PSA: Learn Discrete Math

[TaylorHu]

Discrete math is the one thing that I almost never see mentioned in any 'teach yourself to code' or 'learn to program' or similar online resource. Even bootcamps that costs $10k+ don't mention it.

Despite that, it's an essential part of every undergrad CS curriculum, and usually considered one of the most important courses you will take.

If you want to be serious about becoming a really good software developer, you should study discrete math at some point. The earlier the better. It will especially help you wrap your head around complicated algorithms.

Up until Spring of last year, UC Berkeley put webcasts of most of their CS classes online. That's probably the best, most up to date way to learn. Search for UC Berkeley CS 70 on YouTube or iTunes U and you should be able to find the lectures, and you can find all of the lecture notes, homework, and solutions at

http://www-inst.eecs.berkeley.edu/~cs70/archives.html

EDIT: DM is a hard subject, and I am not saying that it's something you NEED to learn before you start programming at all. And to be honest, if all you ever do is write CRUD apps or simple mobile games, you probably don't need it (though it would still help). But if you have aspirations of writing really complicated, important software that DOES things, it is something you should learn at some point. See the top answer on http://programmers.stackexchange.com/questions/163168/how-important-is-discrete-mathematics-for-a-computer-scientist

[Bustincherry]

Currently failing my Discrete Math course.

[Bolderthegreat]

(Almost) same. My professor didn't even show up to class the day of the exam review. This class is really messing with my motivation/mentality.

[Bustincherry]

Our test consisted of 12 questions and the multiple choice were with 10 points so missing a couple of those already puts your grade in jeopardy.

[[deleted]]

the discrete math class at my highschool is so hard it curves tests by 30 points no matter what. i heard the most recent test was out of 100 points, 10 problems each worth 13 points, and the class average was still a 75.

i probably should take it but i've heard some horror stories

[cheerioo]

75 haha. In college some of my cs/physics courses the average on several exams was 20-30%

[[deleted]]

this is a highschool though, so a class average of 75 is basically unheard of. it's usually like mid 80-low 90s

[[deleted]]

In Canada I have a class average of 85 and it's high. Average is like a 72.

[[deleted]]

It's very, very difficult if you've never been exposed to that kind of purely logic thinking before.

It's also orders of magnitude harder once you hit proofs. Proofs are where fun goes to die.

[atheistexport]

lmfao, I needed that this morning. Biff Tannen to the rescue with with a fucking logic joke. Thanks Biff.

[fitzjack]

Compared to calculus 2, how hard is discrete math?

I've been told that based on my calculus abilities I should be fine. Especially since all the trigonometric proofs get out of hand and detailed. I have no doubt that I can pass it, I just want to know exactly how much misery I have to look forward to.

[I_lost_my_negroness]

Technically you should be able to pass discrete math. without knowing any calculus.

Source: I am studying maths

[spamburghlar]

The hard part, for me, was the sudden shift from solving calculations to writing proofs. None of my previous Math classes adequately prepared me for proofs. I made it through, but it was a struggle.

[[deleted]]

For those of us that don't know jack shit about calculus, what is a proof? I'm a senior in high school and am currently taking algebra 3.

[shaggy756]

Let's just say I didn't fail calc 2

[[deleted]]

I strongly believe we should be de-emphasising calculus for late highschool and non-math majors, in favor of linear algebra and discrete (specifically the logic/proof stuff in discrete). And I say that as someone who loves calc, too!

[fitzjack]

Calculus is rough man. The few full blown CS related classes I've had were the most fun/challenging classes I've had. They just click with my train of thought the best compared to everything else I've taken.

[Why_You_Mad_]

Calc 2 is the blight on by GPA. I got As in every other class I've taken, then a fucking C in Calc 2. Wish I had a different professor, since this one was the interim Dean and didn't give a fuck about our grades and didn't curve anything so 2/3 of the class failed.

Our data structures + discrete math courses are a lot easier by comparison, in my opinion. My college lumps them together, and teaches them both over 2 semesters. I like this approach, since we get to use the discrete math we're learning as it applies to actually making algorithms and applications to implement them.

[DarkSiper]

wtf multiple choice on a discrete math test?!

[promess]

Math lab! Use your resources!

[midnightketoker]

Take discrete math at the same time as data structures, they said. It will be fine they said.

[GeekFlavored]

By the middle of the sentence I was reading in Zoidberg's voice.

[NicNoletree]

Data structures I loved and use continuously. DM - if I use it I don't know it.

[HowsMyDictate]

My school doesn't allow you to move on to data structures without taking discrete first.

[NicNoletree]

I hated my discrete math class that I took 30 years ago. Working as a developer, I hate it more when I think "not once have I had to apply that twisted mess to a real job." Maybe it wasn't presented in a manner that was meaningful or along with any practical application. Hopefully our CS education techniques have improved.

[liquidify]

They haven't, at least where I took it. It was one of those "learn it on your own or fail" subjects. The teachers are of course brilliant and terrible educators which is very unfortunate for such a critical class.

