
Ask HN: How to best acquire theoretical computer science knowledge? - jophde
I didn&#x27;t know what I wanted to do before going to college at Penn State. I just knew that I had to go to college.  I was always interested computers so I ended majoring in Information Sciences and Technology.  About halfway through when I actually got to take some programming classes I discovered that I had a passion for software.  I went to my counselor and inquired about switching over to CS.  Unfortunately, almost nothing from my major would transfer and I had to pretty much start over.  As someone paying for college myself this really wasn&#x27;t an option.  I continued on with IST in the Design and Development option.<p>I ended becoming the first employee at Bay Area startup.  They were a bit desperate and I convinced them I could make their Android apps.  I did and they are both highly rated.  I also made one of my own that ended up getting featured on Google Play and receiving a lot of press.  I have a bit of knack for it but I am so bored with GUIs and UIs.  I want to work on harder problems and not just use other peoples libraries.  The problem is that my lack of knowledge limits my thinking.  I want to fix this.  I am torn between going back to school for another BS in CS, pursuing a MS in CS, or teaching myself from things like MIT Open Courseware and Udacity.<p>I am not really worried about getting a job.  This is about gaining knowledge.  Although having a &quot;real&quot; CS would certainly help keep me from being pigeon holed as an app developer and open a few more doors.  I do think that going back to school would be the quickest route to gaining the knowledge I want.  I am just worried that I wouldn&#x27;t get into a top school and I don&#x27;t know if I should try to do a BS, MS, or just take classes.  I really don&#x27;t want another $50k in debt either.  Especially when things like the Georgia Tech online MS CS is coming out for $7k.<p>So, what is the best way for a proven and largely self taught developer to take their knowledge to the next level?
======
jandrewrogers
There is an alternative approach that inadvertently worked for me that may
work well for you, particularly if your goal is to learn things beyond a
conventional computer science curriculum. I have been working in high-end
theoretical computer science for many years, with significant advances to my
credit, but I went to school for chemical engineering. People are often
curious as to how I acquired so much esoteric domain expertise in theoretical
computer science without spending any time in a computer science class.

Pick an interesting "hard" problem in computer science and attempt to solve
it. This works best if either there are no published solutions (e.g. massively
parallelizing ad hoc graph search) or the solution space varies widely under
the possible parameters (e.g. the design of a unique high-performance database
kernel). Iterate, be creative, search the literature for interesting ideas
that you can borrow from, and evaluate new designs you come up with. If
something does not work, understand how and why and try to fix it. Wash,
rinse, repeat.

This sounds like a lot of work, and it is, but there are three unique upsides.
First, the challenge of it can be quite a bit of fun in its own right and
there is a clear goal of what you are trying to achieve which helps keep you
motivated and measures progress. Second, you will cover more of the phase
space and explore some tangential theoretical areas while hunting for
solutions to narrow sub-problems that you would never be exposed to in a more
structured setting. Third, you will invariably explore some unusual or
unorthodox ideas that you simply would not be exposed to in a directed, formal
program. From the standpoint of being an effective theoretical computer
scientist, it will help you develop a unique perspective of the problem space
that is different than the perspective that arises from more structured
programs.

Also, you might actually solve one of the unsolved theoretical computer
science problems you have as your challenge in addition to developing a deep
understanding of the surrounding problem space. That happened to me (and then
replicated later once I realized it was possible) and it would never happen if
I was simply taking courses on the subject matter.

This was an effective way for me to gain in-depth understanding of a diverse
range of theoretical computer science areas on an informal basis. One of the
downsides is that your rote knowledge will not perfectly overlap what is
taught in CS curricula even though what you do know will likely be more
valuable (e.g. in spatial indexing some CS courses teach priority trees even
though they have no memorable theoretical value).

~~~
eli_gottlieb
_Pick an interesting "hard" problem in computer science and attempt to solve
it. This works best if either there are no published solutions (e.g. massively
parallelizing ad hoc graph search) or the solution space varies widely under
the possible parameters (e.g. the design of a unique high-performance database
kernel). Iterate, be creative, search the literature for interesting ideas
that you can borrow from, and evaluate new designs you come up with. If
something does not work, understand how and why and try to fix it. Wash,
rinse, repeat._

How do you verify your attempted solutions and talk to other researchers? I've
always found it hard enough getting a hold of my own advisor or someone else
in our department, let alone someone at an official research institution if I
weren't in one.

~~~
jandrewrogers
That part has always proven to be pretty easy. For most interesting problem
areas of theoretical computer science, there is rarely more than a handful of
deep experts. Anyone else you talk to would likely need to invest a lot of
effort understanding the nuances of the theoretical problem before they could
have an informed opinion, which they aren't going to do. Identify the few real
experts on the topic and talk to them.

These individuals have two useful characteristics. First, they can identify
99% of non-solutions immediately upon casual inspection. Second, if you show
them something novel in their area of expertise that they cannot immediately
dismiss, it piques their interest and they will invest the time to actually
understand what you've done. I've never run into a case where I developed a
novel algorithm or similar where the other experts working in the field were
not happy to study it if I sent them a cold email.

However, a big part of the learning experience is being able to show that a
particular algorithm must have a desired set of characteristics solely by its
description before you show it to another expert. The unique skill you are
learning by doing things this way is how to take an arbitrary set of complex
behavioral constraints and designing an algorithm or system that conforms to
those constraints. This is very different than the more orthodox course
approach where you learn the constraints within which a given set of well-
known algorithms exist and then select the appropriate algorithm for a use
case. There are many real-world cases where all well-known algorithms cannot
fit within the necessary constraints. Designing custom algorithms is not
particularly difficult, but it requires grokking all the theoretical knobs
that can be turned for a problem space rather than memorizing variants of a
particular solutions.

------
mahyarm
This is the core of a CS degree, each one is class, sometimes multiple classes
that go into more detail. All interview questions will basically only cover
these topics.

1\. Algorithms & Data Structures <\- The biggest one

2\. Baremetal Hardware. ASM, goes into the design of a physical cpu with ALUs,
etc. Sometimes you make your own basic CPU. I suggest using a course with ARM
ASM, simpler than x86 ASM.

3\. Operating Systems & Multithreading Theory. You usually do a bunch of C
language work here. Maybe combine it with a project on an ardunio or similar.

4\. Discrete Mathematics

5\. Databases

6\. (Optional) Compilers. Write your own compiler, do this after the ASM
course.

7\. (Optional) Artificial Intelligence. Learn cool things such as machine
learning. AI can be very statistical at times, so I suggest adding a
Statistics & Probability course to supplement. Statistics is used a lot in
business, so it's useful to know for life in general.

8\. (Optional) Computer Graphics, using OpenGL!

