Anyone that deals with real world data or simulation. CV obviously, but also route/path planning, anything 3d, any simulation like cfd or cad stress and mech sim, etc
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I’m doing CV on embedded (STM, not rasp pi’s). I learned a good bit of math in college and it isn’t enough.
Then again, parts of it are closer to philosophy.
I took descriptive geometry in engineering school (handily the most WTF class ever) and was not surprised to see some of it in CV. Our approach was to prototype algorithms using python numpy etc then pass on to the product team to code in C++ for the target hardware (Freescale 7x series IIRC).
There were some truly epic moments using quaternions (LMAO) and some other obscure math. Very entertaining if you can understand it at least our math whiz kid seemed good at it.
My forte is mostly data analysis related, discrete, probability, optimization etc. These are more common in CS.
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Regardless of what field you study, this. But I'm in ML and use vector calc, matrix algebra, probability, and statistics the most. but mostly oop and network protocols lol
Tbh I think most of everything is just what you end up doing, but I learned some groundwork sql stuff that ended up helping a lot. But like most have said, everything is kinda more of a base level stuff in which a huge step needs to be taken for the next level
That's not what they said. They said the most useful class was learning to type. You learn to read progressively from childhood forward. Learning to use the mechanism that is a keyboard isn't something we teach young children. I'm not sure what age kids learn to use a computer these days, but I'd fully expect they learn digital keyboards prior to learning physical ones. Reading and writing are prerequisites that you learn in service of acquiring your first language.
If you ever get into a federal agency, big tech or a dedicated security company, they pay top dollar for people like you who enjoy assembly and can reverse engineer programs with strong knowledge of systems CS courses like networking, DS&A and operating systems
Working a government job sounds awesome to be honest. I didn't do exceptionally well but I did enjoy it. I think most of the content came together for me around finals. I'll keep at it, maybe revisit the course content and expand with some small projects
i have actually used db in my internship this summer a lot. also dsa and oop. mostly just that tbh. and not even 'advanced' ds - super simple stuff, like lists and stacks.
absolutely. as a professional SWE i am constantly using addition and subtraction. if I am working on something particularly niche I may even find myself reaching for multiplication or division.
I do. I’ve worked in fairly mathy areas.
While it’s very possible to have a career writing software doing very little math, I would advise you to look at math classes not as useless stuff that you can forget immediately, but as important background knowledge that’s intended to make you a less stupid person. You probably don’t “use” the fact that George Washington was the first US president, but what would you think of someone who grew up and went to school in the US who didn’t know that?
Learning math is weight lifting for the logical/mathematical reasoning parts of the brain. It's not *what* you're learning, it's *that* you're learning and creating new pathways in the brain to be able to solve more complex problems. This further develops the ability to critically think, as these pathways will in turn create their own new connections in time.
Source: former teacher, masters in education, and I read it at some point in my schooling.
I’ve used a bit of linear algebra (don’t know if I’ve used row reduction specifically), some calculus, some simple probability and statistics, some other random things.
I've used some deep computer science topics in the rare instances they were needed, but no math pr physics except when trying to understand research on the latest and greatest tech on my own time. I've heard from other engineers who have though, so it's good to have the skills just in case. Also, if you ever need to pivot to electrical or computer engineering, it's nice to have the basics down already.
One of my professors said that you won't even recognize that a problem is a math problem if you don't learn the math first.
All problems have logic to them. Applying logic to those problems so we can model them, allows us to apply math concepts and either equate an exact (absolute) or relative (approximate) value.
Approximate values often lack any meaning or context without some numbering system applied to it. That’s what we’re doing with vector DBs when we map a search space and “vectorize” or index a value into that search space (same with training a data model).
Absolute values are ones where we have rigidly defined and applied mathematical concepts for scientific measurement. Things we can measure directly and convey the value of said measurement. (Now I just have to wait for the guy who writes software for high-precision measurement equipment to tell me how all our values are essentially relative based on this definition. And I wouldn’t necessarily disagree. Probably an argument of orders of magnitude that would apply to relevance of distinction between absolute and relative measurement values).
Without the knowledge of existing math concepts, it becomes much more difficult to model a real world scenario with applicable logic.
I like what your professor said, but wanted to expand on what I think he may have meant!
And to the other comment that said foundational or fundamental math concepts can become more philosophical than them necessarily becoming more computationally complex by design. Totally agree! It’s more how we define the concepts, and can apply logical models for those concepts to model real world situations we would want to calculate or compute the expected outcome or outputs, given a set of inputs or set of initial conditions, rather than math being an end all be all natural body of knowledge with absolutes that broadly apply as mathematical concepts. That’s simply not how numbering systems work, or are used.
For anyone reading this that thinks, “oh great, I suck at math. Maybe not for me”. My comment above is more to demystify how math applies to software engineering. It depends on which mathematical concepts apply to what you are modeling and how. Not all contributors will need to understand this relationship, and may work at a higher level of abstraction in their daily role.
Only "heavy" math I've used was for research and patents
All the other math I've encountered in the industry were simple calculations (cost estimates, mem / cpu requirements, big-O, latency, conversion rates, etc.)
I use vector calculus, trigonometry, statistics, partial differential equations just a couple weeks ago for an interpolation implementation! I work in aviation so there’s some spicy math involved
Logic & sets & graph theory stuff & basic algebraic manipulation from discrete math, yes, pretty frequently.
Recursive functions & base cases & the implications of log/quadratic/exponential/etc for algorithmic complexity, yes, pretty frequently (actually finding a recurrence relationship? Never so far).
