I have a BS in pure math. One of the hottest and best fields for mathematicians is data science, which combines statistics, technology and domain knowledge (e.g. finance, health care etc.) There is often a complaint that most data scientists are great with technology and domain knowledge but lack the depth of statistics, logic and reasoning. We need more math majors to enter this field. Great video as always!
@@drewkavi6327 Applied/statistics/math/computer science/pure math/econometrics students can all aim towards data science assuming they have the requisite mathematical and computational skill. Regardless of what base you have it will be neccessary to complete your education after school. However, the mathematical background is indispensable. I believe applied math or statistics are more applicable than pure but it won't be a deal breaker depending on the focus of the data science job you look for, some may require more coding skill than others for example. The channel dimitri Bianco had an interview recently with one of the data scientists for the pizza brand domino's he talks a bit about the educational requirements and what's important.
I study math in the Czech republic, and it's interesting to see how different is it in a lot of aspects. For example, we don't differentiate between pure math and applied math until after one completes their bachelor's degree. We don't have calculus and instead do rigorous real analysis from the first year. There's also a few obligatory courses not even mentioned here, like measure theory.
I am deciding between studying maths at MFFUK and CS at FI MUNI. I love mathematics (proofs included) but I have a fear of not getting an appropriate job after finishing my maths degree. Could you please tell me where you or your classmates ended up? Thanks!
@@cubeik-jakubvlcek698 Well, what you can do when you finish is largely dependent on what specific mathematical field you want to specialize in. I study probability, and with that, there's plenty of opportunity in statistics, data science, machine learning, finance etc. There's also a decent amount of good opportunities if you study something like numerical analysis or cyphers. But there are also plenty of very theoretical fields that you won't use much outside of academic work. You usually don't have to make these decisions early on in your studies, at MFF pretty much everyone has the same subjects for the first two years. By then you usually know what kind of master's degree you want and choose your courses accordingly. And yes, if you go study at MFF, getting master's is probably necessary, the standard bachelor's course in general mathematics is not very useful on its own, it mostly provides the basics you need for master's.
the comment regarding real analysis has me thinking. I'm DEFINITELY going to use Spivak's Calculus book alongside my courses and teach myself proofs along with whatever we're learning. I hear your situation from a lot of countries and I think we should be doing the same in the US
@@highviewbarbellthe point is not every students are ready for proof writing, or even not all students taking calculus courses have the need to write proofs, say physicians. So i think if you really wanna do so, just go to honour courses
My degree is in pure math. My career is for the past 10 years has been as a Lithium-ion battery engineer in different roles ( electrochemical, process, and continious improvement).
Hello Sir, your degree is in pure maths but your career has leaned towards math applications fields, how? I also want to do PhD in pure math(may be Algebra) and I am interested to know more about your career, it will be very helpful for me
Well, I don't do any proofs or abstract algebra on the job, though I miss that stuff. The vast majority of my on the job math is arithmetic, algebra, some calculus for figuring out battery capacity and impedance. I do some EIS which uses some more advanced mathematics. The vast majority of the math I use is in stats. I use a lot of chemistry and physics as well.
@@ezramantini8078 I started my bachelor's in Mechanical Engineering but had a greater interest in the theory behind the engineering principles. Hence, I considered the double major with applied mathematics. However, I found the best of both worlds through physics actually. It had the rigor and theoretical explanation I longed for, plus I got to study the interesting concepts presented in mathematical physics. I graduated with a B.S. in Applied Physics! Professionally, I am a business analyst for a large tech company (on track to becoming a data scientist, which is what I spent the bulk of my senior year studying).
@@ezramantini8078 I finished my degree in late 2018 with the double major in CS and Applied Math. Now im a software dev for a Bank. Looking back I enjoyed the math courses more than CS, but there was more job opportunities for me as a programmer. But in my case, I got an offer as an intern because I was still going to school for that extra semester, which later led to a full time offer.
I have a B.S. in Math and I can't get a full-time job because I have no experience in anything outside of tutoring... (Edit): 2 years later I have a full-time job as a contractor with the Navy working as a Financial Analyst. So I guess long story short, persistence works eventually.
STEM fields tend to have an attractive opening salary but not much potential for growth. Become a doctor if all you care about is a high starting salary, they're the highest paid stem field. Other than that, business is where the real money is, but the highest risk.
DevoutSkeptic Learn some finance and try that. Honestly, if you were only planning on going for a bachelor's, you shouldn't've chosen math for a major.
Interesting. For my math major, what you described as real analysis was combined into my first year calc 1 class. We started with basic field results e.g. prove x*0=0 for any x in a field F, then shifted our focus onto the field of real numbers for the most part. We learned about how real numbers are ordered, basic theorems involving that, then sequences, limits, series, functions, continuity, limits, and finally derivatives a couple months into class. Then we continued on to cover the various things you'd learn in any single variable calc course. Everything we covered was proved in class, or in our homework. Also we don't have calc 3, it only goes to 2, which is multivariable calc, where we learn basic topological things about Rⁿ, greens/divergence/stokes theorem (not in full generality, only in 3 dimensions). We also have real analysis 1 and 2, but those require these calc 1 and 2 courses, and is basically a baby version of topology, where you work with topological spaces with a metric, a "distance function" that lets you measure the distance between any two points, whereas in full on topology you don't get this luxury. these spaces are called metric spaces, and you generalize results from calc 1 and 2 to these more general objects, where "addition" or "multiplication" may not even make sense. Awesome vids tho
To quote Wikipedia: _"It has been estimated that Leonard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century."_
Meanwhile you got people like me making the conscious decision to become a math teacher. But really I don’t care because it’s what I’ve always wanted. I’d rather be happy teaching than be an engineer and not feel like I’m living my best life.
I watched both your videos about the math major and must say that in my pure math undergraduate program, I learned all the courses in both the applied section and pure section of the videos. These are all very basic courses which any person doing a math degree should know. Now I'm a grad student in pure math
I wish I was advised well when I did my B.Sc degree in Applied Maths. Right now I am a teacher, a good maths teacher. Thanks for creating this informative video.