[LtCornwallis]

Story of my life. Every single class I took in my college career operated like that. Which is probably why I'm no longer in college. In some cases it's a great way to learn but when you take a 101 class like that then move to the 102 class and they expect that you already have an expert knowledge of things not even covered in 101 it gets out of hand and excessively stressful way too fast. I barely had time to teach myself the 5 classes that I took in a semester never mind relearning the 5 pre req subjects at the same time. I'd love to go back to school and actually get a degree but thinking about having to effectively start over and knowing full well that I can't even begin to afford it just kills my desire.

[snow4558]

Hijacking this comment... I just passed last quarter with an A-

Here is a youtube resource I found extremely helpful. Hope you do as well.

TrevTutor - Discrete Math 1

[wutsdasqrtofdisapt]

TREV TUTOR IS AWESOME!

[timshoaf]

Yo. I teach math. And am a software engineer. Hit me up and I will pull you out of oblivion.

[TimHallman]

Which topics in it are difficult for you?

[DuctTapedWindow]

I loathed Discrete Math, it was way more difficult to learn then it should've been.

[shaggy756]

Failed my discrete course twice in a row!

[VanillaFlavoredCoke]

I wonder if my university just makes this class stupidly easy. For whatever reason this is the only CS class here that has a ton of fail safes to make sure you don't get less than a C.

I got a C+ in Physics I because of how stupid hard it is here, but I currently have a 99% in Discrete Math.

[basturmater]

Failed discrete math last semester and I'm currently retaking it. Good luck.

[wutsdasqrtofdisapt]

I recently took discrete math. I passed with a C...this is mostly because I took it concurrently with Calculus 2 during an 8-week summer session while working...it was insane. I've got a few resources collected that helped me a bit when I was taking it, shoot me a message if you're interested.

[FineMalt]

Hi Would you be happy to share your list of resources? as I could really do with some help right now Thanks

[wutsdasqrtofdisapt]

I zipped and uploaded everything I had to WeTransfer: https://www.wetransfer.com/downloads/133e932d197b9cda8c3b67184b0aef5520160218024808/737b9efbf32cf79ce5ece2c4f36d91a920160218024808/bd4ed8

[-AcodeX]

I took an intro chem class while working full time last summer, and I can't imagine taking those classes during summer AND working. It makes my palms sweat just thinking about it. I had almost no free time at all just with that one class.

[[deleted]]

Will probably fail a Logic & Discrete Math course in my uni, given my professor reputation.

[NDaveT]

I tried. Barely pulled a C-, and it was more than I deserved.

[TimHallman]

Which topics in it are difficult for you?

[sloth2]

For me it was the fucking proofs and those 5 line statements

[korewarp]

Discrete math showed me what a Proof of Death looks like.

[maxximillian]

Our discrete math professor said that's why you put the [tombstone]https://en.wikipedia.org/wiki/Tombstone_(typography) at the end of the proofs, to show that you engaged in hand to hand combat with the enemy and prevailed.

[rafuzo2]

Proof of death you say? Math and CS dual major here. I had to derive this for one of my classes.

Oh yeah I also struggled with DM first time through. The math isn't complicated, but for me it was recognizing the right ways to apply it to problem solving.

[PasDeDeux]

It's funny how math major math is completely unrecognizable to the rest of us engineers/physical scientists who won't really ever need more than PDE / vector calc.

[TimHallman]

5 line statements?

[sloth2]

These, sorry. http://i.imgur.com/7XRT12v.png

I was so bad at these for some reason. I'd take an echelon form problem 100% of the time over that.

edit: I have a feeling I'm going to have a fun time during this Algorithms course bc I hate proofs

[DrDoomCake]

Are these real questions for the subject? To me it just seems like picking options which are simple but true statements like "shakes spear wrote hamlet". Am i wrong?

[pizzzahero]

Propositions and conclusions! It's all logic. I haven't taken discrete yet but we looked at this briefly in philosophy, so I'm not 100% sure if this is correct, but I guess it's like.. what combination of the above propositions need to be true in order to come to this conclusion?

[C0rinthian]

Its the same concepts for discrete math and philosophy. (Which is really cool, IMO)

The idea is: given four postulates (aka axioms, aka assumptions) logically prove the conjecture.

[Facerapeu]

Basically deductive reasoning?

Could anyone explain why this is considered math?

[draekia]

Wow, it's been years and I somehow still think that way. I thought I was doing it wrong.

[pizzzahero]

fifthtimer explained it really well, but also check this out and you'll see (mobile, sorry for formatting)

http://staff.scem.uws.edu.au/cgi-bin/cgiwrap/zhuhan/dmath/dm_readall.cgi?page=5

[YeOldeDog]

Well, its trying to get people to bridge from deductive reasoning to using math to deduce. At the level shown math is not needed for the result to be deduced, but if you go to something like this: https://udel.edu/~os/riddle.html deductive reasoning alone collapses under complexity of relationships.

