to reflect that different backgrounds have different needs and prevent overlap depending on the path chosen.

He's a special case, though. The guy has a pretty stellar track record, which understandably offsets his lack of degree.
>2 semester prep
I've never heard of that, but it sounds great. Do you know if that system exists in other countries of the EU or just in Germany?

>it doesn't waste your time with repetitive and extraneous stuff
>different backgrounds have different needs
So you basically removed the introductory books?

The necessary introductory books are still there and are tailored to whatever level you're at and what you're needs are. You still get a proofing book and ample time/preparation for the next step. Need to do applied only? 2a and be done, take other stuff like probability and statistics if you need it. Only care about pure math? 2b. Are you concerned about both? 2c combines books from both elements but without overlap.

use both, according to your needs, i am more or less following the memelist from the pic i posted but i liked some of the recommendations from the new list. I did not write any of lists and i am just brainlet that finished precalculus last week; the other user looks like he knows what he is talking about, so maybe the new list is actually better. Download the books and see what pleases you more

I mean, it's not like the old list is terrible, since the The Art & Craft is still good for what it aims to teach you, How to Think Like a Mathematician is just a watered down (but still nice) version of How to Prove It from what I can tell, Kolmogorov is a good survey of higher division mathematics from what I can tell, etc. They're just not necessary. Good side projects though.

Also, Applied Differential Equations by Dobrushkin is just hard to find, especially online for free, and I haven't seen anybody actually use it and recommend it.

Before I forget, that list also starts off too late with How to Prove It, considering that you have the opportunity to start some proofs in David Lay's linear algebra and you definitely need to prove some basic stuff in Lang's multivariable calculus, so it's not the best order.

Finally, Apostol is overkill if you've already done calculus and have become familiar with the basics of proofing. Might as well go onto the basics of topology or even as far as real analysis.

I'm glad that all of you have been studying well and having a good time learning. That's fucking cool desu. How was Stitz-Zeager?

If you can convince a prof to recommend you for grad school anything is possible. If say you were actually self taught and competent at senior undergrad math and you showed up to free lectures given by visiting mathematicians at a local university on a reg basis and 'networked' with ppl at said talks and conferences they could recommend for direct entry. Some schools in Europe allow you to audit vast amounts of a BSc too from what I've been told

Above poster here, I did

Your list seems concise yet qualitative. So why is the recommended reading list from the Veeky Forums wiki so huge?

I used Axler's book for precalculus since i found it in my native language and only used Stitz-Zeager as complementation/review for some things (Conics, Matrices, Sequences), it was hard but i had a lot of fun. I was aiming to at least finish calculus + start a proof book before my work vacation end, luckily i still have a month, for preparation to uni that i will start next year.

I was not planning on doing all the proof books, i think i will just do Art and Craft of Problem and Solving and How to Prove It (if i feel i need it). Kolmogorov and Lay's Algebra was what i liked most from the last list. I also could not find the Dobrushkin's book and i was unsure about learning Calculus two times but i don't think i am read to learn directly from Apostol (and i really want to use his book, maybe after learning Calculus the first time i will change my mind).

Thanks for you advices, i really appreciate it.

I had overlooked the networking aspect. Would it be a waste of time to simply get an appointment with a member of faculty at the university I'm targeting, and talk about how I'd like to apply despite not having the required credentials?
If not for a PhD, at least for a master's; I'm guessing they'd be more lenient for the latter?

>i am studying for preparation to uni
Fixed.

The Veeky Forums reading list is comprehensive and offers many choices for the same topics. I just went with a list of books that are great and build up in difficulty through manageable increments. Plus some of the good books weren't included on there, which is a shame.

Doing Apostol after doing calculus isn't a terrible idea if you don't mind going slow and steady, and you'll still get a lot out of it that will solidify your understanding and further improve your proofing skills. So don't worry.

Also check out Differential Equations by Shepley Ross. It's easy to find and you won't be disappointed.

Keep up the good work!

Probably, unless you were doing the exact same research they were involved in and volunteered for non credit at first to help them, or you dumped papers to arxiv and they were of decent enough quality to warrant a review. Jacob knew Tanja/djb through doing many security conferences so got in that way.

Look up the math tripos recommended reading list @ Cambridge sometime it has just as many books. 24 lectures per topic and a reading list of 4-7 books per topic.

So either I get in through networking or I'm most likely out of luck. In which case, would I be stupid to just apply to a BSc program and to an MSc/PhD after completing it?
Sorry for asking so many questions, I don't know much about how academia works in practice.

Yes just go undergrad but do enough prep you can skip/audit a lot of first year. Find a uni you want to go to and do some of the curriculum yourself, so like reading lecture notes and finishing their assigned calculus book so you can just bypass 1st yr and get straight into a majors program

Right, there's probably ways to shorten the BSc as much as possible in order to not waste time. It might depend on the country.
To think that I'd have to start all over again after having completed a software eng. curriculum kinda stings, but it can't be helped.

If you alrdy have a bachelors you are graduate standing status and can usually get into most grad programs. Curtin University pretty sure you could go straight to MSc if they accept Edx students for software eng for straight to masters. It's thesis based masters so rigorous

What are signs that a grad program is good aside from its reputation? Or on the other hand, signs that it's shit

Papers/research the students and postdocs have written, and status of the people running the departments/grad programs in the field.

For example DJ Bernstein and Tanja Lange are the two premiere crypto researchers in the fields of side channel attacks/cryptanalysis, engineering/high-speed cryptography (elliptic curves) and post-quantum crypto. They both run the TU/e crypto program in the Netherlands so if you were at all interested in any of those fields you would be applying there. Phil Rogaway is another big name in cryptanalysis and teaches at UC Davis, and his students publish a lot of good papers. That would be another destination for anybody interested in crypto research.

If you were interested in say, number theory you would find the biggest names in said theory who output the most research and apply to their programs, or follow their postdoc students to another university if you couldn't get in. Since we're talking number theory these positions are often posted here numbertheory.org/ntw/additions.html

That's how the state universities/community colleges in my area (Oregon) seem to do it.
"CS 101" is intro to compsci concepts and maybe a little python, then "CS 102" is C++ programming (pic related).

Is that a good introductory book for C++?

Is there a huge difference in the quality of education you get and the kind of people you get to work with, between elite PhD STEM departments (Stanford, MIT, Caltech) and tier 2 departments? The facilities and endowment should be better but is there more to it?
Same question for master's.

The best introductory book is the one Stroustrup wrote.

Sure, if it is some kind of fraudulent paper mill where they are just pumping out shit publications for the sake of looking busy/grabbing grant money. The best way is to use sci-hub to go through journals in whatever field you are doing, and find the most interesting research, find out where those people are and apply to that grad program. Failing that, look up the supervisors of the PhD program(s) individually and follow their students to see what schools they end up.For example say you want to get into a CMU grad program to specialize in Type Theory with all their prominent researchers there. You can't get in so you discover one of their best protege students now teaches at CT dlicata.web.wesleyan.edu/pubs.html and it may even be a better option than CMU, as in a smaller less 'elite' university you will prob have more access to the supervisor of your program, have opportunities to co-author papers with them instead of them just auditing your work and rubber stamping their name on it, ect. This person will also have connections, so can land you a nice postdoc position using all their ivy league/elite school network.

For the most part you don't have to pay for a PhD either, that is usually covered by some grant they receive and then hire you with it as basically an apprentice to learn their field.

Stroustrup's book is shit m8. You're better off with youtube vids.

>youtube vids
Any recommendations?

>You're better off with youtube vids
Implied that the book was even worse than videos. Doesn't mean that videos are a good way to learn.