Do you have any regrets in doing Bsc in Applied Mathematics? What other jobs can you do with Applied Mathematics? I dont like teaching What university did you study in?
About there being a real number between any two distinct rational numbers: Lets assume 00, we know there exists an k such that 1/k1. But now there exists a whole number m between n*a and n*b, and thus m/n is a rational number that lies between a and b
In Germany, as a teacher, i have to take for my bachelor + Master: Calc 1-3 Linear Algebra I +II Differential Equations Proofs Abstract Algebra I Real Analysis I + II Complex Analysis Topology Vector Analysis Euclidian Geometry Spheric Geometry Hyperbolic Geometry And some other stuff Where for example do things like Measure theory, sentence of peano, galoistheory (maybe abstract Algebra?), etc fit in here?
very late response but those would probably end up being electives that the math major can choose to take, and wouldn't necessarily be mandatory colleges usually let u pick your upper level electives so someone could take a bunch of topology courses for instance but they wouldn't be forced to
Huh? Even aspiring teachers for Gymnasium @ Oberstufe don't do any complex stufflike Topology. They only take Algebra 1+2 and Calculus 1+2 like a pure math major would. After that it's completely seperate.
have been watching your vids for a while. just subscribed now because I'm excited about future videos very similar to these on different majors and classes.
Ken MacDonald Well, engineering has the other sciences + math, plus it’s more practical, and you can really only learn theory online. Unless math is too difficult to self learn, then it looks like majoring in engineering is the better idea.
I'm right now an applied mathematics (bachelors) sophamore and love math. I'm thinking about possibly getting a job as a professor and doing my own personal research on the side. But i don't know how hard that could be. I'm worried that it will be hard to find a job and the last thing i want is to work for the department of defense or some other job with military goals. I'm also incredibly interested in electronics. I'm thinking it's reasonable to get a masters degree in electrical engineering after my applied math bachelors and then get a masters in applied math too. We'll see. But I'm excited about learning!
Please inform me about your journey... I am a High school student, but I have similar goals and mindset as you and I really want to know what my future will hold if I chose research instead of some corporate job
@@Random-pk1cs I'm just finishing up my sophomore year in applied math and am applying for several REUs for this upcoming summer. The REUs are student research opportunities that you get paid for. They are between 8-10 week things that pay around $3000 to $6000. They are competitive so I've applied to 6 of them. Besides that, I'm thoroughly enjoying my classes. Some of my classes are fairly difficult, like applied probability. But with a little extra study time outside of class, I'm really gaining a deep understanding of the material. My college offers a 4 in 1 plan where you get a masters 1 year after your bachelor's. I plan to use that to get a master's in electrical engineering, and then get my math master's later.
@@Random-pk1cs@Random-pk1cs dang it I replied and my reply disappeared. Lemme try again. So I'm just finishing my sophomore year as an applied math major. I'm applying for REUs for this summer. REUs are student research opportunities that run for 6-10 weeks and pay around $3000 to $6000 with food stipends and paid housing. They're competitive so I've applied to 6 REUs. You'll want to nurture good relationships with your professors so they'll write you wonderful recommendation letters, as those letters are needed for REU applications. Research seems to be the way to go if you want to get a master's and PhD. That aside, I'm taking some very interesting classes. I have some difficult ones, for example applied probability. But with some extra study time outside of class, I'm able to gain a deeper understanding of the material. If you have any other questions, don't hesitate to ask. Hopefully that helps. I'm excited you're thinking about going to study mathematics. Even if you choose to specialize in something besides math, having a good mathematical foundation will put you ahead of the game. Math majors are the jack of all trades as they say.
@@Random-pk1cs dang it I replied and my reply disappeared. Sorry if my previous attemptsload and you get 3 nearly identical replies. Lemme try again. So I'm just finishing my sophomore year as an applied math major. I'm applying for REUs for this summer. REUs are student research opportunities that run for 6-10 weeks and pay around $3000 to $6000 with food stipends and paid housing. They're competitive so I've applied to 6 REUs. You'll want to nurture good relationships with your professors so they'll write you wonderful recommendation letters, as those letters are needed for REU applications. Research seems to be the way to go if you want to get a master's and PhD. That aside, I'm taking some very interesting classes. I have some difficult ones, for example applied probability. But with some extra study time outside of class, I'm able to gain a deeper understanding of the material. If you have any other questions, don't hesitate to ask. Hopefully that helps. I'm excited you're thinking about going to study mathematics. Even if you choose to specialize in something besides math, having a good mathematical foundation will put you ahead of the game. Math majors are the jack of all trades as they say.
0:34-0:40 Say, S is a set and ● is a binary operation on S, then closure is automatically guaranteed, as ● is a mapping from SxS to S, it's impossible to not have closure. Checking closure is not necessary, unless I misunderstood you: you were actually checking whether (Z,+) is a subgroup of a bigger group that contains Z.
I feel like I'm the only math major not taking abstract algebra or any analysis class. Those requirements were satisfied by axiomatic non-euclidean geometry and probability theory
Hey guys I don’t want to scare any of you but actually it was one of the worst decisions of my life. My mental health suffered so much that I was admitted into hospital. Now my living situation, social life, and mental health were the biggest and most influential part of my breakdown but my advise is if you’re not up to the challenge, mentally stable, and have a comfortable living environment and source of income don’t do it. It’s not worth it.
Start learning right away, if you want to get a feel for what a maths major is about, start by learning how to write proofs with introductory discrete maths. If you're still into it, go ahead and learn some real analysis, linear algebra, group theory, and general topology. Exactly what order you go in isn't too important but I'd recommend some analysis before topology and some linear algebra before group theory & abstract algebra. And have fun, if you go into that degree you'll leave on the brink of something truly amazing!