On top of that I suggest you learn a functional language like Clojure or
Haskell. Or both of them. Also learn a language where you have to do memory
management and deal with pointers (like C, C++, Objective-C) if you don't
include it in your Operating Systems course. After that you can basically do
anything in software. Any new language and platform will be just covering
concepts you already understand at that point, so you'll be able to learn them
extremely quickly.

~~~
jd007
I would add computability and complexity theory to that list. Some
computational complexity should be covered in algorithms and data structures,
but theory of computation is not really (as algorithms by definition solves
only computable problems). A fundamental knowledge of what is and what isn't
computable is quite important in theoretical computer science IMO.

~~~
mtdewcmu
I can't remember if formal languages and automata was an elective or a
requirement for me... I think it might have been required. The textbook was
the one by Sipser, and I thought it was a pretty good book.

------
danieldk
_So, what is the best way for a proven and largely self taught developer to
take their knowledge to the next level?_

It depends on how you learn. Some people will recommend Coursera et al., which
are great. I tried some Coursera courses, but found that I found the pace too
slow and became bored quickly.

For me, reading always works the best, since I can adjust it to my pace. You
could look up a curriculum (as someone else suggests) and compose a reading
list from that. Also, there are some works where you really can't go wrong.
Some examples:

\- Structure and Interpretation of Computer Programs, Abelson and Sussman

\- Algorithms, Sedgewick, Wayne

\- Introduction to Automata Theory, Languages, and Computation, Hopcroft,
Motwani, Ullman

Lesser known, but incredibly fun books:

\- Purely Functional Data Structures, Chris Okasaki

\- The Reasoned Schemer, Friedman, Byrd, Kiselyov (or a good Prolog book).

After learning the foundations, you could branch out to a subfield that
interests you.

(Or as Frank Zappa has bluntly put it: _“If you want to get laid, go to
college. If you want an education, go to the library.”_ )

~~~
narrator
>It depends on how you learn. Some people will recommend Coursera et al.,
which are great. I tried some Coursera courses, but found that I found the
pace too slow and became bored quickly.

You can watch the lectures at 2x speed. ;)

~~~
probably_wrong
Yeah, but you can't jump to the next lesson - unless you wait until the end of
the course and see them all at the time, but then you won't get a certificate
because you miss the quiz deadlines.

~~~
mcintyre1994
One thing I've noticed with Coursera is that if you join before the course
starts, there's often a preview button that seems to show at least the entire
course's video lectures. If the content was useful enough to you, you could
take the time to download all the videos and could watch them at any pace, and
since you'd always be ahead because of your quicker pace you could still do
the quizzes, albeit not straight after watching the lectures.

~~~
auctiontheory
You can download the video, and then you can extract the audio and listen to
the mp3 wherever you are, as often as you want. At least, that's what I did.

I don't think the OP is in it for the certificates.

------
nohuck13
The other responses are great. But one meta point I think is worth making.
Don't overestimate how much competency you gain from just getting a CS degree.
Lots of people coasted their way through undergrad without internalizing a
heck of a lot. The fact that you are motivated to go out and get knowledge
puts you, IMO, at a great advantage.

My background: I did a BS in CS/Economics but spent most of my time playing
online poker and skipping class. I managed to get a job I love on mostly
potential, and I've had a great time re-learning all the stuff I was
superficially exposed to but didn't work that hard at.

The most important thing is caring about what you do and taking ownership over
your own development.

~~~
jophde
This is why I am considering the BS. I already had the college experience at
Penn State. Meaning parties, friends, girls, football, etc. This time it would
be purely about going to class and learning. I bet I wouldn't even have to do
Gen Eds since I already have a BS.

~~~
nandemo
I think the marginal benefit of a second BS-level degree is small given the
cost in time and money.

If you're going back to school then you should definitely consider an MS.
Maybe you're worried that you wouldn't be accepted or that it would be too
challenging? In that case, narrow down a list of universities/departments
where you would like to enroll, and identify what you need to study in order
to get accepted.

Alternatively, teach yourself, and try to join a top tech company that focus
on making the kind of software you're interested in. Working with great
programmers has a large impact on your learning. Perhaps you're
underestimating this impact because your first job wasn't challenging enough.

------
petercooper
I'm going to keep this reply shallow but my advice is dig up a curriculum and
course guide for a CS degree (there are many publicly discoverable with
Google), establish what all of the main topics and threads are, grab the
best/most recommended textbooks for a couple of topics at a time, work through
the books a few pages at a time and for anything you don't understand, Google
and learn about it. Take copious notes as you go to refer back to. Read papers
that pop up from time to time, get a feel for what you know you _don 't_
understand and quickly get up to speed with them (even if it's just reading
Wikipedia for 20 minutes).

The above is deliberate practice and learning but also keep an eye out for CS-
level posts linked on HN and
[http://www.reddit.com/r/compsci](http://www.reddit.com/r/compsci) and relate
them to what you're learning. Read a post about AI data structures in Prolog?
Don't understand Prolog that sounds interesting? Get a feel for what Prolog
is. Write a simple program. Get a feel for implementing the data structure in
a language you _do_ understand. Then try and bring both Prolog and the
structure together. Rinse and repeat with anything that interests you. Again,
be sure to TAKE NOTES or you'll forget things using this scattershot approach.

It'll take a TON of time but if you keep your sessions relatively short,
you'll get a shallow knowledge of all of the major CS areas quickly, and then
you can use your job or natural interest to drive you into going deep on areas
that affect or motivate you.

I'm starting an MSc in software engineering later this year but my own CS
knowledge has mostly been learned in the above ways (that is, I don't have a
bachelors in CS).

 _Clarification: As cliveowen got me to realize (below), the above approach
might not be for you if you have a very specific target in your career
development. My experiences and recommendations are specifically around
getting a broad level of experience rather than aiming at a specific role
(which, perhaps, you should be doing)._

~~~
cliveowen
Frankly I think that's the worst advice you could give anyone for whatever
subject: i.e. "when you find something you don't know about, study it". The
best course would be to pursue a targeted learning, and by that I mean, do you
wanna be a data scientist? Then you should study probability theory and
statistics along with the relative algorithms instead of reading something
about Prolog. Do you wanna become a software engineer? Then you should study
software engineering, programming, algorithms, advanced algorithms and data
structures, patterns, and so on. Getting a "shallow knowledge of all of the
major CS areas quickly" with a "scattershot approach" is a recipe for
disaster. The ultimate goal is to gain skills needed for your dream job.

~~~
petercooper
I concede it's not the best approach if someone has a specific goal like, as
you suggest, becoming a "data scientist", a "compiler developer", or a quant,
etc.