Generally understanding things like logs/exponents for orders of magnitude, and how hexadecimal & octal counting systems work to make sense of memory addresses & file permissions, yes somewhat frequently.
Bit-manipulation logical operations & binary, infrequently but yes.
Haven’t needed calculus or heavy stats & probabilities, but in a previous job other people made extensive use of those concepts.
I never took linear algebra or beyond Calc II, but I’m also not doing anything w/“AI”/ML so I haven’t missed it. Yet.
I've been a software engineer for over 30 years and have very rarely used any of the math I learned, which was about 4 courses after calculus. It does come up occasionally for example I was doing some computer graphics work and the geometry came in handy, and certain kinds of GPU or parallel processing work can use some linear algebra, but that's rare.
The same is mostly true of the CS content you'll learn too. Like I thought my compilers and assembler classes were really neat but I never used any of that.
What is really happening is that by getting this degree you are showing that you can learn and assimilate huge amounts of math and CS knowledge, and apply it well enough to get passing grades in your classes, which frankly most of the population can't or won't do. If you get a CS degree you immediately stand out from other people who are applying for jobs who couldn't get into the CS program or make their way through it. Unfortunately, very little of what you learn is going to be applied knowledge, and you'll learn more CS in your first 1-2 years on the job than you will in 4-8 years at university.
Actually no. If you are working a programming job and DON'T know those things, you're in trouble. The higher level classes about design, architecture, security, data stores, etc. are more applicable. But a lot of what happens on today's jobs isn't taught in school as far as I know. Cloud architecture, multi-region deployments, CI/CD pipelines, devops, resiliency, all of the 100's of tools and open source things that you'll need. That is all learned on the job.
And honestly I think that CS curriculums should teach teamwork, which is essentially to any programming job. Communication, working as a team, doing your part, supporting your team mates, etc. is as important or more important than your tech skills.
There are a few classes that have group projects but most are individual ones.
Web development class is probably one of the more directly applicable since I did a full stack group project there.
Swe class too.
I do have experience with aws and gcp too.
If you want to be a run of the mill developer, no it doesn't matter at all. Literally your entire degree will probably not matter.
If you want to get hired quickly and work on things that other engineers in other fields would call you an engineer (and not call you a developer), then yes it's very important.
People don't call NASA software engineers "developer" for instance.
And web developers are rather uncommonly called "web engineer" (I'm a web dev myself).
Choice is yours. Neither choice is wrong.
Hi! I'm an incoming CS major who really likes math proof-based classes but am not good at them. Can I ask specifically what the analyses is and what the proof was/was about?
I’m an ML engineer and it was a statistical proof! Can’t talk too much about it but it’s technically 0.0001% of my job, with the rest being fixing bugs etc. So it was a nice little break.
How much you use any single thing you're taught varies greatly by position.
The more important thing is how it teaches you to think and problem solve.
Also, it lays the foundation for later things you learn. Calculus, statistics, linear algebra, etc. all parts the foundation for algorithmic analysis, vector calculations, data structures, computer graphics, computer vision, logical proofs, impact analysis, optimization theory, etc.
You're probably literally never going to be doing hand calculations. But having a good vertical understanding of all the layers of your craft makes you significantly better and more well rounded engineer.
If you don't enjoy it or aren't good at it, that's fine. I struggled auth Cs and Ds in math for 17 years. But I pushed through it and built up my knowledge all the way up through some post graduate level courses. And it's been incredibly useful to my career, even if I don't strictly USE most of it day to day. It shapes how you think, what you can learn, and your understanding of what you make.
If you do ML/DL, you will have to use plenty of Linear Algebra and Calculus. For most other kinds of software engineering, no, you don't need to use the math learned in CS.
If you do ML it’s good to know math to know the theory behind why things work
Also maybe against what most people will say here. Computer science is extremely valuable as a compliment to another field of study. Computer science majors who work in areas that have financial fields or mechanical engineering for example will highly benefit from supplementary math.
You will specialize in something and end up using it. For some that's databases, for others it's stats, optimization, number theory (cryptography) and so on
Math is huge in CS. Big O notation, AI/ML, Curve fits, computer vision, Encryption, anomaly detection, frequency analysis, data analysis, the list is huge and seemingly endless.
While much of the math used in CS is conceptual, you need to be comfortable with the ideas to be able to access them naturally and use them easily. I have a math BS and 40 years of exp, 15+ at Google. Every position that I have had benefited from my math degree. They didn't always require the degree. But there were things that I saw, knew, understood, recognized because of that math degree.
I would also say that Math/CS is the single most common combination of degrees for the SWEs that I have seen over time.
Actually, I surveyed a bunch of Senior Software Engineers in the last quarter of 2023 regarding this. 62% of the ~1200 engineers (rounded down to the nearest hundreth) that took this survey confirmed yes, math is important in their day to day tasks.
And you're probably thinking "Senior, well that just means they're old". Think again. Of that 62%, only about 1/3 indicated that they are above the age 40. Of the remaining 2/3 the average Senior SWE age was 33. Now mind you, companies have different criteria for what they regard as "Senior", and what we found is that for those engineers that work for larger companies (where the total number of employees vs a smaller company is usually greater by a factor of 4x or more) the delta of time from starting their career to senior generally is longer than a Senior who works for a smaller company (remember smaller = .25 size of larger company employee count)...
But I digress - you can learn more about this study at `www.math.com`
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Honestly, the math the first year is hardest. That's not because it doesn't get harder, it's because first year CS students typically just fucking suck at math. You'll get used to it.
Most of the math you wont actually use for a majority of jobs out there. The real value of learning math for most people is that it develops your critical thinking and reasoning skills.