Blox117 kinda, you just have to change your mindset on how you see math honestly. I’m not some expert but I’m open minded about math, and if I don’t know something I go back learn I, and continue. Takes a lot of studying and reviewing. I’d say you don’t have to be some expert or even extremely good, but definitely know the foundation
The Flagged Dragon solid advice with learning analysis before topology. I did the reverse back in college and the hill was steep in topology. As a result, real and complex analysis were a breeze lol
I just took my linear algebra final. We covered groups, sets, vector space, subspace, basis, span, and proving all of it... and even more. All I can say is wtf. Did the prof cover more than he should've?
I am about to enrol in an economic major and my uni lets me do a concurrent diploma in math alongside it. I was interested in pure math as I thought this would look good to potential employers, but from your video it seems applied maths might be more useful and practical - is this what you think?
My university's math major (intended for those who don't want to do graduate studies) doesn't require students to do real analysis or abstract algebra... You don't even need to know something as basic as an epsilon-delta proof.
@@Michael_Livingstone Can your computer write proofs? No, it can't -- that would require a human-level AI. Math is not about computation. In formal math classes, being asked to actually compute something hardly ever happens. Instead of finding the answer to specific problems, you're more likely to prove that there exists an answer to those types of problems, in general. These aren't the kinds of problems your computer can solve for you. If they could, nobody would bother studying them -- it'd be trivial. In fact, we wouldn't even have computers if a couple mathematicians didn't generalize the concept of computation so that it could be implemented by simple mechanical systems.
It is very fun as long as you study and have fun with it :) Just got my bachelors in it and working on my masters! I can recommend a pure maths concentration whole heartedly. Currently in research right now and it is amazing
I Have a question... is it okay for me to pursue a Master's degree in Mathematics with a bachelor's degree in mechanical engineering? Do I need to study by myself all of the Mathematics topics that I missed out on the Bachelors degree in Mathematics?
in pure math? that might be very difficult Applied math would be more plausible. I'm sure it is possible but you should look at the math GRE to see what basic concepts are required to have the knowledge and ability to pursue and advanced math degree.
Corey Holcomb not pure maths... just maths; msc in maths... I'm sure there are some universities that offer that.. is it also difficult to be enrolled?
yup MEng mechanical eng. The classes that I am taking is engineering mathematics 1 and 2, differential eq and calculus for engineers, advanced dynamics of mathematics, advanced mathematical techniques in ordinary differential equation for engineer, and mathematical techniques in partial differential equation for engineer..... there are the modules that I am taking and plan to take.
I would suggest taking courses in the actual math department because engineering math usually lacks the rigor needed to pursue serious math. Take a linear algebra course in the math department that covers vector spaces and linear transformations in depth, take some sort of advanced calculus or partial differential equations in the math department, and I would try to take a computational math/numerical methods course in the math department. You should at least go for a math minor and specialize your elective courses for math in the area that you would be interested in studying in grad school. Also usually grad schools have programs in math and/or applied math not just "maths". As an engineer if you develop a good understanding of PDEs and numerical methods for PDEs I think going to grad school in applied math might be possible. For pure math you would definitely need to take the math GRE and do well to show that you understand the pure math concepts not covered in your engineering degree; so you would need to understand all of calculus very well, real analysis, general (modern) algebra and linear algebra, and topology.
Hi, thank you for your awesome videos ! If I basically lean more towards theoretical physics, but really like math and want to focus on it, which math will be advised? applied or pure ? generally I find the pure math very appealing from your videos, but would it help further if I'll want to continue into theoretical physics ?
You’re honestly gonna do all kinds of math, pure and applied (especially if you go to grad school). I say lean more towards applied while still taking classes in various pure math courses when you can.
I'm interested in majoring in applied math, and getting a phd so I can become a research professor. What are some of the things a research professor doing applied math might do? Also, you're math major videos have been incredibly helpful, thank you!
Trust me it gets better, their is a learning curve and sooner or later you will get ahead of that curve if you work hard. Once you are their it is not very hard.
It sucks. Pure math is so useless. I only do it because it has so many overlapping courses with my physics degree. But I do harder and more interesting math in physics than i do in math
I've heard algebraic geometry is a really hot subject area for oure mathematicians. Do undergraduate math majors take an intro class to this? And what's the significance of it? And why are physicists into it?
Would it be a little easier for me to find a job after graduating if I'm in a major that's a hybrid between Maths and CS like Data science and Scientific Computation ?
Having knowledge in CS related subjects will definitely help with getting a job. And if you are talking about just a bachelor's then yes those things will definitely be a plus. Plenty of computer science majors do a minor in math and vice versa to get the best of both as well.
I’m currently a 3rd semester EE undergrad and considering switching to a pure math major, minoring in EE and then doing EE or CompE for my masters degree. What do you think of this? What could be good about it and what could be bad about it? If more context is needed just lmk
I love math but I have no interest in any of the jobs that were listed except for research or teaching. Even then, I doubt my intelligence to reach that level of education. Sometimes you just have to do jobs though and so maybe ill go ahead but I just don't know.
Why do I have this feeling that I'm going to end up jobless even with the phd in pure math? chances for getting any of those jobs you mentioned are very slim
@@abcd-hw8io Do you think you can do just research at a university with a Phd? I really don't care about a big salary (30-40k a year sounds fine to me tbh), I just want to be able to do Math until I die without worrying about starving or homelessness
My uni doesn’t have Applied mathematics. Can I apply to AMath if I plan to go to graduate school? (Suppose I can double major in (pure)math and another engineering’s major?)