In my case (and what I _felt_ was the case for the OP) a general, broad level
of knowledge is paramount. I then study deeper on an as-needed basis off the
back of my broad but shallow knowledge. Being able to tie together the basics
of many unrelated areas really helps in my work, but is surely not for
everyone. I already have my dream job for life so my goal is more on becoming
well rounded rather than getting a specific job.

From a career POV, should the OP specifically focus on a specific target
rather than just aim to get a general CS understanding? Quite possibly! But
that's a different discussion/recommendation that I think you could kick off
in your own response to OP. So I'm voting you up not because I agree with your
criticism, but because perhaps the OP _does_ need to think more solidly about
the end goal.

~~~
jophde
The goal is simply acquire a much deeper understanding of computing that I
feel I missed out on by not studying CS in college. I see myself as extremely
employable doing app and web development for the immediate future. Under the
hood everything is like magic to me and I don't want to feel like that. I also
feel like I don't know enough to know what my dream job in computing is yet.
Your thoughts are limited by your knowledge.

~~~
petercooper
You might like to try the old "go down the stack" process as a first exercise
then. There was a post about it recently on here. A Web app developer who
knows a lot about things work right down to the metal is a lot more valuable
than one who doesn't.

How do the processes behind your webapps work? Why or why can't your app
support 10,000 clients hitting it at once? What's happening at the HTTP level?
The TCP/IP level? Just understanding some of the algorithms behind routing and
TCP congestion avoidance could give a ton of food for thought, still get you
into learning algorithms, notation, and reading CS papers, but still be more
directly beneficial to the day job. I wish you luck however you end up
approaching it! :-) The only bit I want to repeat is take a lot of notes.. do
blog posts, write articles.. anything to ensure you retain that knowledge
because it's so easily lost as you get older.

~~~
jophde
Taking notes has always been my weakest point as a student so that is
something I will definitely have to focus on. I think it's sound advice
though.

------
stiff
Doing a BS in CS would be the best, otherwise you will need a ton of self-
discipline to learn even a half of what you would learn in a degree program.
If you decide to self study, and have enough "mathematical maturity", you will
find everything you need on MIT OpenCourseWare, they have all the core courses
available online with video lectures, solved homeworks etc. I would start with
going through those two first:

Structure And Interpretation Of Computer Programs:

[http://ocw.mit.edu/courses/electrical-engineering-and-
comput...](http://ocw.mit.edu/courses/electrical-engineering-and-computer-
science/6-001-structure-and-interpretation-of-computer-programs-
spring-2005/video-lectures/)

Mathematics For Computer Science:

[http://ocw.mit.edu/courses/electrical-engineering-and-
comput...](http://ocw.mit.edu/courses/electrical-engineering-and-computer-
science/6-042j-mathematics-for-computer-science-fall-2010/video-lectures/)

The first one is pretty much a master class in software engineering, the other
prepares you for studying algorithms, I would consider those the two main more
theoretical facets of programming at a professional level. With that
background you can try to work on their algorithms course:

[http://ocw.mit.edu/courses/electrical-engineering-and-
comput...](http://ocw.mit.edu/courses/electrical-engineering-and-computer-
science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/)

It would also be very valuable to eventually take all the core mathematics
subjects from OCW: Single+multivariable calculus, linear algebra and
probability theory - the profit is less immediate but those things do come
very useful. All those six courses on the MIT OCW are top notch.

~~~
flatline
It is hard to beat a good CS curriculum with real teachers, peers,
assignments, tests and grades. These things don't work well for everyone, and
the pressure can be pretty intense at times, but damnit that pressure can
really burn stuff into your neurons that would otherwise go in one ear and out
the other. The overlapping of topics and repetition of important concepts are
also typically lacking in a self-learning environment, and these things really
helped me to pick out what was important in terms of building blocks for more
complex things. Coursera et al. are great, they fill a niche, just probably
not what you are really looking for.

~~~
mindcrime
_It is hard to beat a good CS curriculum with real teachers, peers,
assignments, tests and grades._

I dunno... I think it depends on the individual a bit. OK, to be fair, I did
drop out before finishing my B.S., but up to where I was at, I can honestly
say that I learned 90% or more of what I learned, outside of class, reading
and practicing on my own. The only class I really remember the teacher's
explanations helping a whole lot, was in certain parts of Discrete Math.

I could be wrong, but I feel like some people are just "wired' for teaching
themselves stuff, learning from books and videos and websites, and then
throwing the occasional question up on the Theoretical Computer Science Stack
Exchange[1], or /r/askcomputerscience or whatever.

At the very least, I would posit that most people can learn an awful lot
through self-study. Maybe not enough to do ground breaking research in C.S.,
but certainly enough to bump up their knowledge of the "basics" to where they
aren't clueless when somebody else in the room starts talking about
algorithmic complexity or finite state machines or whatever.

[1]: cstheory.stackexchange.com

[2]:
[http://www.reddit.com/r/askcomputerscience](http://www.reddit.com/r/askcomputerscience)

------
tel
Read papers.

Read lots of papers. Start with easy ones to learn how to best digest highly
academic technical writing then keep pushing.

CS is remarkable in how much of its academic knowledge is online, available,
for free. Taking advantage of that resource is beyond key.

If you know roughly what you want to learn, search out a seminal paper in that
area. If it's deep CS, you'll probably find a good one from the 80s. Seek out
every citation that's proximal to a sentence in that paper that confuses or
excites you. Search on Google Scholar for all the recent papers that cite the
one you found and begin eating up the chain that direction. When you find a
deep topic you want to learn more of—set theory, logic, formal languages,
discrete math, matrix analysis, automata theory, geometry, topology, &c.—don't
be afraid to look for a good book on the topic. There are resources around the
internet answering "What's a good introductory book to X" for all kinds of X.

If you don't know the general area you're interested in then I recommend the
exact same strategy but with greater emphasis on following citations that make
connections to other areas of CS. Additionally, pick a few disjoint topics
(Category theory, system architecture, graph theory) and follow them all
simultaneously looking for connections.

Formal languages, automata, and process algebras form a really fundamental
mathematical course of study that I'd highly recommend to anyone interested in
"why" CS works. Optimization, matrix analysis/linear algebra, and diffeq form
a great basis for simulation and machine learning.

Generally, for any of these routes, learn to find your boundary of knowledge.
Studying source material is very challenging because any given paper will tend
to assume many things about your background. Most of those assumptions will be
false and lead to density of the paper. You can often power through without
them, but you can also take it as an indication of a new place to study.

Finally, see if you can find a study group or journal club. I'm not there, so
I don't have firsthand experience, but I'm sure there are many in the bay
area.

(Oh, and if you read mathematical papers/books don't skip the proofs and
exercises. That'd be like reading the iOS documentation without ever
programming anything.)