Probability theory and discrete math are kind of important (based on your field). When it comes to calculus it's only particularly important if your field is really math heavy.
I've worked in a few different fields, including embedded and signal processing.
The 'most complex' math that I've needed to understand are fourier transforms, matrix operations, trigonometry, and regression analysis, for processing data of different kinds (images, RF, time-series data).
I haven't had to use Diff EQ, but i could see that being needed for software certain fields (flow controls, simulators, etc).
For my experience, calculus has had the benefit of helping me understand how stuff works on a deeper level, which means it helps me ask the right questions. But i've never had to code something that integrates an equation or anything.
Regardless of whether you like/use it or not, all CS degrees I know require at least Calc 1-3 + matrix algebra. That said, matrix algebra may come very handy if you wanna to predictive modeling.
I mostly use statistics. Nothing else is relevant for my space.
Edit: directly relevant, maybe. I'm sure if I thought hard enough to relate concepts to math, more topics would stand out.
I've used a lot of linear algebra to help solve mesh networking problems. It can also be very useful to be able to know how to write proofs, if you need to prove that something you're modeling will hold in all scenarios and not dead-end your project a year out.
Depends a lot in what are you gonna work on.
I would suggest you learn as much as you can and retain as much as you can. Prioritizing whatever you like the most.
I’ve used statistics, linear algebra and graph theory quite a bit. No calc though
Math is needed in solving problems, but not those Calculas or extreme mathematics that we do in College/univarsity. But making your mental math model stronger is very crucial to solve and understand problems. Hope you get it and Don't stress about it. You will see those we solve in real life development is very simple unless you are working with Ai Stuffs:)
The more math you learn, the bigger and better mental toolbox you'll have to solve problems. Same goes for your humanities courses. Don't be the CS student who only focuses on your programming courses. My students who are intellectually well-rounded do way better on the job market than my students who only focus on programming courses.
It largely depends on the job. Most people won't use much math, I didn't expect to either. And yet, I use math on most days in my job, at least at a conceptual level because of the product I work on. It's mostly linear algebra though.
Arithmetic, linear algebra, and calculus are common in computer graphics, AI, and simulating physical and models. I'll warn here that graphics shows up more than just "making video games", but unless you're interested in those fields I wouldn't sweat it.
Graph theory and combinatorics comes in \_extremely\_ handy nearly daily if you're dealing with distributed systems, highly concurrent systems, algorithm analysis, or domains that work with networks (anything with a "share" button). Not many CS jobs need you to care about that, but a lot of the best CS jobs do.
Beyond that eh, it's really helpful to be good at math but not necessary. I joke with my product team that if it involves any number that isn't 0, 1, or 2, I'll pull it from a config value and let them sort it out.
As always, it depends…
Writing CRUDs, being a full stack developer? Likely not.
Working as a Data Scientist, with Robotics, Computer Vision, or game dev? Hell yeah!
Not directly, but i do attribute struggling through hard classes (not just math, but definitely math included) to have made a big difference in my ability now.
You’ll probably end up working for some staff engineer with a background in finance or literature or psychology whose never heard of formal models anyway
It depends 50% on the job and 50% on your preferences. I love math, and I've used math in some cases when someone else in my role would have solved the problem some other way.
Be technically good at as much as possible. If math isn't your strength, make sure you're rock solid on other stuff. If it is, it can get you some innovative solutions sometimes, as with any other technical skill.
I have used my maths degree for work on two occasions.
On the first, we sold a predictive dialler, and the regulation in the uk changed. I wondered how hard it could be to design an algorithm that would work in the uk. It was very hard, but the maths used was probability theory that we covered in the first year.
The second was when I needed a language classification algorithm to support an ai translator again, probability theory from the first year plus a few additional ideas.
I’m a manager, so not normally expected to work these things out myself.
Unless you end up just doing really vanilla full stack stuff (basically just connecting apis together) you will end up using math quite a bit. After a certain point, any cutting edge work involves heavy use of math. Be it when figuring the best performance profile or ML or graphics or etc. Anything where you have to thing about the actual algorithms.
I've used the math exactly once.
Bosses demanded an inventory tracking system based on key flags like A for red, B for blue, second char A for 4', B for 6', and so on with each character being from 0-9-A-Z. They demanded that the database be PRE-FILLED with every possible combination up to 30 chars per item, so that operators could select the Red 6' etc. etc. from a list. It was an absurd design.
I used math to show them that the number of entries in their list would be more than the number of molecules in the known universe. They backed off and let me create something actually useful. So far the useful design has been used for hundreds of millions in profit, so there's that.
You'll want it eventually. Just knowing it exists is important. When you need it, you'll know what to look up.
For example I learned in physics how to calculate the pressure a fog over water exerts onto the water. I thought I'd never have to know this. Then I was tasked for automating a mass air flow system and I absolutely needed to calculate partial water vapor pressure to know what air it was flowing. I didn't immediately remember that calculation but I knew what to look up. The system works perfectly by the way.
Computer science and all other sciences are related.
Almost 10 years into my career and just had my first app that needed to use multiplication and division which was a formula provided to me by the data analysis team I just had to translate into Java.
As the people here have stated, it depends on the type of work you do. Could be every day, could be twice in your career.
For me, it's nice to know I won't break production because of a simple conversion from hex to decimal - which I've seen another developer do recently. But, my math knowledge helped me debug it when I was called in at 10 last Thursday.
Interesting question. The answer is complicated.
Math is extremly important in the tech industry. Cryptography, AI, computer vision, are just a few fields, that use lots of advanced math and are dependent on a small numbers of advanced researchers.