@seth923 Feel free to respond and message me. I'm a mathematician on the job market. In short, I'm not worried about getting a job but you need to realize the pay is probably way less. Most of pure mathematics is meant for academia for like teaching or research. Do you want to go to graduate school? Get a M.S. or a Ph.D.? I'm about to get my Ph.D. in mathematics and have been procrastinating applying for jobs and somehow ended up here. I'm not worried about my job opportunities personally. But I know some people with a Ph.D. in math and are in a 45k or 50k / 9 month paying job teaching. I guess there's a possibility of more money on that if they do stuff over the summer, but that isn't always guaranteed. And keep in mind that's WITH A Ph.D. We're talking typically 5 -6 years AFTER undergraduate school. However, there are some positions that start at 80k, 90k, 100k at "better" institutions. In general, teaching jobs don't pay much. I generally view Ph.D. as a career preference and NOT a financial decision and I strongly encourage everyone to view it as such. Community college jobs aren't that bad actually. And all you need is a master's. In my opinion, it isn't a bad option to consider if you want to teach low level mathematics. I personally would go crazy always teaching calculus because it's not a challenge to me anymore. So it depends on your preferences. But there's plenty of teaching jobs around if you are okay with that. But if pay matters, then you should take that into consideration. And yes, you may not now think pay doesn't matter, but what if you have a family? Do you want kids? It may affect what kind of spouse you want too. My SO is going to work and she realizes how much money I expect to make when I take a job. I'm still trying to get the nicer jobs, but I did not go to a "top 20" uni for my Ph.D., so that's harder for me. But there's always a demand for people in math. It is everywhere so it is a flexible degree if you want to make it that way. There's options to morph it into something useful. The biggest advice I can tell you is to get a MENTOR and someone who can help guide you. A mentor can save you from making poor decisions and guide you through the correct decisions. But a good mentor is hard to find. It helps to talk to several people so that you can hear when someone says "oh that piece of advice is garbage and awful." I think your question can only be answered by a deep discussion of what you want in your life and if I can help let me know, but maybe you can find someone you know more personally that can answer that better. But if you're looking for advice, I'm happy to give more I happen to notice your response of a message or anything. Best of luck.
@@pavith3817 One of the biggest employers of mathematicians in the United States is actually the NSA (National Security Agency). There's also a lot of people who go into math who also learn some statistics and computer programming. If you learn languages like Python or R, you can go into data science. However, data science degrees themselves are starting to become offered and I'm not sure how viable this option will be in the future as more and more people get actual data science degrees. But I know several people who went into data science after they were in math. There's also other companies that employ mathematicians as "problem solvers." It's in general difficult to find these jobs but usually they are called things like "data analyst, research scientist, etc." But sometimes these jobs want a Ph.D., not a master's. Some labs also hire math people to help contribute with their research. So like Fermilab, etc hire mathematicians for that as well. I'd have a hard time saying what works with a master's and what doesn't though as I'm mostly familiar with Ph.D. opportunities because that's what I paid attention to. Best advice is to find someone who did make it into that sort of job and ask them. If you go to big math conferences, there are usually sessions on finding a career in math outside of academics. There's a lot of people there who would be great resources to find out about all this more so than what I could say. Hope that helps.
@@Ecoi1 Hi I'm interested in doing Applied Mathematics and I have some few questions that needs someone who is informed and on the job market Would you help me with answering them?
When I was in college, I had the misfortune to take Modern Algebra, probably now called Abstract Algebra. This was during the Vietnam era and colleges were hotbeds of protests and student activism. In that class a student asked what we would DO with this stuff. Clearly the prof had never been asked, let alone even considered such a question. It was a deer in the headlights moment.
Mathematics is the study of things named after Euler.
I was mislead by the Houston Eulers.
Yes, if you exclude the things named after euler for which he invented these equations and theorems
Newton*.
And Gauss
Nah I win, them mf that invented counting. Math wouldn’t exist without their big brains
I have a BS in pure math. One of the hottest and best fields for mathematicians is data science, which combines statistics, technology and domain knowledge (e.g. finance, health care etc.) There is often a complaint that most data scientists are great with technology and domain knowledge but lack the depth of statistics, logic and reasoning. We need more math majors to enter this field. Great video as always!
Hi wouldn't applied maths be better for a data science career perhaps?
@@drewkavi6327 Applied/statistics/math/computer science/pure math/econometrics students can all aim towards data science assuming they have the requisite mathematical and computational skill. Regardless of what base you have it will be neccessary to complete your education after school. However, the mathematical background is indispensable. I believe applied math or statistics are more applicable than pure but it won't be a deal breaker depending on the focus of the data science job you look for, some may require more coding skill than others for example. The channel dimitri Bianco had an interview recently with one of the data scientists for the pizza brand domino's he talks a bit about the educational requirements and what's important.
But I don’t like statistics
@@username8644 Probability is a part of pure mathematics get ur facts right bitchbox
True
I study math in the Czech republic, and it's interesting to see how different is it in a lot of aspects. For example, we don't differentiate between pure math and applied math until after one completes their bachelor's degree. We don't have calculus and instead do rigorous real analysis from the first year. There's also a few obligatory courses not even mentioned here, like measure theory.
I am deciding between studying maths at MFFUK and CS at FI MUNI. I love mathematics (proofs included) but I have a fear of not getting an appropriate job after finishing my maths degree. Could you please tell me where you or your classmates ended up? Thanks!
@@cubeik-jakubvlcek698 Well, what you can do when you finish is largely dependent on what specific mathematical field you want to specialize in. I study probability, and with that, there's plenty of opportunity in statistics, data science, machine learning, finance etc. There's also a decent amount of good opportunities if you study something like numerical analysis or cyphers. But there are also plenty of very theoretical fields that you won't use much outside of academic work. You usually don't have to make these decisions early on in your studies, at MFF pretty much everyone has the same subjects for the first two years. By then you usually know what kind of master's degree you want and choose your courses accordingly. And yes, if you go study at MFF, getting master's is probably necessary, the standard bachelor's course in general mathematics is not very useful on its own, it mostly provides the basics you need for master's.
@@cubeik-jakubvlcek698 if you have a math degree, you'll be able to find a place.
the comment regarding real analysis has me thinking. I'm DEFINITELY going to use Spivak's Calculus book alongside my courses and teach myself proofs along with whatever we're learning. I hear your situation from a lot of countries and I think we should be doing the same in the US
@@highviewbarbellthe point is not every students are ready for proof writing, or even not all students taking calculus courses have the need to write proofs, say physicians. So i think if you really wanna do so, just go to honour courses
My degree is in pure math. My career is for the past 10 years has been as a Lithium-ion battery engineer in different roles ( electrochemical, process, and continious improvement).