~~~
sillysaurus2
In case you want to read papers but don't really know where to get started,
here's my collection I've read over the years:
[http://dl.dropboxusercontent.com/u/315/articles/index.html](http://dl.dropboxusercontent.com/u/315/articles/index.html)
... feel free to browse through it and pick up anything that looks
interesting. You'll probably want to scroll all the way to the bottom and work
your way up the list.

Many of the classics are in there, such as the Plan9 paper and Paxos Made
Practical.

If the images are distracting, here's the list without them:
[http://dl.dropboxusercontent.com/u/315/articles/index_no_ima...](http://dl.dropboxusercontent.com/u/315/articles/index_no_images.html)

Actually, looking over it, that list isn't very curated. Just Ctrl-F "unix"
and that'll take you to some good papers.

~~~
sethkojo
Thanks for this. I actually like that it's not curated, it's a good way to
discover things I didn't know about. The fluid simulation stuff looks
especially interesting.

~~~
sillysaurus2
Sure, no problem. Let me know if you have any questions or want to chat about
random compsci topics.

~~~
sethkojo
I'll probably have some questions after looking over some more of the papers.
We seem to have a healthy intersection of common interests. What's the best
way to get in touch?

~~~
sillysaurus2
Cool! You can mail me at sillysaurus2@gmail

What sort of projects are you interested in?

------
jkbyc
Theoretical computer science is probably not what you mean. Theoretical
computer science are things like complexity theory (up to arithmetical
hierarchy and randomized and approximation algorithms), theory of recursion
(up to e.g. Gödel's theorems), (various kinds of) logic, algorithms and
datastructures (full of hardcore probability and statistics), etc.

Subjects like that give you a firm grounding in the area of computer science
but you could study them for ages especially on your own. These subjects are
also not very practical in terms of everyday engineering and on top of that
before you even get to that level, a top school would require you to study a
bunch of mathematics to gain a certain level of rigor of your thinking. My
guess is that this is hard to do on your own.

On the other hand, since you have a related degree already and since you know
programming, I would heartily recommend you to study on your own combining two
approaches: bottom-up to learn the basics and top-down to immediately start
increasing your market value and to start opening doors and to keep yourself
motivated to go forward with the more tedious study of the basics.

E.g. say you are interested in distributed systems - you can start reading up
on them (top-down) while digressing here and there to learn some of the
basics.

Make use of online resources like Coursera for the necessary basics (bottom-
up): at least some maths heavy on proofs [1], at least some complexity theory,
at least some graph theory, ....

I think a purely bottom-up approach (going to a university) could be a waste
of time and money in your case. But you need to emulate it a bit because a
purely top-down approach could be too superficial and wouldn't teach you some
of the more rigorous thinking you might need.

Whatever you do and learn try to do it in-depth. Superficial knowledge of many
things will not benefit you much in the long term while in-depth study of many
computer science fields will likely lead you through a series of small
enlightenments.

[1] My professor of linear algebra used to insist that we as computer
scientists have to know all the proofs of the theorems we were learning - in
contrast to mathematicians learning the same subject - simply because we have
to know how things are done to the last detail and we have to develop that
kind of thinking.

~~~
rivalis
IamA graduate student in theoretical computer science.

I don't know that I agree with the poster above with respect to:

"a top school would require you to study a bunch of mathematics to gain a
certain level of rigor of your thinking"

Most good schools require only two courses in "pure theory": first an
introduction to discrete mathematics, where you learn about logic and how to
prove stuff, a smattering of number theory/crypto, graph theory, probability,
and automata theory; second an algorithms course that teaches you to analyse
and construct algorithms according to certain design methods. Together this is
really only a year of mathematics, and both courses are quite fun.

Note that discrete mathematics as taught by a good CS program is NOTHING like
the math you learned in high school or elementary school, it teaches you to
think creatively about mathematical structures and then justify that
creativity with logic.

If you're already a developer, you'll probably have a bunch of latent
structures hanging around in your brain that will let you have an easy/fun
time with the material in these two courses. I suggest that you study discrete
mathematics and algorithms in depth, to the level of some decent undergrad
course on each. Learning this material will give your thinking the sort of
quantitative/logical "edge" you might want -- these two courses contain the
basic mathematical tools common to much of computer science. I do agree with
the post above that they are not the most practical things in terms of
everyday engineering, though.

Addendum: if you find that you really enjoy the mathematical angle and you
think machine learning is cool, also learn linear algebra, because a bunch of
machine learning theory and implementation relies on linear algebraic
algorithms and concepts. Linear algebra actually would be practical to know if
you ever do anything with data analysis.

~~~
kotakota
I think your off base with this. A good school with a good theoretical cs
program will always require up to multivariable calc, linear algebra, stats
with calc, and discrete math. These are required because they will almost
always be essential for doing theoretical work. Sometimes you just need it to
properly express and explain complexity of a problem but many times in
theoretical work knowledge of advanced mathematics is integral to to the
actual research. Your advice is more geared towards what most good schools
consider a general cs degree.

~~~
rivalis
My advice is indeed geared towards general CS, it was unclear to me if the
original poster wanted to get into heavy-duty theory or just gain a more
rigorous understanding of CS in general.

Even at good schools (in the US, anyway) the calc up to multivar that is
required isn't done with what I would call good proofs. They'll generally do
epsilon-delta definitions of the limit and a few other fun things, but will
fall far short of a truly rigorous development of the calculus. Same goes for
many introductions to linear algebra and stats with calc courses. Some math
departments use linear algebra to introduce proofs and creative mathematical
thinking, though, so this isn't always the case.

So if someone is looking to develop how they think in mathematics and they
already have a good programming background, they are much better served by
taking a discrete math course than any of those sorts of math courses. If they
then want to learn calculus, I would recommend self-study from Spivak's
"Calculus" book which is a fun and elementary but rigorous treatment of the
subject. You get to see not just _how_ calculus works, but _why_ it works,
which is sorely lacking in most undergrad calc courses, even up to multivar.

~~~
kotakota
What do you call good proofs? I think what you consider a "good school" is not
what I consider a good school. In my calc classes we studied tons of awesome
proofs that were very applicable to theoretical cs stuff. Plus most of my
linear algebra classes and stats classes were just engineering, cs, and math
majors so we once again focused on very useful real world applications and
fields of active research.

If someone wants to develop their mathematical thinking and is good at
programming descrete math isn't going to help them much because they have
probably already seen much of it. They need to be exposed to high level calc
and linear algebra to develop their mathematical thinking.

------
jclos
Is it theoretical CS as in "CS topics that are more theoretical" (NLP? AI?
Search engines? Software engineering?), or as in "Theoretical CS" (the
mathematical subdisciplines: combinatorics, type theory, lambda calculus,
etc.)?