However, the majority of people who study those subjects will never get the chance to work as leading researchers or developers in the field. Most people just learn it and never use it again. People say it helps you learn how to think, but that answer seems like mostly cope. I do think it's true that sometimes knowing the math underneath can be helpful and sometime in unexpected ways.
Tons of people use libraries that were required advanced math knowledge to create. But the number of people actually using that math is relatively small.
When I went to graduate school for CS + Applied math, the faculty warned me upon entry, that most people who intend to study advanced math and use it to build great things in industry settings, most are disappointed and frustrated. Many of those types can get really nice salaries upon graduation, but the jobs typically involve extremely basic stuff that you don't need the fancy graduate education for.
The more math you know, the more places you will find it useful. Even if you're stuck writing CRUD or boilerplate, having excellent math skills gives something to flex on your peers with.
Discrete math is probably the most applicable. It teaches you how to approach resolving more complex logical problems much faster so in the future, instead of being stumped on some logical proof in your head for days you can do it in the span of an hour or less. I don't find myself doing the same formal math proofs I used to do, but learning how to even begin tackling the problem was a game changer for me.
It depends way too heavily on the type of work you'll be doing. If you're going into ML then you'll need a lot of math. Even a subfield that doesn't seem math heavy like NLP still requires you to understand the basic ML stuff and be able to read equations.
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You’d be surprised what you might use for different projects. I think knowing what methods /topics there are is a big part of it. I was using linear algebra topics on a project recently. Learned those years ago and had no idea how to calculate them anymore. But just knowing *of* them was all i needed to go relearn enough to use them. So absorb what you can and get the good grades.
I've used linear algebra, quaternions and vector math directly in my game and defense industry jobs. Also a lot of basic high school geometry and trigonometry. I've never had to do a Laplace transform or anything else from Diff Eq though (which was 35 years ago for me).
I'm a developer who did my degree Math rather than CS. Do I use all the Math I learned? No (though the linear algebra has certainly come in handy).
What I do think though is that studying Math taught me how to think in a way that has been super beneficial for my career in Software.
The math you learn sharpens your abstract problem solving ability. It's using the same part of the brain. It may not apply directly 1:1, but it definitely is useful.
I noticed during undergrad I could take weeks off programming, while only studying calculus. When I'd finally come back to an editor I'd find writing code was much easier and fluid, despite the extended break.
In a typical day-to-day task? No. At least not high level math.
But I’ve been trying to upskill and develop deep expertise in data platform. The math definitely comes into play when trying to deeply understand different database architectures and optimizations.
You don’t need any of it or even a degree unless you specialize in a niche that needs it (games, deep learning, quant, etc).
Think about what you want to do and know that stack inside and out.
Trigonometry? Yes, if you work on robots.
Calculus? Not really.
Discrete math? No.
However, discrete math teaches you an essential way of thinking and working through problems in coding. While you probably will never use the math itself, you will definitely use the method of finding a solution and proving it with logical steps. I think you’ll see what I mean at the end of your degree when it all comes together.
The math portion is a “solved” aspect of CS. We merely learn it to be aware of all the quantitive reasoning that goes into computing. With abstraction in code we only need to interface with the code at the API level and not the nitty gritty implementation level unless we want to reinvent the wheel
formal education past 5th grade is useless. but you're expected to play along with it so numbers can go up and its an easy metric for management. the dumbest people i know are math people. they know this so they gate keep it hard and the normal people play along because they don't really care or keeping the illusion of math wizards going makes them look better. i suggest cheating if you're struggling with math in anyway.
Computer vision requires some heavy duty math...
Anyone that deals with real world data or simulation. CV obviously, but also route/path planning, anything 3d, any simulation like cfd or cad stress and mech sim, etc
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I’m doing CV on embedded (STM, not rasp pi’s). I learned a good bit of math in college and it isn’t enough. Then again, parts of it are closer to philosophy.
I took descriptive geometry in engineering school (handily the most WTF class ever) and was not surprised to see some of it in CV. Our approach was to prototype algorithms using python numpy etc then pass on to the product team to code in C++ for the target hardware (Freescale 7x series IIRC). There were some truly epic moments using quaternions (LMAO) and some other obscure math. Very entertaining if you can understand it at least our math whiz kid seemed good at it. My forte is mostly data analysis related, discrete, probability, optimization etc. These are more common in CS.
Quartenions are super useful in graphics programming and simulations as well Once you wrap your head around them they’re an amazing tool
Philosophy in computer vision?
Somewhat. I also have taken comp neuro courses, so some of what I use is based on that. And we’re like 60% CV, 40% ML.
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Don’t worry, you won’t use most of the cs knowledge you are expected to learn either.
I just got through assembly and it was awesome. What classes/topics did you find most useful in your work?
Depends on what you do but realistically network protocols and OOP make up 95% of the dev experience imo.
Regardless of what field you study, this. But I'm in ML and use vector calc, matrix algebra, probability, and statistics the most. but mostly oop and network protocols lol
Games/3D UX: vector, matrix, trig, geometry.
Databases are a big part of it, as well.
I like this. I added a fullstack-type course as an elective for the fall while taking OOP in parallel so I'll start cutting my teeth on this. Thanks!
Tbh I think most of everything is just what you end up doing, but I learned some groundwork sql stuff that ended up helping a lot. But like most have said, everything is kinda more of a base level stuff in which a huge step needs to be taken for the next level
SQL indeed helps, in present or in future it definitely benefits
I have a BS CS and an MS DS. The single most helpful class that I've taken in my educational career was Typing in 8th grade.