Hello Sir, your degree is in pure maths but your career has leaned towards math applications fields, how? I also want to do PhD in pure math(may be Algebra) and I am interested to know more about your career, it will be very helpful for me
How much degree level math do you actually use in your current role?
Well, I don't do any proofs or abstract algebra on the job, though I miss that stuff. The vast majority of my on the job math is arithmetic, algebra, some calculus for figuring out battery capacity and impedance. I do some EIS which uses some more advanced mathematics. The vast majority of the math I use is in stats. I use a lot of chemistry and physics as well.
God damn eular did soo much
yeah it's insane how often he comes up
Dylan John ikr. F(x), e, sqrt(-1)=i, π and so much more.
This Is An Alias by π, you mean the notation
Stelios Toulis duh
This Is An Alias im sorry I meant to have a question mark
im getting a double major in CS and applied math, deffinetly worth the extra semester changing my math minor to a major
I am thinking of doing the same but with ME in lieu of CS. Never hurts to be more educated in math, right.
@@anxiousmonk7 please how did it go? It’s 4 years later now
Well it’s 4 years later now. How are things?
@@ezramantini8078 I started my bachelor's in Mechanical Engineering but had a greater interest in the theory behind the engineering principles. Hence, I considered the double major with applied mathematics. However, I found the best of both worlds through physics actually. It had the rigor and theoretical explanation I longed for, plus I got to study the interesting concepts presented in mathematical physics. I graduated with a B.S. in Applied Physics! Professionally, I am a business analyst for a large tech company (on track to becoming a data scientist, which is what I spent the bulk of my senior year studying).
@@ezramantini8078 I finished my degree in late 2018 with the double major in CS and Applied Math. Now im a software dev for a Bank. Looking back I enjoyed the math courses more than CS, but there was more job opportunities for me as a programmer. But in my case, I got an offer as an intern because I was still going to school for that extra semester, which later led to a full time offer.
I have a B.S. in Math and I can't get a full-time job because I have no experience in anything outside of tutoring...
(Edit): 2 years later I have a full-time job as a contractor with the Navy working as a Financial Analyst. So I guess long story short, persistence works eventually.
Damn dude, did you minor in anything?
thats like 3k mate.
STEM fields tend to have an attractive opening salary but not much potential for growth. Become a doctor if all you care about is a high starting salary, they're the highest paid stem field. Other than that, business is where the real money is, but the highest risk.
DevoutSkeptic
Learn some finance and try that.
Honestly, if you were only planning on going for a bachelor's, you shouldn't've chosen math for a major.
Pure math bachelor's, perfect grades and NO JOB.
Interesting. For my math major, what you described as real analysis was combined into my first year calc 1 class. We started with basic field results e.g. prove x*0=0 for any x in a field F, then shifted our focus onto the field of real numbers for the most part. We learned about how real numbers are ordered, basic theorems involving that, then sequences, limits, series, functions, continuity, limits, and finally derivatives a couple months into class. Then we continued on to cover the various things you'd learn in any single variable calc course. Everything we covered was proved in class, or in our homework. Also we don't have calc 3, it only goes to 2, which is multivariable calc, where we learn basic topological things about Rⁿ, greens/divergence/stokes theorem (not in full generality, only in 3 dimensions). We also have real analysis 1 and 2, but those require these calc 1 and 2 courses, and is basically a baby version of topology, where you work with topological spaces with a metric, a "distance function" that lets you measure the distance between any two points, whereas in full on topology you don't get this luxury. these spaces are called metric spaces, and you generalize results from calc 1 and 2 to these more general objects, where "addition" or "multiplication" may not even make sense. Awesome vids tho
Please make a video on Statistics as a major
I promise I will!
@@zachstar I am waiting~~~~. Please keep the promise
@Alexander Leblanc just study mathematics, then learn to apply it to the job you want, then apply to the job
@@zachstar hurry up
Zach Star
Why did you lie :(
I always think that Euler is a fanatic with too much time in his hands..... Amazing yet crazy how he spot that one
You have to be either a fanatic or a lunatic to be a top mathematician
To quote Wikipedia: _"It has been estimated that Leonard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century."_
Meanwhile you got people like me making the conscious decision to become a math teacher. But really I don’t care because it’s what I’ve always wanted. I’d rather be happy teaching than be an engineer and not feel like I’m living my best life.
Same it’s a very difficult decision
I'm glad there are people like you out there. I like math but prefer to be in engineering. I would find teaching stressful.
@@flyingdutchman773 may I know more about the engineering work you do?
@@rols2840 I guess not lol
@@macon8638 😂😂
Dude your videos are still excellent. I applaud you.
Thanks man!
I watched both your videos about the math major and must say that in my pure math undergraduate program, I learned all the courses in both the applied section and pure section of the videos. These are all very basic courses which any person doing a math degree should know. Now I'm a grad student in pure math
I wish I was advised well when I did my B.Sc degree in Applied Maths. Right now I am a teacher, a good maths teacher. Thanks for creating this informative video.
Do you have any regrets in doing Bsc in Applied Mathematics?
What other jobs can you do with Applied Mathematics? I dont like teaching
What university did you study in?
About there being a real number between any two distinct rational numbers:
Lets assume 00, we know there exists an k such that 1/k1.
But now there exists a whole number m between n*a and n*b, and thus m/n is a rational number that lies between a and b
One of the very right thing I did in my life is subscribing your youtube channel... God bless upload more video we are waiting...