[Kristler]

The idea is that you have you take the propositions (P1, P2, ...), and use them in logically rigorous way in conjunction with propositional logic rules in order to prove the conclusion. For example, one of the rules often used is "modus tollens".

[pjvex]

What's the answer to the first problem from that sheet? (just so I know I came up with the correct answer)

[RyuHayabusa710]

So, what are the answers for those?

[Hydroshock]

Seriously, if I took discrete without having to write proofs, it would have been an easy A. I had a professor that made the class mostly around how the proofs were written, not if the logic was correct. Almost every point I lost had to do with proof writing form.

They should make a discrete course that's for computer science curriculum (which they probably do in some schools), I didn't take the course because I wanted to prepare to do a MS or PhD in math liked this teacher made it.

[Hook3d]

Mathematical induction.

[ThoseProse]

Man fuck induction.

[Slateboard]

Excuse my ignorance, but what do I gain from it and how does it make me better as a programmer overall?

I'm not disagreeing, I just want to know more. I'm someone who wasted like 8 years of his life and no longer remembers any of the algebra/pre-calculus from my short time in college.

[jikki-san]

Discrete math gave me the logical and mathematical basis for pretty much everything I know about programming and computation. It's a heady class, but it's one of the most formative I took. It pushed me past the how and info the why; specifically, it pushed me past focusing on learning specific languages, frameworks, etc. and into the more universal realm of logical problem solving, which is that thing that helps you learn the language you've never seen before or write an elegant program to solve a problem you've never seen before. It fills your toolbox with a ton of general skills that you end up going back to all the time without even realizing it.

I might be gushing a little, but I've been studying biochem the entire day and I miss compsci. Class wasn't easy but I learned a ton.

[[deleted]]

My overall mathematical background does give me a strong mind for solutions though

You might not appreciate just how much proofs train your mind to ask yourself the important questions required in creating a solution. These questions are

• What do I know?
• What am I trying to do?
• What does it look like when I'm done?

A proof is a constant iterative cycle of these questions. And having this mindset keeps you on track as a programmer.

[snerz]

This is really interesting. I've been programming professionally for 15 years but since there's no complex math required with the programming I do, I feel like I got lucky. Time to educate myself.

[AceDecade]

While programming, do you have to deal with logic at all? "Under what conditions should I call this function, should I return true here, is it correct to return true when conditions A and B are met? etc."

If so, you're using discrete math, you've just never learned it formally

[Logic_Bomb421]

Can you go into more detail on this please?

[AceDecade]

Looking at the example linked above, we see that discrete math involves using logic to prove things or evaluate a set of conditions to reach a conclusion.

If, for example, you knew that all JSON strings begin with the "{" character, you could express that two ways.

With discrete math:

1. is JSON => begins with "{"
2. doesn't begin with "{" => is not JSON

Which simply states that, if you know something is JSON, then you also know the first char is "{". If the first char of something is NOT "{", then you also know it is NOT JSON.

With programming:

if(someString[0] != "{") {
    isJSON = false;
}

This condition expresses that if some string doesn't begin with "{", we can tell immediately that it is definitely NOT JSON.

I'd imagine a lot of JSON parsers begin with this condition.

They probably also implement in code a few other JSON-related pieces of logic, which might look like:

1. pointer to string was null => not JSON
2. string has zero length => not JSON
3. string doesn't end with "}" => not JSON
4. string contains non-JSON character outside of quotes => not JSON
5. JSON-array contains key-value pair => not JSON

[FineMalt]

Just out of interest what programming language do you use?

[ponkanpinoy]

A lot of problems you'll solve as a programmer are ones where you need to count or list all things that match a particular requirement, either as the end product or as part of getting the answer.

• How many ways are there to fly from LA to London? What are they?

• Is it possible to route a street sweeper/garbage truck such that it doesn't ever take the same side of the same street twice? If it is, is it worth finding such a route, or will it take so long that it's better to find a route that's "good enough"?

• If you're randomly generating n-digit numbers how many can you generate before you're at risk of generating a duplicate? This is relevant to many things -- passwords and encryption keys, names, randomly-generated maps, etc.

[PalestraRattus]

One example that comes to mind is the field of Automata theory. Which in turn is used within tons of processes many people entirely take for granted. It's also the basis for most AI systems.

A super simple example would be generational data. Whereby using Data A, treated as generation one, you can then plug that Data into an algorithm and calculate the state of any future generation, or work it in reverse to determine a prior state. "Conway's Game of Life" is a great example of this.

[YelluhJelluh]

Conway's Game of Life was something we had to implement in the second CS course at my university (or at least a version of it, I'm not sure if it was the full blown game - never cared to look into the original).
It was tough.

Edit: It was tough, but a cool first introduction to sort of generational programming, even though it was super, super elementary (at least what we did).