The single most helpful thing for maintaining VMs is flaming people in League of Legends.
or getting QQ out before they quit after the 8 pool (sc2)
The best advice I ever got from my late Mother was: “If you don’t want to have to work a McJob, you’d better learn how to type.”
That's not what they said. They said the most useful class was learning to type. You learn to read progressively from childhood forward. Learning to use the mechanism that is a keyboard isn't something we teach young children. I'm not sure what age kids learn to use a computer these days, but I'd fully expect they learn digital keyboards prior to learning physical ones. Reading and writing are prerequisites that you learn in service of acquiring your first language.
Welp, I did poorly in 8th grade so I'll get back to basics
Pretty bold of you to put learning to type as more helpful over learning to read
If you ever get into a federal agency, big tech or a dedicated security company, they pay top dollar for people like you who enjoy assembly and can reverse engineer programs with strong knowledge of systems CS courses like networking, DS&A and operating systems
Working a government job sounds awesome to be honest. I didn't do exceptionally well but I did enjoy it. I think most of the content came together for me around finals. I'll keep at it, maybe revisit the course content and expand with some small projects
i have actually used db in my internship this summer a lot. also dsa and oop. mostly just that tbh. and not even 'advanced' ds - super simple stuff, like lists and stacks.
This depends on what job you take. I work in embedded and almost everything I learned in my college classes is relevant to my job.
How do you like working in the embedded space? What does the work look like at a high level?
absolutely. as a professional SWE i am constantly using addition and subtraction. if I am working on something particularly niche I may even find myself reaching for multiplication or division.
I'm a data masseuse. I massage data from one form to another. Sometimes there's a happy ending. Mostly frustration and depression.
I saw this and went, i dont use anything beyond basic algebra for 99% of the math i do, and that goes for both work and private
I do. I’ve worked in fairly mathy areas. While it’s very possible to have a career writing software doing very little math, I would advise you to look at math classes not as useless stuff that you can forget immediately, but as important background knowledge that’s intended to make you a less stupid person. You probably don’t “use” the fact that George Washington was the first US president, but what would you think of someone who grew up and went to school in the US who didn’t know that?
Learning math is weight lifting for the logical/mathematical reasoning parts of the brain. It's not *what* you're learning, it's *that* you're learning and creating new pathways in the brain to be able to solve more complex problems. This further develops the ability to critically think, as these pathways will in turn create their own new connections in time. Source: former teacher, masters in education, and I read it at some point in my schooling.
What math do you use most and what specific area of it? For example, linear algebra and matrix row reduction?
I’ve used a bit of linear algebra (don’t know if I’ve used row reduction specifically), some calculus, some simple probability and statistics, some other random things.
You will find discrete math, set theory, and graph theory much more applicable than calculus.
Do you have recommendations of beginner material on discrete math? YouTube channels or books or something
Not really. Neither is that useful
I've used some deep computer science topics in the rare instances they were needed, but no math pr physics except when trying to understand research on the latest and greatest tech on my own time. I've heard from other engineers who have though, so it's good to have the skills just in case. Also, if you ever need to pivot to electrical or computer engineering, it's nice to have the basics down already. One of my professors said that you won't even recognize that a problem is a math problem if you don't learn the math first.
All problems have logic to them. Applying logic to those problems so we can model them, allows us to apply math concepts and either equate an exact (absolute) or relative (approximate) value. Approximate values often lack any meaning or context without some numbering system applied to it. That’s what we’re doing with vector DBs when we map a search space and “vectorize” or index a value into that search space (same with training a data model). Absolute values are ones where we have rigidly defined and applied mathematical concepts for scientific measurement. Things we can measure directly and convey the value of said measurement. (Now I just have to wait for the guy who writes software for high-precision measurement equipment to tell me how all our values are essentially relative based on this definition. And I wouldn’t necessarily disagree. Probably an argument of orders of magnitude that would apply to relevance of distinction between absolute and relative measurement values). Without the knowledge of existing math concepts, it becomes much more difficult to model a real world scenario with applicable logic. I like what your professor said, but wanted to expand on what I think he may have meant! And to the other comment that said foundational or fundamental math concepts can become more philosophical than them necessarily becoming more computationally complex by design. Totally agree! It’s more how we define the concepts, and can apply logical models for those concepts to model real world situations we would want to calculate or compute the expected outcome or outputs, given a set of inputs or set of initial conditions, rather than math being an end all be all natural body of knowledge with absolutes that broadly apply as mathematical concepts. That’s simply not how numbering systems work, or are used. For anyone reading this that thinks, “oh great, I suck at math. Maybe not for me”. My comment above is more to demystify how math applies to software engineering. It depends on which mathematical concepts apply to what you are modeling and how. Not all contributors will need to understand this relationship, and may work at a higher level of abstraction in their daily role.
Only "heavy" math I've used was for research and patents All the other math I've encountered in the industry were simple calculations (cost estimates, mem / cpu requirements, big-O, latency, conversion rates, etc.)
I use vector calculus, trigonometry, statistics, partial differential equations just a couple weeks ago for an interpolation implementation! I work in aviation so there’s some spicy math involved
Company ?
Logic & sets & graph theory stuff & basic algebraic manipulation from discrete math, yes, pretty frequently. Recursive functions & base cases & the implications of log/quadratic/exponential/etc for algorithmic complexity, yes, pretty frequently (actually finding a recurrence relationship? Never so far). Generally understanding things like logs/exponents for orders of magnitude, and how hexadecimal & octal counting systems work to make sense of memory addresses & file permissions, yes somewhat frequently. Bit-manipulation logical operations & binary, infrequently but yes. Haven’t needed calculus or heavy stats & probabilities, but in a previous job other people made extensive use of those concepts. I never took linear algebra or beyond Calc II, but I’m also not doing anything w/“AI”/ML so I haven’t missed it. Yet.