Awesome video. A video about measure theory would be interesting as a suggestion. Thanks
In Germany, as a teacher, i have to take for my bachelor + Master:
Calc 1-3
Linear Algebra I +II
Differential Equations
Proofs
Abstract Algebra I
Real Analysis I + II
Complex Analysis
Topology
Vector Analysis
Euclidian Geometry
Spheric Geometry
Hyperbolic Geometry
And some other stuff
Where for example do things like Measure theory, sentence of peano, galoistheory (maybe abstract Algebra?), etc fit in here?
very late response but those would probably end up being electives that the math major can choose to take, and wouldn't necessarily be mandatory
colleges usually let u pick your upper level electives so someone could take a bunch of topology courses for instance but they wouldn't be forced to
Huh? Even aspiring teachers for Gymnasium @ Oberstufe don't do any complex stufflike Topology. They only take Algebra 1+2 and Calculus 1+2 like a pure math major would. After that it's completely seperate.
lol group theory sounds super intimidating but when you defined a group, i just realized i learned some of this stuff in lower div linear algebra haha
it s actually a lot harder than that
but of course if you give it some thought you ll be able to get through a lot
It's likely because matrices in linear algebra are elements of a vector space and vector spaces are groups, so the properties of groups apply.
have been watching your vids for a while. just subscribed now because I'm excited about future videos very similar to these on different majors and classes.
Fellas, if your girl:
>Is closed;
>Has an identity;
>Is associative;
>And all her elements have an inverse,
Then that's not your girl. That's a group.
Before these videos I was finding it very difficult to decide between applied and pure math. Thanks for making it easier to decide. :)
Glad it helped!
As someone who will probably have to make this decision soon, what did you choose?
Great content! Was wondering if you could ever do a video on Data Science or Cognitive Science?
A video on Engineering Physics/Science would be awesome
I love math but I always feel like I forgot everything I learned as soon as I'm on break from school
Thank you so muchh.You really cleared up a lot of things for me.
Your videos are amazing!
Pretty helpful video!
Looking at this, I guess it’s best I go for engineering, and teach myself pure math on the side.
Ken MacDonald
Well, engineering has the other sciences + math, plus it’s more practical, and you can really only learn theory online.
Unless math is too difficult to self learn, then it looks like majoring in engineering is the better idea.
I should have watched this look time ago u have me so much confidence thank you
Extremely useful
Thank you
I'm right now an applied mathematics (bachelors) sophamore and love math. I'm thinking about possibly getting a job as a professor and doing my own personal research on the side. But i don't know how hard that could be. I'm worried that it will be hard to find a job and the last thing i want is to work for the department of defense or some other job with military goals. I'm also incredibly interested in electronics. I'm thinking it's reasonable to get a masters degree in electrical engineering after my applied math bachelors and then get a masters in applied math too. We'll see. But I'm excited about learning!
Please inform me about your journey... I am a High school student, but I have similar goals and mindset as you and I really want to know what my future will hold if I chose research instead of some corporate job
@@Random-pk1cs I'm just finishing up my sophomore year in applied math and am applying for several REUs for this upcoming summer. The REUs are student research opportunities that you get paid for. They are between 8-10 week things that pay around $3000 to $6000. They are competitive so I've applied to 6 of them. Besides that, I'm thoroughly enjoying my classes. Some of my classes are fairly difficult, like applied probability. But with a little extra study time outside of class, I'm really gaining a deep understanding of the material. My college offers a 4 in 1 plan where you get a masters 1 year after your bachelor's. I plan to use that to get a master's in electrical engineering, and then get my math master's later.
@@Random-pk1cs@Random-pk1cs dang it I replied and my reply disappeared. Lemme try again. So I'm just finishing my sophomore year as an applied math major. I'm applying for REUs for this summer. REUs are student research opportunities that run for 6-10 weeks and pay around $3000 to $6000 with food stipends and paid housing. They're competitive so I've applied to 6 REUs. You'll want to nurture good relationships with your professors so they'll write you wonderful recommendation letters, as those letters are needed for REU applications. Research seems to be the way to go if you want to get a master's and PhD. That aside, I'm taking some very interesting classes. I have some difficult ones, for example applied probability. But with some extra study time outside of class, I'm able to gain a deeper understanding of the material. If you have any other questions, don't hesitate to ask. Hopefully that helps. I'm excited you're thinking about going to study mathematics. Even if you choose to specialize in something besides math, having a good mathematical foundation will put you ahead of the game. Math majors are the jack of all trades as they say.
@@Random-pk1cs dang it I replied and my reply disappeared. Sorry if my previous attemptsload and you get 3 nearly identical replies. Lemme try again. So I'm just finishing my sophomore year as an applied math major. I'm applying for REUs for this summer. REUs are student research opportunities that run for 6-10 weeks and pay around $3000 to $6000 with food stipends and paid housing. They're competitive so I've applied to 6 REUs. You'll want to nurture good relationships with your professors so they'll write you wonderful recommendation letters, as those letters are needed for REU applications. Research seems to be the way to go if you want to get a master's and PhD. That aside, I'm taking some very interesting classes. I have some difficult ones, for example applied probability. But with some extra study time outside of class, I'm able to gain a deeper understanding of the material. If you have any other questions, don't hesitate to ask. Hopefully that helps. I'm excited you're thinking about going to study mathematics. Even if you choose to specialize in something besides math, having a good mathematical foundation will put you ahead of the game. Math majors are the jack of all trades as they say.
Would you mind if I request about Engineering Physics.
Definitely a popular request! I am looking for someone in that major to help make a video
Can you make a video of Math major teaching option and what classes entails.
Linear Programming is also applied math.
And part of Operations Research
0:34-0:40 Say, S is a set and ● is a binary operation on S, then closure is automatically guaranteed, as ● is a mapping from SxS to S, it's impossible to not have closure. Checking closure is not necessary, unless I misunderstood you: you were actually checking whether (Z,+) is a subgroup of a bigger group that contains Z.
I feel like I'm the only math major not taking abstract algebra or any analysis class. Those requirements were satisfied by axiomatic non-euclidean geometry and probability theory
Think video is FANTASTIC thank you!!
I’m gonna start uni in sept.. idk if I’ll be able to do this. Actually freaking out right now.