In any case you first need to investigate what is interesting to you, free
resources are far from rare and you can probably build yourself a decent
curriculum from MIT OCW, Coursera, Udacity and similar websites which you can
then study at your own pace with videos and books. If finding a job is not
your concern I wouldn't advise putting yourself into debt. See
[http://www.saylor.org/majors/computer-
science/](http://www.saylor.org/majors/computer-science/) for an example of
curriculum.

------
evanb
If you're OK learning on your own, you might try buying a book before
committing to the cost of tuition, also. If you really mean "theoretical CS" I
don't think you can go wrong with Sipser. The latest edition[1] is expensive,
but a used copy of the second edition [2] isn't TOO bad, considering the cost
of another few years of education.

[1] [http://www.amazon.com/Introduction-Theory-Computation-
Michae...](http://www.amazon.com/Introduction-Theory-Computation-Michael-
Sipser/dp/113318779X)

[2] [http://www.amazon.com/Introduction-Theory-Computation-
Michae...](http://www.amazon.com/Introduction-Theory-Computation-Michael-
Sipser/dp/0534950973)

~~~
oftenwrong
I second Sipser's book. Probably the best textbook I used in university. You
can find international editions for a very low price.

~~~
pessimizer
International Editions:

[http://used.addall.com/SuperRare/submitRare.cgi?author=sipse...](http://used.addall.com/SuperRare/submitRare.cgi?author=sipser&title=Introduction+to+the+Theory+of+Computation&keyword=&isbn=&order=PRICE&ordering=ASC&binding=Any+Binding&min=&max=&exclude=&match=Y&dispCurr=USD&timeout=20&store=ABAA&store=Alibris&store=Abebooks&store=AbebooksAU&store=AbebooksDE&store=AbebooksFR&store=AbebooksUK&store=Amazon&store=AmazonCA&store=AmazonUK&store=AmazonDE&store=AmazonFR&store=Antiqbook&store=Biblio&store=BiblioUK&store=Bibliophile&store=Bibliopoly&store=Booksandcollectibles&store=ILAB&store=Half&store=LivreRareBook&store=Powells&store=Wbm&store=ZVAB)

------
samatman
Read. Focus on foundational texts. I'm talking about texts like K&R, SICP,
Lisp In Small Pieces, RFC 791. I'll add Gödel, Escher, Bach, because I
genuinely believe it will make anyone a better computer programmer. There are
far more than I could mention in a paragraph; L.I.S.P is not as well known as
the others I mention, and got added mostly because I'm reading it at present.
It's _really_ good.

Also, read actual code. Want to know how diff works? Read diff. Getting better
at code forensics is the second-best way for a self-taught programmer to learn
real CS.

EDIT: I am a largely self-taught programmer.

------
msg
My story is somewhat similar.

I took a BA in Linguistics, worked for a while, then discovered computers. I
spent a year on prerequisites and then did an MS in CS. I got good grades and
did a thesis and it opened a lot of doors for me.

Some things that an MS CS degree will teach you that you may not have learned
as a seasoned developer are: How to invent solutions to cutting edge problems.
How to operate at scale using efficient algorithms and appropriate data
structures. How to think about problem spaces. How to research. How to operate
at the correct level of abstraction and how to get a level deeper when the
abstraction leaks. The intersection between math, stats, and software. How to
think like a computer.

To me it sounds like that's exactly what you want to do. One way or another
you want these skills.

You may want to separate your desire for these skills from your desire to be
credentialed for these skills. It is going to take a while to see how
employers react to the Georgia Tech online MS. I believe the vast majority
will treat it as second-class for a while. The judgment of HR departments is a
lagging indicator. But the top tier employers may not care and just test you
to see if you walk the walk.

You don't need a top tier school to get a good job. My MS is from a state
university, and I work for Amazon.

~~~
jophde
In order to get into an MS program would I need to do a BS in CS or just do
the prerequisites I am missing. Off the top of my head I know that I am
missing Calc 2, Calc 3, Linear Algebra, Algorithms, and Operating Systems.
Does it matter where I do the prerequisites? I imagine I could just do the
maths at a community college.

~~~
tspike
I did the exact same thing. You only need to do the prerequisites. No, it
doesn't matter where you do them, but it's obviously best if you do them at
the same school you intend to attend, as you'll be able to get recommendations
from professors in the same department, and obviously the courses will
transfer fine.

EDIT: FWIW, at the University of Colorado, I had to do 2 courses above calc 1
- for me that was calc 2 and statistics, as well as 5-6 CS courses.

~~~
jophde
That's a really a good point about the letters of recommendation. I think this
is the route I will be going down. I had no idea how I was going to get the
letters otherwise.

Do you have to apply to take the prerequisites or do you just pay them and go?

~~~
tspike
At most schools, you can just take courses without a competitive admission
process until you intend to enroll in a degree program.

------
TimPC
I think it's far and away self-study or if you can find a good online course
among the free solutions you can start there. The Art of Computer Programming
by Knuth has a lot of the theory included and doesn't hold back on the Math.
Similarly, Introduction to Algorithms by Cormen, Leiserson, Rivest and Stein
is quite good for the basis of Algorithm theory.

That being said, theory plays a small role in everyday development. If your
primary goal is to increase your knowledge as it relates to development you
don't want to focus on theory until it becomes a pain point. Algorithm theory
helps with scalability, but practice is far more useful to programming.
Conferences in your field that can expose you to new things to learn and
different tool chains in your language are valuable. Learning a new related
language can also be valuable you might consider learning iOS and then
JavaScript which would let you work on Android, iOS and Cordova (formerly
PhoneGap) applications at a level where you'd be comfortable going from
JavaScript to native to write unavailable features.

If you're happy and have good opportunities on Android, focus on getting a
deeper understanding: what are good open source repos, what coding conventions
do they use, what frameworks and approaches could you know better. Are there
parts of the OS you haven't worked with and wanted to? For instance, I built a
demo app for LG designed for in-store promo devices where we hacked around in
the OS to intercept the display of screens that would let the user delete apps
from the phone and throw up a password lock that would kick them out to the
main screen. Try and get a sense of where your best (however you measure it)
opportunities are and focus your learning in that direction.

------
kenjackson
At the end of the day I think its a question of what you value more "money" or
"time". If money is your main concern, use books and online courses. If time
is your main concern, get an MS at a good CS program.

My problem with teaching myself is that it's hard for me to stay motivated
after the first couple of weeks. Now this just me -- it's not you. So maybe
you don't have this problem at all, but I've found school to be a good
motivator.

Plus having a good professor can help get through the tough spots. I studied
complexity under Papadimitriou and he was great at explaining things I
struggled with.