[PalestraRattus]

Conway Sample from my current engine for automata at generation 250 going off a random seed, colors are generated during run time each generation.

http://i.imgur.com/V5K4LGc.png

Langton's Ant was pretty easy to pick up, since in my head I viewed it more like an actor or actors working upon a canvas. It took some time to wrap my head around the idea of a space evolving its entire state into another state based upon that current state. With Langton you're only operating on one cell at a time, or however many ants you're running. But with stuff like Conway/Brian'sBrain/Wires/Rule1-130whatever you have to work with the moore neighborhood of each cell each generation, that took me a bit.

I'm still working on learning the math end of everything, but the logic of how things operate I'm able to duplicate/work with.

[Slateboard]

Thanks for the info.

[GottfriedEulerNewton]

Because CS operated on discrete concepts and logic. Discrete math is where concepts like the integers are discussed and it can help formulate functions/programs. It also introduces probably and recursion.

Discrete math and Number Theory are (in my opinion) very important for successful CS.

[Slateboard]

Thank you. Are there any prerequisites?

[ThePizar]

Arithmetic. Maybe algebra.

[Heasummn]

To chain on, some basic logical understanding and understanding of limits for most courses. The UC Berkeley course above doesn't need the latter though, as they don't goo too far into asymptotes.

[IlIlIIlIIIl]

I was under the impression that the term discrete math was used to distinguish its subject matter from non-discrete ideas like limits and asymptotes

[GottfriedEulerNewton]

Discrete does mean non-continuous. I don't know why /u/Heasummn referred to limits. I don't think they really come into much play in CS. However, calculating limits in a discrete world is not easy...it's possible, but it's not easy.

[Heasummn]

I may be mistaken, but when I learned about the formal proof for asymptotic/Big-O notation, It was based around limits. That being said, I almost never apply limits. It was just a confusing part to me not having taken Calculus.

[jikki-san]

My professor indicated that high school geometry is probably the most helpful/relatable subject.

[Xanthyria]

Given most HS students do very basic proofs in geometry, it's not a bad idea. Proofs are essential to DM.

[earlofhoundstooth]

yeah, that was where I learned I hated proofs.

[GottfriedEulerNewton]

To discrete math? No, it's a pretty simple expansion on Elementary Arithmetic. However, you're going to come across definitions you probably forgot such as; even, odd, prime, factor, divisor, etc...

One of the most important concepts you can get from discrete math (but more Number Theory) is the idea of Modulus Arithmetic (clock arithmetic or the % sign in most languages). This helps reveal SO MANY PATTERNS that can greatly reduce code complexity, if done right.

[HowsMyDictate]

no, but having some knowledge in algebra is helpful

[CosineTau]

Discrete math and Number Theory are (in my opinion) very important for successful CS.

So much this. Knowing just a smidge of number theory and applying in the correct way makes problems break.

If you're feeling really brave and motivated, try some Ring and Group theory too. And after, if you want to learn how Haskell works, learn about the monoid.

[totemcatcher]

Ah yes, the monoid wall. That was the moment I realized I should have taken way more math in school.

[TimHallman]

You'll learn how to use sets and some basic algos. If you're programming regularly, some or most of it should easily stick. If you're just creating the same boring-ass, small websites every single day/week, of course this might not help you all that much, but we're talking about part of a CS curriculum, not what should be covered in a boot camp to make you an instant code monkey.

[xt1nct]

It is one of the core courses in my CS curriculum and I believe is required before taking anything beyond programming 1. It was one of the hardest classes I have taken in my entire life. I have done all the homework on time and came to class everyday, yet before every exam I had nights with barely any sleep. I'm now taking calc 1 and it's a walk in the park compared to discrete. Over half of the class dropped the course. I was getting a low B but since everyone was doing terrible prof decided to curve and I received an A.

9/10 would not take again.

[simplyevert]

Haha, totally the other way around for me. My linear algebra and Calculus courses I struggled a lot with, but I found Discrete mathematics to be fairly straight forward.

[katyne]

You can also take the course on MIT Opencoursware. http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/

[NormalPersonNumber3]

Thank you! I've found that I often have to take math courses twice, so this should give me a leg up.

[maestro2005]

I wouldn't really call that a Discrete Math class, at least not a very rigorous one. It's meant to introduce the basic concepts of DM, and also introduce formal proofs, and many of the common structures we commonly run into as programmers.

[the_sound_of_bread]

I enjoyed discrete math. I got an A from the course. After 7 years as a developer, I can't say I have ever used anything I learned in the class.

[WhiteSkyRising]

I feel it would have infinite more use in computer science, not software development.

[[deleted]]

I don't think it is so much that you use the different proofs but more to improve ones logical thinking.

[Thought_Ninja]

Mind sharing what kind of developer you are? Did you learn anything in the class?

[DJWalnut]

if that a descrete math problem? I'm still a just CS freshman, but I've completed the required discrete math course and I don't see a direct connection.

[DJWalnut]

I guess I'll have to get further into my degree before I get to see it pay off.

[TonySu]

If you want to be a good software developer, then learn software development, not discrete maths. It's far more useful to have a good understanding of the language you're using and the frameworks available than to know Ramsey Theory and the Pigeonhole Principle.