Jimmy M omg how’d it go ?? I’m thinking about majoring in pure mathematics
I'm interested in Jimmy's progress as well.
How are you doing rn 👀
How are you doing rn?
Hey guys I don’t want to scare any of you but actually it was one of the worst decisions of my life. My mental health suffered so much that I was admitted into hospital. Now my living situation, social life, and mental health were the biggest and most influential part of my breakdown but my advise is if you’re not up to the challenge, mentally stable, and have a comfortable living environment and source of income don’t do it. It’s not worth it.
You should discuss the statistics major :)
I want to major in Math so badly
Start learning right away, if you want to get a feel for what a maths major is about, start by learning how to write proofs with introductory discrete maths. If you're still into it, go ahead and learn some real analysis, linear algebra, group theory, and general topology. Exactly what order you go in isn't too important but I'd recommend some analysis before topology and some linear algebra before group theory & abstract algebra. And have fun, if you go into that degree you'll leave on the brink of something truly amazing!
@@elijahr_1998 Maybe they were just giving a physical description so the original commenter knows what to look for?
do I have to be good at math to get a degree in math?
Blox117 kinda, you just have to change your mindset on how you see math honestly. I’m not some expert but I’m open minded about math, and if I don’t know something I go back learn I, and continue. Takes a lot of studying and reviewing. I’d say you don’t have to be some expert or even extremely good, but definitely know the foundation
The Flagged Dragon solid advice with learning analysis before topology. I did the reverse back in college and the hill was steep in topology. As a result, real and complex analysis were a breeze lol
small nitpick. the set is not associative, the operator '+' is associative.
I
This was very helpful. Thank you!
@MajorPrep
Could you talk about Mathematical Physics?
In Greece we have no job industry for applied mathematicians.
Mathematicians normally have only 2 choices: teaching and research.
I just took my linear algebra final.
We covered groups, sets, vector space, subspace, basis, span, and proving all of it... and even more.
All I can say is wtf. Did the prof cover more than he should've?
Our prof covered Quaternions in the first lecture, so i don't know at all what's normal
I am about to enrol in an economic major and my uni lets me do a concurrent diploma in math alongside it. I was interested in pure math as I thought this would look good to potential employers, but from your video it seems applied maths might be more useful and practical - is this what you think?
agreed.
My university's math major (intended for those who don't want to do graduate studies) doesn't require students to do real analysis or abstract algebra... You don't even need to know something as basic as an epsilon-delta proof.
Because they're smart and forward thinking. There isn't much point in teaching math as computers do it all. Let the few programmers deal with it.
@@Michael_Livingstone Can your computer write proofs? No, it can't -- that would require a human-level AI. Math is not about computation. In formal math classes, being asked to actually compute something hardly ever happens. Instead of finding the answer to specific problems, you're more likely to prove that there exists an answer to those types of problems, in general. These aren't the kinds of problems your computer can solve for you. If they could, nobody would bother studying them -- it'd be trivial. In fact, we wouldn't even have computers if a couple mathematicians didn't generalize the concept of computation so that it could be implemented by simple mechanical systems.
shit, math major seems really fun
It is very fun as long as you study and have fun with it :) Just got my bachelors in it and working on my masters! I can recommend a pure maths concentration whole heartedly. Currently in research right now and it is amazing
garrett smith what did you choose to focus on?
B T the real question i've seen in the UA-cam history
i am moroccan and a lot of the stuff in pure maths and proofs we actually did in high school in the math stream.
Great video!
The things you taught in beginning is binary operations
other than teaching, what can be a side profession to do along with research for pure math person?
I Have a question... is it okay for me to pursue a Master's degree in Mathematics with a bachelor's degree in mechanical engineering? Do I need to study by myself all of the Mathematics topics that I missed out on the Bachelors degree in Mathematics?
in pure math? that might be very difficult Applied math would be more plausible. I'm sure it is possible but you should look at the math GRE to see what basic concepts are required to have the knowledge and ability to pursue and advanced math degree.
Corey Holcomb not pure maths... just maths; msc in maths... I'm sure there are some universities that offer that.. is it also difficult to be enrolled?
what math have you taken? are you an undergrad now?
yup MEng mechanical eng. The classes that I am taking is engineering mathematics 1 and 2, differential eq and calculus for engineers, advanced dynamics of mathematics, advanced mathematical techniques in ordinary differential equation for engineer, and mathematical techniques in partial differential equation for engineer..... there are the modules that I am taking and plan to take.
I would suggest taking courses in the actual math department because engineering math usually lacks the rigor needed to pursue serious math. Take a linear algebra course in the math department that covers vector spaces and linear transformations in depth, take some sort of advanced calculus or partial differential equations in the math department, and I would try to take a computational math/numerical methods course in the math department. You should at least go for a math minor and specialize your elective courses for math in the area that you would be interested in studying in grad school. Also usually grad schools have programs in math and/or applied math not just "maths". As an engineer if you develop a good understanding of PDEs and numerical methods for PDEs I think going to grad school in applied math might be possible. For pure math you would definitely need to take the math GRE and do well to show that you understand the pure math concepts not covered in your engineering degree; so you would need to understand all of calculus very well, real analysis, general (modern) algebra and linear algebra, and topology.
i think t1(c2) is like a function
Can you do one on statistics please
Thank you so much
Hi, thank you for your awesome videos !
If I basically lean more towards theoretical physics, but really like math and want to focus on it, which math will be advised? applied or pure ? generally I find the pure math very appealing from your videos, but would it help further if I'll want to continue into theoretical physics ?
You’re honestly gonna do all kinds of math, pure and applied (especially if you go to grad school). I say lean more towards applied while still taking classes in various pure math courses when you can.
I see, thank you so much sir ! you are awesome
Great videos!
Im suprised that you listed combinatorics under pure math not applied ?
Combinatorics is good in reliability engineering a close cusin to sats.
Where is algebraic geometry ？
Or symplectic ...