10 years after learning it, I finally used matrix math to debug a CSS transform.
I've been a software engineer for over 30 years and have very rarely used any of the math I learned, which was about 4 courses after calculus. It does come up occasionally for example I was doing some computer graphics work and the geometry came in handy, and certain kinds of GPU or parallel processing work can use some linear algebra, but that's rare. The same is mostly true of the CS content you'll learn too. Like I thought my compilers and assembler classes were really neat but I never used any of that. What is really happening is that by getting this degree you are showing that you can learn and assimilate huge amounts of math and CS knowledge, and apply it well enough to get passing grades in your classes, which frankly most of the population can't or won't do. If you get a CS degree you immediately stand out from other people who are applying for jobs who couldn't get into the CS program or make their way through it. Unfortunately, very little of what you learn is going to be applied knowledge, and you'll learn more CS in your first 1-2 years on the job than you will in 4-8 years at university.
Would you say Intro programming, Data Structures and Algorithms, OOP, and Databases are the most useful classes to real world application?
Actually no. If you are working a programming job and DON'T know those things, you're in trouble. The higher level classes about design, architecture, security, data stores, etc. are more applicable. But a lot of what happens on today's jobs isn't taught in school as far as I know. Cloud architecture, multi-region deployments, CI/CD pipelines, devops, resiliency, all of the 100's of tools and open source things that you'll need. That is all learned on the job. And honestly I think that CS curriculums should teach teamwork, which is essentially to any programming job. Communication, working as a team, doing your part, supporting your team mates, etc. is as important or more important than your tech skills.
There are a few classes that have group projects but most are individual ones. Web development class is probably one of the more directly applicable since I did a full stack group project there. Swe class too. I do have experience with aws and gcp too.
If you want to be a run of the mill developer, no it doesn't matter at all. Literally your entire degree will probably not matter. If you want to get hired quickly and work on things that other engineers in other fields would call you an engineer (and not call you a developer), then yes it's very important. People don't call NASA software engineers "developer" for instance. And web developers are rather uncommonly called "web engineer" (I'm a web dev myself). Choice is yours. Neither choice is wrong.
Most of the time no, but one time my manager was grading my proof for one of the analyses we want to do!
Hi! I'm an incoming CS major who really likes math proof-based classes but am not good at them. Can I ask specifically what the analyses is and what the proof was/was about?
I’m an ML engineer and it was a statistical proof! Can’t talk too much about it but it’s technically 0.0001% of my job, with the rest being fixing bugs etc. So it was a nice little break.
Thanks!
How much you use any single thing you're taught varies greatly by position. The more important thing is how it teaches you to think and problem solve. Also, it lays the foundation for later things you learn. Calculus, statistics, linear algebra, etc. all parts the foundation for algorithmic analysis, vector calculations, data structures, computer graphics, computer vision, logical proofs, impact analysis, optimization theory, etc. You're probably literally never going to be doing hand calculations. But having a good vertical understanding of all the layers of your craft makes you significantly better and more well rounded engineer. If you don't enjoy it or aren't good at it, that's fine. I struggled auth Cs and Ds in math for 17 years. But I pushed through it and built up my knowledge all the way up through some post graduate level courses. And it's been incredibly useful to my career, even if I don't strictly USE most of it day to day. It shapes how you think, what you can learn, and your understanding of what you make.
If you do ML/DL, you will have to use plenty of Linear Algebra and Calculus. For most other kinds of software engineering, no, you don't need to use the math learned in CS.
Yep. I’ve used differential calculus, trig, geometry, finite math, and so so so much statistics.
If you do ML it’s good to know math to know the theory behind why things work Also maybe against what most people will say here. Computer science is extremely valuable as a compliment to another field of study. Computer science majors who work in areas that have financial fields or mechanical engineering for example will highly benefit from supplementary math.
I am a recent graduate. And my only advice is pay attention to your data structures and algorithms class.
You will specialize in something and end up using it. For some that's databases, for others it's stats, optimization, number theory (cryptography) and so on
Math is huge in CS. Big O notation, AI/ML, Curve fits, computer vision, Encryption, anomaly detection, frequency analysis, data analysis, the list is huge and seemingly endless. While much of the math used in CS is conceptual, you need to be comfortable with the ideas to be able to access them naturally and use them easily. I have a math BS and 40 years of exp, 15+ at Google. Every position that I have had benefited from my math degree. They didn't always require the degree. But there were things that I saw, knew, understood, recognized because of that math degree. I would also say that Math/CS is the single most common combination of degrees for the SWEs that I have seen over time.
Actually, I surveyed a bunch of Senior Software Engineers in the last quarter of 2023 regarding this. 62% of the ~1200 engineers (rounded down to the nearest hundreth) that took this survey confirmed yes, math is important in their day to day tasks. And you're probably thinking "Senior, well that just means they're old". Think again. Of that 62%, only about 1/3 indicated that they are above the age 40. Of the remaining 2/3 the average Senior SWE age was 33. Now mind you, companies have different criteria for what they regard as "Senior", and what we found is that for those engineers that work for larger companies (where the total number of employees vs a smaller company is usually greater by a factor of 4x or more) the delta of time from starting their career to senior generally is longer than a Senior who works for a smaller company (remember smaller = .25 size of larger company employee count)... But I digress - you can learn more about this study at `www.math.com`
I work in AI, and even I don’t
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I do very much for my work, one class in particular
No but its good for your brain
yes and quite a bit more.