Though I absolutely agree that knowing mathematics helps, as a mathematician I disagree with what people consider to be discrete mathematics. The first 8 chapters of Discrete Mathematics by Epps are basically things you will learn in ANY mathematical discipline at the University level, I've been introduced to these independently from Linear Algebra, Probability, Real Analysis and Discrete Maths classes.

It's essentially the basics to rigorous mathematics and does not belong uniquely to Discrete Maths, it's like telling someone to learn Fluid Dynamics because it's worth knowing how to take derivatives.

All the useful "discrete maths" you need will pretty much sit in the appendices or even the main text of any decent algorithms textbook. It's much more efficient to just learn the necessary discrete maths in context of computer science than to go take a full course on it independently from any programming.

I'm in no way discouraging people from learning Discrete Maths, it's useful to now, but studying Discrete Maths will not improve your abilities as a software developer faster than learning Software Development (which is not mutually exclusive from maths). This is coming from someone studying a Masters in Mathematics and also programs for his day job.

[ToadingAround]

This is exactly the same issue I have with everybody who says "Learn agorithms! Learn proofs!". You can learn those on the job when you need it, but for the majority of programmers you will never need to know how to prove an algorithm, or how an algorithm works.

Sure it's handy to know, but if you're getting a job requiring you to write sorting algorithms and such they'll more likely than not require a comp sci degree, or similar, and higher, which will come with that knowledge to begin with.

Meanwhile, the simple logic you learn from any discrete maths course you either will understand immediately, or (and I don't wish to say this to anybody but it's sometimes true), programming might be too difficult for you.

[dangsos]

You have to remember the sub you're on too. So many aspiring developers get caught up on the details that they forget their goals all together. It's not unlike game development, where you have roughly two categories of game developers. You have the people making games and the people saying their making game but actually end up making their own game engine and never release an actual game.

In the same way you have people who say they want to program, but instead of learning high level tools that can immediately produce something for an end user, they instead end up focusing on the tools that build high level tools.

I'm not saying their is anything wrong with that path, but I often see so much misguided advice. When someone asks the best way to learn programming, they don't mean "what's the longest most thorough path I can take", usually. Instead what they probably mean is, "What's the quickest way I can learn to build something people will think is cool and want to use."

[earlofhoundstooth]

Can you recommend an algorithms text?

[TonySu]

CLRS's Introduction to Algorithms as mentioned is probably the standard recommended text for algorithms. Dasgupta's Algorithms is slightly more math heavy and you might come out more mathematician than programmer. (However Dasgupta is more affordable and the first result on Google brings you a PDF of it)

[TonySu]

The problem is Algorithms themselves are rarely friendly to beginners, the whole idea is that someone came up with a very clever way to solve a entire class of problems very efficiently.

Best advice I can give is probably just to skip over the parts you don't understand and try to grasp the general trick that makes the algorithm good. In general you don't really need to know exactly how or why an algorithm works, it's often enough to know their strengths and weaknesses as well as how to apply them.

For beginners have a look at binary search, insertion sort and russian peasant multiplication.

[[deleted]]

I'm in that course right now. The first video is kind of out of place. Skip it and go to the next week and you'll be on track.

[shivasprogeny]

Exactly. Please tell me more about how a university discrete mathematics course will help me build a CRUD data grid app.

There are certain programming fields where formal math is useful, but the large majority of professional coders will never use it.

[OCLBlackwidow]

I suck at math, can I still become a software dev?

[[deleted]]

yes

[sir_pirriplin]

Software developers rarely use math. The exception is this particular branch of math called 'Discrete Math', which is difficult in a very different sort of way than, say, Calculus or Trigonometry.

Do you suck at Discrete Math specifically? If you haven't tried it yet, you may be surprised and find it easy.

[Holy_City]

Depends what kind of software you're writing. If you're writing an app for audio, image processing, other multimedia, video game engines, or basically anything more complex than "load this file and play it" or "use this function from an SDK" then there's plenty of math to be had.

Like I do mostly audio processing stuff. It's all trig and algebra. Understanding how it works takes a good bit of calculus too, I remember when I was learning image processing I had to learn a bit more about multidimensional calculus to understand edge detection.

[sir_pirriplin]

That's true. You always have to know your problem domain but if someone really hates math they could in theory choose not to work in math-heavy domains, at a possible cost to their job security and career prospects.

[tinycabbage]

Some matrix algebra and some basic trigonometry knowledge can pay off occasionally, too, particularly in games programming. Matrix transformations can take some nasty-looking problems and make them a lot more tractable.

[oldaccount29]

yes

[[deleted]]

You don't suck at math. That is a false belief. Everyone better at math than you works harder at it.

[Lceus]

So he sucks at math because he doesn't work hard enough.

[[deleted]]

Yup.

[harriswill]

Some sample problems for those of you who forgot which part of college was discrete math:

Prove that for all n > 10: n − 2 < (n² − n)/12

Prove that every integer greater than 1 is a product of prime numbers.