One problem with school though is you'll have less flexibility to skip things
you don't care about, and investigate those things you do. That can be a
blessing or a curse.

------
shawndrost
You might be interested in my school,
[http://hackreactor.com](http://hackreactor.com). Our course is 50% CS (data
structures, algorithm design and analysis) and software engineering
(modularity, refactoring) and 50% web fundamentals and writing a lot of app
code, and students are constantly working together on extracurricular study.
This weekend, they're throwing a machine learning workshop (developed by
students; alums invited), and in two weeks we're playing host to a PL
design/implementation class
([http://proglangmasterclass.com/](http://proglangmasterclass.com/)). You can
reach out to me at shawn@hackreactor.com.

------
rkabir
SICP: [http://mitpress.mit.edu/sicp/](http://mitpress.mit.edu/sicp/)

6.004: [http://ocw.mit.edu/courses/electrical-engineering-and-
comput...](http://ocw.mit.edu/courses/electrical-engineering-and-computer-
science/6-004-computation-structures-spring-2009/index.htm)

6.042: [http://ocw.mit.edu/courses/electrical-engineering-and-
comput...](http://ocw.mit.edu/courses/electrical-engineering-and-computer-
science/6-042j-mathematics-for-computer-science-spring-2010/index.htm)

CLRS: [http://mitpress.mit.edu/books/introduction-
algorithms](http://mitpress.mit.edu/books/introduction-algorithms)

------
nhamann
Sorry if this is obvious, but: read books. A good place to start is here:
[http://cstheory.stackexchange.com/questions/3253/what-
books-...](http://cstheory.stackexchange.com/questions/3253/what-books-should-
everyone-read)

There was another reading list that I remember seeing, I think it was from
Stanford's TCS website, but I no longer can find it.

Self-teaching is fun because you get to choose your own curriculum, but it's
often frustrating too because if you get stuck, there is no professor or TA to
unstick you. This issue can somewhat mitigated via the internet.

------
jypepin
I'm a Devbootcamp alumni, now working in a full time position. Just like you,
I wanted to continue my learning and get more knowledge on algorithms, data-
structures, and other things DevBootcamp doesn't teach you.

I strongly recommend \- Algorithms in a nutshell from O'Reilly
([http://www.amazon.com/Algorithms-Nutshell-In-
OReilly/dp/0596...](http://www.amazon.com/Algorithms-Nutshell-In-
OReilly/dp/059651624X))

and \- Cracking the Coding interview ([http://www.amazon.com/Cracking-Coding-
Interview-Programming-...](http://www.amazon.com/Cracking-Coding-Interview-
Programming-Questions/dp/098478280X))

Those two books are perfectly concise and straight to the point to understand
and learn exactly what you feel you are lacking as a self-taught programmer.

The first one will teach you what you have to know, putting everything into
work context, making it really easy to understand why and how this or that
algorithm is useful.

Cracking the coding interview then offers really good challenges to practice
and master those algorithms. And of course, if you are interested in getting a
job, will perfectly prepare you for that ;)

------
jlees
In answer to the first part of the question (how to get more theoretical CS
knowledge), I studied an extremely theoretical degree and the materials are
online to dig through - if I were to self-teach now, I'd start at the final
year's course list
([http://www.cl.cam.ac.uk/teaching/1314/part3.html](http://www.cl.cam.ac.uk/teaching/1314/part3.html))
and work backwards to chart a path to the modules that sounded most
interesting.

In terms of "taking knowledge to the next level", though, it could mean
anything from you wish you knew what red-black trees and big-O notation were,
to you'd love to be able to design your own programming language and write a
compiler, to you wish you could administer a Linux box. I would actually
suggest the best approach here is to find someone with the job you want and
talk with them 1:1 to figure out where your knowledge could be most improved.

Also, for Coursera, etc, there are local study groups at places like Hacker
Dojo you could join to get some of the benefits of college without the
expense.

------
etler
One of the biggest factors I think you should consider if you want to go the
self learning route is if you'll have the time to while juggling a full time
job as well. You might be able to take a few courses, but will you be able to
dedicate your full attention to it, and really dig into the subjects?

If I were you I wouldn't add on any more debt until I've settled my current
one. With a good CS job, that shouldn't take more than 2-3 years, considering
you have no dependants and presumably relatively low living costs. In the
meantime, maybe take part time courses where you can get class credit, and if
you plan it right you might be able to complete your degree in a year or so,
considering you already have your basic requirements done. Just do some
research into making sure your class credits will be able to transfer. Good
luck.

------
jzelinskie
I'm a current senior Design & Development option at Penn State. The degree is
basically worthless in terms of teaching you real software development. I did
learn a lot about the social aspects of working for clients and working in
teams, but I did not learn the proper structure to actually work on software.
I literally spend all of my free time studying software development and
computer science, because I know going to school will only yield me a piece of
paper that will get me taken more seriously.

Here's a list of what I've done:

\- Learn more languages. Penn State only teaches Java. I've worked
professionally with Python, have open source projects in Go, and have read
books on Erlang, Haskell, Scala, Clojure. The more languages you know the more
abstract concepts you'll know that you can apply in any language.

\- Watch online lectures in your free time. MIT Open Courseware, UC Berekely,
Coursera, YouTube, InfoQ are all really good resources.

\- Start a reading collection. I have tons of books and white papers
downloaded that I read.

\- Get an interest. I like distributed systems. I honestly don't know much
about them, but I think the problems are interesting and I've read some of the
important white papers that establish the field. Establishing an interest will
help guide you down the rabbit hole.

\- Get out there and do stuff. Find a project on GitHub or make one with a
circle of friends. Pick something outside your comfort zone. Even if the
project never sees the light of production use, you'll learn from the
experience. Having your name in open source projects AUTHORS/CONTRIBUTORS
files is also very nice.

I'm getting closer to graduating, so I've been reading up on algorithms and
data structures again because I know I need brushing up on it. I'm close to
getting a compsci minor and was recently debating just getting a masters in it
instead. If you want someone to vent your experiences at PSU, feel free to
drop me an email.

------
porter
I studied finance in college. A few years later I asked a similar question,
ended up enrolling as a post-bac student, and taught myself web development.

First, you need to figure out exactly what you want to learn. By theoretical,
what do you mean? If your goal is to be on the same level as other programmers
who are CS grads, then you might consider digging into algorithms and data
structures and discrete math. This is pretty much the base of anything
theoretical you'll do in computer science.

If you're in it to learn, go the udacity route. If, after completing all of
their courses, you still feel you have some gaps, then you can go back to
school if need be. If, on the other hand, your goal is to go into research,
then you'll just have to bone up and go back to grad school to be taken
seriously. In research, credentials matter.