I do, but I work in data science now
Honestly, the math the first year is hardest. That's not because it doesn't get harder, it's because first year CS students typically just fucking suck at math. You'll get used to it.
Most of the math you wont actually use for a majority of jobs out there. The real value of learning math for most people is that it develops your critical thinking and reasoning skills.
I’ve had a couple of internships but no FTE role, so take it with a grain of salt- but I’ve never taken a math class for my degree and been fine lol
Probability theory and discrete math are kind of important (based on your field). When it comes to calculus it's only particularly important if your field is really math heavy.
I've worked in a few different fields, including embedded and signal processing. The 'most complex' math that I've needed to understand are fourier transforms, matrix operations, trigonometry, and regression analysis, for processing data of different kinds (images, RF, time-series data). I haven't had to use Diff EQ, but i could see that being needed for software certain fields (flow controls, simulators, etc). For my experience, calculus has had the benefit of helping me understand how stuff works on a deeper level, which means it helps me ask the right questions. But i've never had to code something that integrates an equation or anything.
Yes, discrete math and statistics.
Regardless of whether you like/use it or not, all CS degrees I know require at least Calc 1-3 + matrix algebra. That said, matrix algebra may come very handy if you wanna to predictive modeling.
I mostly use statistics. Nothing else is relevant for my space. Edit: directly relevant, maybe. I'm sure if I thought hard enough to relate concepts to math, more topics would stand out.
Like 75% of your standard undergrad algorithms course is just discrete math.
Im transitioning from web dev to ai and have had to refresh a lot of my statistics.
I've used a lot of linear algebra to help solve mesh networking problems. It can also be very useful to be able to know how to write proofs, if you need to prove that something you're modeling will hold in all scenarios and not dead-end your project a year out.
Depends a lot in what are you gonna work on. I would suggest you learn as much as you can and retain as much as you can. Prioritizing whatever you like the most. I’ve used statistics, linear algebra and graph theory quite a bit. No calc though
Never used advanced calc. But knowing trigonometry benefited me a lot in making animations for my apps (also for game development it's used heavily)
Math is needed in solving problems, but not those Calculas or extreme mathematics that we do in College/univarsity. But making your mental math model stronger is very crucial to solve and understand problems. Hope you get it and Don't stress about it. You will see those we solve in real life development is very simple unless you are working with Ai Stuffs:)
The more math you learn, the bigger and better mental toolbox you'll have to solve problems. Same goes for your humanities courses. Don't be the CS student who only focuses on your programming courses. My students who are intellectually well-rounded do way better on the job market than my students who only focus on programming courses.
It largely depends on the job. Most people won't use much math, I didn't expect to either. And yet, I use math on most days in my job, at least at a conceptual level because of the product I work on. It's mostly linear algebra though.
Arithmetic, linear algebra, and calculus are common in computer graphics, AI, and simulating physical and models. I'll warn here that graphics shows up more than just "making video games", but unless you're interested in those fields I wouldn't sweat it. Graph theory and combinatorics comes in \_extremely\_ handy nearly daily if you're dealing with distributed systems, highly concurrent systems, algorithm analysis, or domains that work with networks (anything with a "share" button). Not many CS jobs need you to care about that, but a lot of the best CS jobs do. Beyond that eh, it's really helpful to be good at math but not necessary. I joke with my product team that if it involves any number that isn't 0, 1, or 2, I'll pull it from a config value and let them sort it out.
Learning the math will not hurt your career prospects, and if the day ever comes where you do need it you’ll be incredibly thankful
Nope
Discrete Math. It's all about logic, and I use that knowledge 100% every day while coding.
I work in ML, and my background in math is pretty helpful for understanding certain concepts from research in order to apply it.
As always, it depends… Writing CRUDs, being a full stack developer? Likely not. Working as a Data Scientist, with Robotics, Computer Vision, or game dev? Hell yeah!
Not directly, but i do attribute struggling through hard classes (not just math, but definitely math included) to have made a big difference in my ability now.
Nope
I don't. Didn't even finish the degree. But some of my colleagues absolutely are! And it's somewhat amazing.
The only math I do at my job is calculating my net pay after taxes
I do lol. I use regression in my ml model to predict the timeline of our automation. It's helpful lol.
You’ll probably end up working for some staff engineer with a background in finance or literature or psychology whose never heard of formal models anyway
You can forget the tests but you’ll never lose the mental scars.
I’ve been in the industry 3 years. Never seen any of the linear algebra, calculus since those classes in college.
Yup. The intense stuff, not as often though.
It depends 50% on the job and 50% on your preferences. I love math, and I've used math in some cases when someone else in my role would have solved the problem some other way. Be technically good at as much as possible. If math isn't your strength, make sure you're rock solid on other stuff. If it is, it can get you some innovative solutions sometimes, as with any other technical skill.
I have used my maths degree for work on two occasions. On the first, we sold a predictive dialler, and the regulation in the uk changed. I wondered how hard it could be to design an algorithm that would work in the uk. It was very hard, but the maths used was probability theory that we covered in the first year. The second was when I needed a language classification algorithm to support an ai translator again, probability theory from the first year plus a few additional ideas. I’m a manager, so not normally expected to work these things out myself.
Unless you end up just doing really vanilla full stack stuff (basically just connecting apis together) you will end up using math quite a bit. After a certain point, any cutting edge work involves heavy use of math. Be it when figuring the best performance profile or ML or graphics or etc. Anything where you have to thing about the actual algorithms.