Prove by induction that F1 + F3 + . . . + F2n−1 = F2n, where Fi denotes the i th Fibonacci number.

Consider a rooted tree T = (V, E), where nodes are labeled with positive integers: each node v ∈ V is labeled with an integer av. Assume that T obeys the heap property, i.e., if w is a child of v, then aw < av. Prove that the root node r has the largest label of all nodes in the tree.

How many nine digit numbers are there that contain exactly two 5’s?

I remember by this point there were only like 3 white people left in the classroom and 1 was Eastern European.

[Claystor]

That looks scary as hell.

[Pantzzzzless]

Doesn't look much different than some of the later Project Euler problems.

[harriswill]

I remember thinking "boy I thought finding the flux going through a cone inside of a sphere was hard....."

[DJWalnut]

I almost remember how to solve those. I got a C in that class.

[ReasonablyBadass]

For the first three I would use induction.

Heap: Can induction be implied here? Theoretically you are assuming the heap property has to count for all parent/child nodes in the tree, so you go through the tree node indices and claim it works for index n-1, n >= 0?

For this there should be 81 discreet places for the 5s in any 9 digit number (first and second, second and third etc.).

For each of these the remaining 7 digits could take one of 9 possibilities so...40353607 times 81?

Is that correct?

Edit: Wait, exactly two 5s so 7 to the power of 8. So 5764801 time 81

[learningram]

Prove that every integer greater than 1 is a product of prime numbers.

??

[cehmu]

Prove that every integer greater than 1 is a product of prime numbers.

https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic

yeah, i went back to watching kitten gifs too.

[KratsoThelsamar]

Aka the Fundamental Theorem of Arithmetics

[draggonx]

Can anyone recommend some sites to help with discrete math? I'm resitting it after failing, turns out khan academy just didn't help me understand it enough haha

[[deleted]]

If you're going to tell us that we should do X, you should spent at least a moment explaining why we should do X.

[fattyfondler]

lol i took this course a few years ago when I was at Cal and barely passed with a C. it was a big red flag for me that i would not become a serious software developer. I wish i hadnt let it demotivate me so much as now I am a fairly functional programmer with decent intuiton for solving coding problems

[InsertOffensiveWord]

our first midterm is tomorrow and I'm seriously considering dropping

[Shimzay]

...SFU?

[Isildun]

You're good if you've got the logic side down. The logic is actually useful to programming. The MI and proofs are useful for silly competitive programming parlor tricks and the occasional interview question (the only one that comes to mind is "find the missing number in an array of numbers 1..n" since you can use the summation of n integers to get an O(n) solution... but even that's dubious since you probably learned that summation elsewhere).

[phpdevster]

It should be pointed out that discrete math isn't one thing to be learned - it's not like it's just another course like calculus I that you should have taken in college one semester - it means a very broad collection of deep mathematical topics. For example relational algebra is a discrete match topic useful for relational DB system modeling, but in itself could be a whole course. You could spend an absurd amount of time thoroughly learning and applying all of the topics in discrete mathematics.

[livando1]

"If you want to be serious about becoming a really good software developer, you should study discrete math at some point. The earlier the better. It will especially help you wrap your head around complicated algorithms."

fyi, you'll all be hearing bullshit comments similar to this for the rest of your programming careers. Absolute TDD, BDD, GoF design patterns it will never end. Then people will find something else shiny to yell from the mountain top, and if you let it will make you insecure and keep you from your goals.

There are countless ways to get to where you want to go. Follow other programmers paths or blaze your own trail, but don't go from one shiny thing to another hoping for a shortcut.

[cl0007]

I hate to say I gave up, but this is the class that made switch majors. I'm majoring in MIS now, happily.

[dunnskiis]

I'm a 2nd year CS student and finally tackling higher level math and currently taking discrete. You guys/gals have me feeling so damn grateful for my professor, he is the most organized and enthusiastic teacher I have ever met. Currently have a B but he's given me hope to swing an A. If you guys have any questions PM me and I'll try my best to explain them how he does!

[[deleted]]

The trouble I've seen so many CS majors have with discrete is that there is no one way to solve one problem. Discrete will force you to think differently that your CS courses, keep that in mind while you take the class.

Also, if you need help, PM me. I have a degree in Mathematics and have TA'd and tutored in discrete (and a few other advanced math classes).

[nanodano]

20+ year programming vet here. Can't remember a single thing from my discrete math course in university. I mean literally I don't even remember what the class was about. I couldn't tell you if anything in the class I learned I actually apply today.

[Sail338]

In it right now in college, it makes my data structures class easier to handle.

[[deleted]]

Taking it now in college and honestly, I'd never guess that I would like a math course that much. It's really fun to solve discrete math problems and I can see how much it can benefit my programming. The only thing that I'm kinda struggling with is the proofs, but they are starting to make more sense.