------
karanbhangui
In addition to all the great advice here, if you want a bit of a more
structured approach, check out Scott Young's MIT challenge:
[http://www.scotthyoung.com/blog/mit-
challenge/](http://www.scotthyoung.com/blog/mit-challenge/)

------
kotakota
Personally I would recommend doing a ms if you can afford it but if you can't
I would recommend that you study the following areas Algorithms and data
structures (this is a must) Systems organizations and architecture Systems
programming Discrete math Math for cs books (generally proof based descrete
and calculus based) Statistics and probability Then Start diving into areas
that interest you like Metaheuristics Ai Machine learning Computer vision
Compilers Device drivers Graph theory Computer Graphics (if your working in
theoretical computer graphics strong maths skills are recommended) And the
list goes on. Also read papers were in areas of interest. Papers are a great
way to learn high level theoretical concepts.

------
lucasrp
I am a law major, who did 1 year of engineering a long time ago. I always been
a math geek, but 0 in CS. In my last year of college, i created a startup with
some friends. It was a ERP for small lawyers firms. That didnt work out, but
turned me on into CS.

Now i work as a product manager in a bigger firm (also law related), and i'm
learning how to code through Coursera and Edx. I HIGHLY recommend them.

They are the future. The classes are very good. Way better than a regular
class over here (Brazil).

If you are intereste in theoretical CS, here are 2 classes that you may be
interested:

Programming Languages
([https://www.coursera.org/course/proglang](https://www.coursera.org/course/proglang)):
It focuses on functional programming. The first edition was VERY high
recommended. Here you will learn about functional paradigm, and the
differences in using it in several languages (some purely functional, like
SML, some hybrid, like Ruby)

Automata
([https://www.coursera.org/course/automata](https://www.coursera.org/course/automata)):
It cant get more theoretical than this. The professor is Jeff Ullman. A
legend. For free.

Machine Learning: A second version of Andrew Ng just ended. The third edition
will be offered soon.

see.stanford.edu is also a very nice place to learn. They are actual stanford
classes taped, and offered for free, online. I`m taking the three introdutory
classes, and the machine learning classes.

Also, there are several architecture, compilers and algorithms classes too.
After my first course (cs50.net), i realized that colleges (at least for CS)
are redundant right now. They can be awsome. But, if you are short of money,
or are already working, these online classes can fill the gap, easily.

add me on skype if you want to talk about more classes: lucasribeiropereira

See you!

PS. They can be VERY challenge. Take one, at most two at a time. 10-20 hours
per week per course is a good rule of thumb

------
beloch
If you can get a decent prof (not necessarily the most famous or well-
published) to take you on to do a M.Sc., that beats the hell out of doing
another B.Sc.. (Caveat emptor: Choosing a bad prof will bring you nothing but
pain! Your supervisor is not just another prof. He will have an insane impact
on you!) B.Sc.'s are the Honda Civics of academia. Universities mass produce
them because they bring in the most cash per head. Grad school is more like a
bespoke roadster or F1 car. The resources universities spend on grad students
and research are disproportionate compared to what they spend on undergrads.
Also, just as you learn more than just the core knowledge of your major in
undergrad, you learn a lot of additional things in grad-school. Teaching,
speaking, etc.. Above all, grad students are placed under pressure to actually
_think_ instead of just regurgitating. If you do another B.Sc. you'll be
repeating a lot of stuff you already know.

A good prof will figure out where your knowledge is lacking and give you the
resources to catch up fast. You'll likely be thrown into some grad-level
courses that are way outta your league and will have to work like a crazy
bastard to catch up with students who have a CS B.Sc., but you'll have great
student-teacher ratios and your best teachers will actually be the other
students. You'll probably have to TA material you'll be learning the night
before, and teaching something is a fantastic way to learn it well.
Eventually, you should do some research, and hopefully you'll have chosen a
prof doing something you're interested in. Do NOT do a course-based M.Sc., as
those are just upgraded Honda Civics!

You'll be under intense pressure to learn a lot fast, but you'll have the
resources to do it. A B.Sc. will likely take longer and you'll spend a lot of
time slacking off because undergrad courses are pretty damned easy. Also, a
M.Sc. is a better credential to have than another B.Sc..

When you're choosing a prof, talk to the other grad-students. DO NOT just
choose the guy who was nominated for a nobel prize. As the saying goes, "Happy
students never won anyone a Nobel!".

------
john_sp92
Here are my picks. Hope they are helpful.

[http://cstheory.stackexchange.com/questions/3253/what-
books-...](http://cstheory.stackexchange.com/questions/3253/what-books-should-
everyone-read)

[http://www.nand2tetris.org/](http://www.nand2tetris.org/)

[http://rys.sommefeldt.com/2012/07/30/getting-by-in-a-
technic...](http://rys.sommefeldt.com/2012/07/30/getting-by-in-a-technical-
industry-without-a-degree.html)

[http://catb.org/~esr/faqs/hacker-
howto.html](http://catb.org/~esr/faqs/hacker-howto.html)

------
skadamat
There are some good suggestions for topics and what all to learn, here are
some links to actually go and learn em!

[http://stackoverflow.com/questions/194812/list-of-freely-
ava...](http://stackoverflow.com/questions/194812/list-of-freely-available-
programming-books)

and

[http://hackershelf.com/browse/](http://hackershelf.com/browse/)

Should have everything you need, they're all free / open-source books!

------
asselinpaul
Coursera, edX and Udacity.

I have myself taken half a course on Udacity(did not finish) and a Startup
Engineering Course on Coursera. I've started a new course on Coursera and
really enjoy the material on there.

Also, I'd suggest you read a lot, the internet is a treasure trove of
information. I've learnt from long blog posts and free online books. Have a go
and explore, you'll reach a point where you don't have enough time to study
everything you want.

Goodluck

------
soora
One way of improving your knowledge is something you have already done.

Get another job that will force you to expand your knowledge. I am sure your
job experience with your first start up is serving you better than a CS
degree.

Similarly, a job which involves doing low level computer programming would
force you to learn a lot of very practice CS, and you would be getting paid
for it instead of the other way around.

~~~
jophde
I have definitely been considering this approach. The issue with this is I
don't think I am currently that desirable for anything that isn't Java.

------
jiggy2011
It sounds like you're not quite sure what specifically you are interested in.
CS is a very broad field and you could probably study it for a lifetime
without scratching the surface.

Maybe better to choose a particular hard problem that is interesting and focus
on that. Something that would be neat to do but isn't as simple as just
calling a few library functions.