I've used the math exactly once. Bosses demanded an inventory tracking system based on key flags like A for red, B for blue, second char A for 4', B for 6', and so on with each character being from 0-9-A-Z. They demanded that the database be PRE-FILLED with every possible combination up to 30 chars per item, so that operators could select the Red 6' etc. etc. from a list. It was an absurd design. I used math to show them that the number of entries in their list would be more than the number of molecules in the known universe. They backed off and let me create something actually useful. So far the useful design has been used for hundreds of millions in profit, so there's that.
I use i++ occasionally
You'll want it eventually. Just knowing it exists is important. When you need it, you'll know what to look up. For example I learned in physics how to calculate the pressure a fog over water exerts onto the water. I thought I'd never have to know this. Then I was tasked for automating a mass air flow system and I absolutely needed to calculate partial water vapor pressure to know what air it was flowing. I didn't immediately remember that calculation but I knew what to look up. The system works perfectly by the way. Computer science and all other sciences are related.
Almost 10 years into my career and just had my first app that needed to use multiplication and division which was a formula provided to me by the data analysis team I just had to translate into Java.
As the people here have stated, it depends on the type of work you do. Could be every day, could be twice in your career. For me, it's nice to know I won't break production because of a simple conversion from hex to decimal - which I've seen another developer do recently. But, my math knowledge helped me debug it when I was called in at 10 last Thursday.
Interesting question. The answer is complicated. Math is extremly important in the tech industry. Cryptography, AI, computer vision, are just a few fields, that use lots of advanced math and are dependent on a small numbers of advanced researchers. However, the majority of people who study those subjects will never get the chance to work as leading researchers or developers in the field. Most people just learn it and never use it again. People say it helps you learn how to think, but that answer seems like mostly cope. I do think it's true that sometimes knowing the math underneath can be helpful and sometime in unexpected ways. Tons of people use libraries that were required advanced math knowledge to create. But the number of people actually using that math is relatively small. When I went to graduate school for CS + Applied math, the faculty warned me upon entry, that most people who intend to study advanced math and use it to build great things in industry settings, most are disappointed and frustrated. Many of those types can get really nice salaries upon graduation, but the jobs typically involve extremely basic stuff that you don't need the fancy graduate education for.
The more math you know, the more places you will find it useful. Even if you're stuck writing CRUD or boilerplate, having excellent math skills gives something to flex on your peers with.
Discrete math is probably the most applicable. It teaches you how to approach resolving more complex logical problems much faster so in the future, instead of being stumped on some logical proof in your head for days you can do it in the span of an hour or less. I don't find myself doing the same formal math proofs I used to do, but learning how to even begin tackling the problem was a game changer for me.
The statistics courses are very relevant
It depends way too heavily on the type of work you'll be doing. If you're going into ML then you'll need a lot of math. Even a subfield that doesn't seem math heavy like NLP still requires you to understand the basic ML stuff and be able to read equations.
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You’d be surprised what you might use for different projects. I think knowing what methods /topics there are is a big part of it. I was using linear algebra topics on a project recently. Learned those years ago and had no idea how to calculate them anymore. But just knowing *of* them was all i needed to go relearn enough to use them. So absorb what you can and get the good grades.
If you want to do anything that isn't webdev yeah
Compiler dev here. Compiler optimizations require understanding of some decent amount of math.
I've used linear algebra, quaternions and vector math directly in my game and defense industry jobs. Also a lot of basic high school geometry and trigonometry. I've never had to do a Laplace transform or anything else from Diff Eq though (which was 35 years ago for me).
I haven't been in a maths class since 1989, personally. I do regret not taking it further though.
I'm a developer who did my degree Math rather than CS. Do I use all the Math I learned? No (though the linear algebra has certainly come in handy). What I do think though is that studying Math taught me how to think in a way that has been super beneficial for my career in Software.
Depends on what you end up doing but I've used the crap out of linear algebra and statistics.
The math you learn sharpens your abstract problem solving ability. It's using the same part of the brain. It may not apply directly 1:1, but it definitely is useful. I noticed during undergrad I could take weeks off programming, while only studying calculus. When I'd finally come back to an editor I'd find writing code was much easier and fluid, despite the extended break.
Math is beautiful. Learn it, you ignoramus :P
In a typical day-to-day task? No. At least not high level math. But I’ve been trying to upskill and develop deep expertise in data platform. The math definitely comes into play when trying to deeply understand different database architectures and optimizations.
You don’t need any of it or even a degree unless you specialize in a niche that needs it (games, deep learning, quant, etc). Think about what you want to do and know that stack inside and out.
Nope
Nope. The most complicated math related thing I’ve done in 8 years was the one time I used the sqrt function for scaling an image down.
Depends on your career path, but it is mostly "no" and if you are asking this question then the answer for you will probably be "no" too.
No
Trigonometry? Yes, if you work on robots. Calculus? Not really. Discrete math? No. However, discrete math teaches you an essential way of thinking and working through problems in coding. While you probably will never use the math itself, you will definitely use the method of finding a solution and proving it with logical steps. I think you’ll see what I mean at the end of your degree when it all comes together.
The math portion is a “solved” aspect of CS. We merely learn it to be aware of all the quantitive reasoning that goes into computing. With abstraction in code we only need to interface with the code at the API level and not the nitty gritty implementation level unless we want to reinvent the wheel
formal education past 5th grade is useless. but you're expected to play along with it so numbers can go up and its an easy metric for management. the dumbest people i know are math people. they know this so they gate keep it hard and the normal people play along because they don't really care or keeping the illusion of math wizards going makes them look better. i suggest cheating if you're struggling with math in anyway.