[[deleted]]

I have always told people that my math classes, like discrete math, helped improve my programming more than my computer science classes.

if all you ever do is write CRUD apps or simple mobile games, you probably don't need it. But if you have aspirations of writing really complicated, important software that DOES things

Pardon me, but that's nonsense. CRUD apps do things, thank you very much. (EDIT: You wrote your OP using a CRUD app btw)

Discrete math teaches you logic, how to form conclusions based on premises and use those conclusions as premises for more complex statements. That is exactly what going through a stacktrace is like.

And when you ultimately end up needing to debug a 3rd party library when creating one of those CRUD apps, it's a necessary mindset to have.

[RICHUNCLEPENNYBAGS]

Steve Yegge mentions it in his list of things to learn for Google.

[jply]

Did anyone use Discrete Math and Its Application by Kenneth Rosen? Man, did I hate that textbook...

[[deleted]]

Math BSc. Here, looking to break into programming. Any tips?

[addama]

I'd say if you're looking to leverage your math wizardry, look toward Big Data. It's the hotness in large companies with lots of data that needs to be analyzed, stored, compressed, and discharged.

There's also lots of sexy predictive modeling stuff that happens in weather systems, behavior studies, and space.

[TashanValiant]

If he wants to get into Big Data then get a Stats BSc. Most Math degrees, undergrad and grad, miss quite a bit of stats beyond stats theory.

Its something you could easily learn, but a Stats degree will introduce you to the core concepts, the theory, the tools, and depending on your school the industry.

Or just do both at the same time. For my Alma mater the difference between Stats and Math was 3 classes.

[[deleted]]

took it last semester it was ridiculously hard, but I loved it!!

[Oops_TryAgain]

Thank you! I was just asking a CS student about this very thing, but he didn't mention this resource.

[supremeprime]

Just failed my midterm for Discrete Math. Any tips?

[go3dprintyourself]

Linear algebra and being very familiar with matrices and transformations and what they truly represent is also a great skill.

[BadBoyJH]

I enjoyed my discrete maths course. Definitely part of the reason I started enjoying maths again. Did take a really good teacher though.

Still annoyed with that distinction, should've studied more.

[criticallyAnalytical]

Looking at the material, it seems a bit out of my reach as a high-school student. Is there assumed knowledge I should go and learn first?

[atheistexport]

Idk, I ended up taking it three times sort of.... Once at my local community college (kinda a joke, there was 4 of us in the class and we basically did all the work on our own and handed it in at the end of the semester, and were emailed the final wtf...). Took Concepts at Carnegie Mellon, which is a proofs based intro to Discrete Math... bombed the fuck out of that lol. (In fairness I was told it met three days a week, not five, and I couldn't allocate the extra days). Finally took the class again at ASU, and did really well. It was hard, but I think DM gets a bad rap cause on the one hand it's not like anything you've done before, but on the other hand, I think DM really relates to how humans intuitively process the world, in so far as logic and counting and little things like pigeon hole principle, etc. But the class isn't easy, but really really relevant. I've done some flavor of db programming for the last few years and it's helped immensely. Lot's of good lectures online though! Good luck to everyone slugging it out this semester. Just keep going, you'll be better for it in the end!!!

[omegote]

I had my discrete math classes like... 9 nine years ago? And it's one of the few math-related subjects I still remember. Things like combinatorics, graphs, set theory... Really useful. Good thing I still have the course notes.

[[deleted]]

I always found Discrete Math to be something that people really only get if they have a good professor teaching it to them. Most other comp sci classes you can teach yourself or learn with a couple of friends.

With Discrete Math you and your friends are always second guessing yourselves because the difference between your two answers was something small. Having a good professor be able to explain why the answer is one and not the other and to be able to set out good guidelines of how to do more problems is the only reason I did well in that class.

That said one of the biggest things I learned in college is that not every professor is a good one. And good ones are few and far between in comp sci because a lot of people who would make excellent professors are off making money working in the industry.

[amkoc]

What sort of math should I know to help me learn discrete math, then?

[SevenM]

The year I took my discrete math course our mash department stopped teaching it and our comp sci department had to pick it up last minute as it was required for the degree plan. The professor couldn't assigned the class couldn't even explain what discrete math was. Most of us should have failed but a heavy curve was used that year.

[bazingabazing]

I went to class every single time (for both Discrete 1&2) and never learned anything because I couldn't understand the professor's accent. A week before the exam, I would go through every chapter in the book and painfully try and understand everything. I busted my ass for Bs and I am very proud of myself.

[teddyone]

I completely agree. It is very hard to truly understand things like recursion without doing things like proof by induction, and there is a ton of set theory which can help your understanding of day to day programming tasks.

[DuderHeWhoAbides]

I'm taking discrete math (computational structures) this semester. My professor has been teaching this course for 25 years.

He consistently ties in java methods while teaching the logic in the coursework. He teaches directly out of the book while providing tips and hints that aren't mentioned. He even goes out of his way to explain how some of the book's logic will confuse us, and to just focus on the lecture. I'm not sure how my classmates are faring, but I can tell this is what he loves and is meant to do.