~~~
jophde
I feel like I need to get the foundation that most people get in a BS before i
can answer the question specifically. At this point I only know that I have a
strong desire to know how computers work on a deep level.

~~~
jiggy2011
There isn't really a standard foundation that everyone with a BS in CS has.
Curriculum are different and different colleges will emphasize different
things, not to mention that many courses are elective.

It also depends upon what you consider to be a deep level?

Are you interested in electronics and signal processing, mathematics or the
structure/design of programming languages? Are you interested in individual
computers or distributed systems? Are you just interested in computers or are
you interested in using computers to model other things, like economics,
physics or virtual worlds?

At a minimum you could brush up on algorithm / data structure understanding
and some of the math behind that. Problem is that as soon you gain
understanding of something it will simply expose you to deeper subjects that
you don't fully understand. You will never reach the bottom of all of these
rabbit holes.

~~~
jophde
I have no illusions that I could possibly learn it all. I just want to learn
enough so that I can go deeper on something more specific, such as virtual
worlds, and no how to proceed.

~~~
jiggy2011
Having a general CS education does not necessarily make you able to explore
arbitrary fields. CS programs are ultimately designed by course administrators
and professors and can be slow to change, so there's no guarantee that they
will prepare you sufficiently to explore whatever avenues you wish to explore
later.

Ultimately it depends on where you see your shortcomings that are preventing
you from doing what you want. Do you wish you had better credentials so that
you could get a job with better pay or more interesting work? Or do you find
yourself frustrated because you are not able to sufficiently grok a certain
subject area.

------
shail
I am suggesting an approach rather than a source. Sources, as someone already
said it, are far from rare.

I would say pick up a single system, say database (relational or document) or
routing, OS, DNS, Web server, A compiler, Filesystem, NFS, etc. and study the
hell out of it.

Once you know how to understand a particular system in depth, everything else
will start falling in place.

------
poppingtonic
There's a guy called Scott H. Young who, supposedly, did the entire (4 year)
MIT EECS curriculum in a year. So, if you'd like to do it the REALLY hard way,
try something like this: [http://www.scotthyoung.com/blog/mit-
challenge/](http://www.scotthyoung.com/blog/mit-challenge/)

------
cipher0
I would also suggest professor Matt Might's blog post "What every CS major
should know?" [http://matt.might.net/articles/what-cs-majors-should-
know/](http://matt.might.net/articles/what-cs-majors-should-know/) also, check
out his other posts, they're excellent.

------
kabouseng
"I am not really worried about getting a job. This is about gaining
knowledge."

Even so you want to be smart about it, and gain the knowledge in such a way
such that employers will recognize your expertise. It is for this reason that
I would rather recommend the MS. It will at least get you an interview next
time you want to change jobs.

------
ahmicro
Grow Beyond with Google: Guide for Technical Development
[https://docs.google.com/file/d/0B_Y4kz709TVwaVZfdnl3blI3UWs/...](https://docs.google.com/file/d/0B_Y4kz709TVwaVZfdnl3blI3UWs/edit?hl=en-
GB&forcehl=1)

------
apw
It might be worth your time to look at the course slides for "Gems of
Theoretical Computer Science":

[http://www.ccs.neu.edu/home/viola/classes/gems-08/](http://www.ccs.neu.edu/home/viola/classes/gems-08/)

------
justinhj
I'm doing the Algorithms course on Coursera. It's fantastic. Interesting and
practical, and taught by Princeton's Sedgewick. I have a BSc in AI and 20
years professional experience yet I'm still learning a lot from this course
each week.

------
adestefan
Don't forget about the math side, too. Discretet math and linear algebra
should be the minimum. Probability and statistics is also useful. Abstract
algebra has interesting applications in CS, too.

------
dsugarman
honestly? take a grad class in algorithms and sit in in as many relevant
seminars as you can. conversation is much stronger for theoretical knowledge
than it is for memorization. the idea is to work through the problems yourself
with strong mentor support, so there really isn't a shortcut here.

------
MaysonL
The previous suggestions are all good, but here's another tack, possibly
better for self-teaching.

Tackle a big project: write an extensible text editor, design and implement a
language and runtime, design and implement a new garbage collection system, or
the currently quite popular RSS reader and feed provider.

------
ulisesrmzroche
Same way you get good everything else, really. Train, learn, rest.

------
ExpiredLink
CS or SE? Not clear from you statement.

------
ninh
Universities tbh are more for meeting likeminded people nowadays: most of the
stuff taught at CS can be learnt on your own given you're disciplined enough.

Just to underline some of the points others have made, here is a short list of
things I found most valuable from my CS degree:

\- Algorithms, Datastructures & Computational/space complexity (ADC). <\--
This one is huge imo and will allow you to discern efficient code from
inefficient ones.

\- Discrete Mathematics. It's the lingua franca when talking about CS and you
will need it to understand ADC for example. It introduces set theory, graph
theory and so forth, which are used in ADC/AI etc... to describe and solve
problems.

\- Linear Algebra: if you ever want to work with 3d stuff, this one will be
essential. It'll also work out nicely for 2d work, and seeing as you mentioned
you've got a knack for UI work, you probably will appreciate this one. It'll
allow you to get an understanding of for example affine transformations etc...
You will need a computer graphics course too, but this is definitely a
prerequisite course to do those.

\- Probability and statistics. I really hated this course (it's also one of
the harder ones coincidentally), but once you "get it", you really do "get
it". Ever wondered how gesture recognition works? Or how spam filters work?
Well, the math required for this will be addressed here, together with the
following subject.

\- Artificial Intelligence. Extremely useful if you're interested in game dev,
or just want to learn to solve problems in a smart and efficient manner. It
combines ADC with discrete mathematics with probability & statistics.

\- Calculus. If not for the math, it'll definitely make you look at things in
a different way, which imo in turn, contributes to your way of looking at
problems. Partial derivation / integrals and how it can relate to 3d surfaces
for example. And let's not forget taylor series etc... It'll give you an idea
of how mathematical functions such as sin(1) etc... can be implemented etc...

\- Operating systems, Computer Architecture/organization. Essential for
understanding what happens under the hood. Allows you to reason about what the
best code path is for solving a problem. Should you use the GPU for example
instead of the CPU etc... and if so, why? etc... It also introduces models
such as finite state automatons etc... which are also applicable in language
processing for, say, compilers.

And that brings us to the last, but certainly not least subject, my all time
favorite: \- Compiler construction. Gives you an insight in how languages are
being processed, and how to design your own language and build a compiler for
it. It should also give you additional insights on how runtimes/virtual
machines work.

The software engineering courses were more about processes, philosophies and
patterns etc... and even though they're definitely useful, I think most
experienced software engineers have already "got this". Either via books,
company policy/culture or via experience.

Again, these are my experiences, YMMV :) Good luck!

------
rorrr2
Solve any 300 problems of the ACM problemset.

[http://uva.onlinejudge.org/index.php?option=com_onlinejudge&...](http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=1)