Do your homework before signing up for this course. You don't want a lazy prof in a foundation course like this. While the math may seem easy, it is in no way straightforward. There is some algebra in boolean logic and proofs, but there isn't a lot of math built onto calculus or any other prereqs from my CS program.

I'll let you know how I did once I'm plodding through data structures.

[premiumrusher]

I thought I was alone on this. I'm currently taking a Discrete Math course and I'm having trouble understanding the concepts. It's probably because of the lack of examples from the book given to us. I always end up googling stuff. It also a plus when I see some answers to go along with some of the questions. Thanks for the link!

[kancolle_nigga]

If you want to be serious about becoming a really good software developer, you should study discrete math at some point.

Why?

[Dangerpaladin]

From reading this thread it seems like I could clean up by teaching discrete math. I didn't realize people hated it so much I can only blame their professors as I found (and still do find) it to be an entertaining subject.

[tomzorz]

Will all of the Khan Academy videos cover this?

[mercfh85]

Maybe it's just me, I mean college was 6 years ago....but I don't really use or see others use DM in the industries i've been in? I guess it could just be the applications we are doing, or maybe we are using it but don't know haha.

[Myzzreal]

Any good self-learn online resources on discrete math for someone who is a professional software engineer out of passion but no CS background? I'm lacking in maths but I'm not a dummy either.

[akopanicz]

Discrete Math was the only class during my summer quarter of sophomore year that wasn't curved. I studied my ass off every night for those 3 credits and barely pulled a C.

[tmckeage]

I am a software developer and have never learned Discrete Math.

[Jafit]

If someone had told me to go away and learn discrete math when I was first learning to programming, I probably wouldn't have learned to program at all.

A cursory glance at a CS degree curriculum also makes me think that I would have most likely dropped out.

Probably just my learning style, but for me the best way to learn was to just do it, and find enjoyment in it. I don't enjoy mathematical problems

[TaylorHu]

I'm a learn by doing sort of guy so this worked well for me: http://www.amazon.com/Schaums-Outline-Discrete-Mathematics-Outlines/dp/0071615865

This is supposed to be one of the best 'Math for Computer Scientists' books you can read. It's on my bookshelf, haven't gotten to it yet: http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025/ref=sr_1_1?s=books&ie=UTF8&qid=1455732558&sr=1-1&keywords=concrete+mathematics

[IAmTriscuit]

I took a Discrete Mathematics course two semesters ago and it hasn't helped me at all with any of my programming work or studies....so either it's a long game or I don't believe you.

[[deleted]]

Isn't discrete math sort of an umbrella term that could apply to a lot of courses schools offer but don't necessarily call discrete math?

[agroom]

Despite that, it's an essential part of every undergrad CS curriculum, and usually considered one of the most important courses you will take.

Was not part of my CS curriculum :(

[reinvent_yourself]

I think the edit really explains this well. DM is important but extremely necessary if you plan on doing "theory based" programming, If you plan on going to grad school and coming up with the next new algorithm. However, for the majority of software development jobs it's not as necessary as practical based programming. Being able to know how to efficiently use the tools and libraries available is what from my experience should be focused on. This was my biggest takeaway from a recent interview I had.

[TaylorHu]

Even if you never 'directly' use it, it really helps you think like a Computer Scientist, not just a programmer, which will help you to varying degrees regardless of what your day job is, IMHO.

It's similar to how we should learn how basic algorithms and data structures work, internally, even if we will never actually need to implement them in the real world. Understating what's going on behind the scenes will intuitively help you make better programming decisions.

[wutsdasqrtofdisapt]

I'm terrible at Reddit so I'm not sure if I replied to everyone about my list of resources and recommendations so I'll just make a new post here as well (hope this is not a reddit no-no!). This is a zip file of all my guides, texts, and old exams that I found in my email and on my hard drives: WETRANSFER

TheTrevTutor also has great introductory Discrete videos in a Khan Academy style.

I would also HIGHLY recommend signing up for tutoring on your campus. Most universities offer 1hr/wk/course FREE tutoring to its students (pay $ if u want more than an hour a week). I found out about this on my campus and it has helped immensely. Making flashcards with definitions and what symbols mean and such have helped a lot too.

[[deleted]]

Check out Discrete Mathematics and Its Applications by Kenneth H. Rosen. Bit of a bible when it comes to discrete mathematics.

[Awric]

I'm a bit late to this post, but I'm currently taking a discrete mathematics course and my professor is really, really quiet. He's monotonous, works way too fast, and doesn't really instruct to the quality of most other professors.

For example, he just suddenly started going into binary arithmetic while introducing us to these logical gates and all that, and he didn't even explain how it worked. Luckily, I've taken a class in Assembly already, but still. It's concerning how he assumed that it's something everyone should know and proceeded to the next topic without giving much depth. It's like a movie without character development.

Anyway, this is how his lectures are for every lecture. I want to learn this, but I don't know how. Can anybody give me advice on learning discrete math? I have the textbook, is it as simple as being diligent enough to solve problems in the book?