I'm interested in majoring in applied math, and getting a phd so I can become a research professor. What are some of the things a research professor doing applied math might do? Also, you're math major videos have been incredibly helpful, thank you!
Could you please do a video on chem major
I'm first year, and this is honestly challenging.sigh
i got subscribers without videos don't worry, it gets worse
Trust me it gets better, their is a learning curve and sooner or later you will get ahead of that curve if you work hard. Once you are their it is not very hard.
It sucks. Pure math is so useless. I only do it because it has so many overlapping courses with my physics degree. But I do harder and more interesting math in physics than i do in math
What? First year should primarily be general education my guy.
I've heard algebraic geometry is a really hot subject area for oure mathematicians. Do undergraduate math majors take an intro class to this? And what's the significance of it? And why are physicists into it?
Wow! Cool stuff! 😂
After seeing the other video, I thought I might have proved that square root 2 is irrational when i was like 7 years old
Who is proving that there's no quintic solution in Algebra I? You need Galois Theory for that.
Would it be a little easier for me to find a job after graduating if I'm in a major that's a hybrid between Maths and CS like Data science and Scientific Computation ?
Having knowledge in CS related subjects will definitely help with getting a job. And if you are talking about just a bachelor's then yes those things will definitely be a plus. Plenty of computer science majors do a minor in math and vice versa to get the best of both as well.
I think you made a mistake when combining those two permutations. (1 2 3)(1 2) should equal (2 3) not (1 3) as you said
That shape with 0 euler characteristics looks scary af lol
Insatiable Lechery that’s the famous Klein bottle
What you talking about? It is pretty.
Great I like your videos thanks
13:23 "and more"
I’m currently a 3rd semester EE undergrad and considering switching to a pure math major, minoring in EE and then doing EE or CompE for my masters degree. What do you think of this? What could be good about it and what could be bad about it? If more context is needed just lmk
T R I P L E T O R U S = F I D G E T S P I N N E R
euler wants to know your location
What about the jobs in pure math ?
Make a video on mathematical modeling..plz
Yep. I would have killed myself before I got thru the math major. After 1 year I switched to something else and it was the best decision I ever made.
What about discrete mathematics and operation research ? I have that as a major in my university, idk what its about though..
Discrete Math is where many students first learn to do proofs.
I love math but I have no interest in any of the jobs that were listed except for research or teaching. Even then, I doubt my intelligence to reach that level of education. Sometimes you just have to do jobs though and so maybe ill go ahead but I just don't know.
You can become a data scientist or a developer for a tech giant
So now I realize I might choose Applied over Pure
Super video! I applauded for £50.00 👏👏👏👏
So who is smarter professor in maths or science
Why does both pure and applied students need to take 2 semester of real analysis?
Why do I have this feeling that I'm going to end up jobless even with the phd in pure math? chances for getting any of those jobs you mentioned are very slim
pretty much yeah. only way to get a decent job is to pair it with something that in the eyes of HR, more practical like computer science
@@abcd-hw8io Do you think you can do just research at a university with a Phd? I really don't care about a big salary (30-40k a year sounds fine to me tbh), I just want to be able to do Math until I die without worrying about starving or homelessness
Good videos :)
My uni doesn’t have Applied mathematics. Can I apply to AMath if I plan to go to graduate school? (Suppose I can double major in (pure)math and another engineering’s major?)
Please answer my question.
If I get admitted at undergraduate programme of mathematics, which compulsory courses I should take?
Well if they're compulsory you dont really have a choice, do you?
nice
Maths is the study of ghosts.
et cetera is the worst thing to expect ever
I am much more interested in pure than applied but fear I won’t get as much job opportunities. Should I worry about that
@seth923 Feel free to respond and message me. I'm a mathematician on the job market. In short, I'm not worried about getting a job but you need to realize the pay is probably way less. Most of pure mathematics is meant for academia for like teaching or research. Do you want to go to graduate school? Get a M.S. or a Ph.D.? I'm about to get my Ph.D. in mathematics and have been procrastinating applying for jobs and somehow ended up here.
I'm not worried about my job opportunities personally. But I know some people with a Ph.D. in math and are in a 45k or 50k / 9 month paying job teaching. I guess there's a possibility of more money on that if they do stuff over the summer, but that isn't always guaranteed. And keep in mind that's WITH A Ph.D. We're talking typically 5 -6 years AFTER undergraduate school. However, there are some positions that start at 80k, 90k, 100k at "better" institutions. In general, teaching jobs don't pay much. I generally view Ph.D. as a career preference and NOT a financial decision and I strongly encourage everyone to view it as such.
Community college jobs aren't that bad actually. And all you need is a master's. In my opinion, it isn't a bad option to consider if you want to teach low level mathematics. I personally would go crazy always teaching calculus because it's not a challenge to me anymore. So it depends on your preferences. But there's plenty of teaching jobs around if you are okay with that. But if pay matters, then you should take that into consideration. And yes, you may not now think pay doesn't matter, but what if you have a family? Do you want kids? It may affect what kind of spouse you want too. My SO is going to work and she realizes how much money I expect to make when I take a job. I'm still trying to get the nicer jobs, but I did not go to a "top 20" uni for my Ph.D., so that's harder for me.
But there's always a demand for people in math. It is everywhere so it is a flexible degree if you want to make it that way. There's options to morph it into something useful. The biggest advice I can tell you is to get a MENTOR and someone who can help guide you. A mentor can save you from making poor decisions and guide you through the correct decisions. But a good mentor is hard to find. It helps to talk to several people so that you can hear when someone says "oh that piece of advice is garbage and awful."
I think your question can only be answered by a deep discussion of what you want in your life and if I can help let me know, but maybe you can find someone you know more personally that can answer that better.
But if you're looking for advice, I'm happy to give more I happen to notice your response of a message or anything. Best of luck.
@@Ecoi1 so apart from teaching, what other viable opportunities do I have if I get a master's in math?
@@pavith3817 One of the biggest employers of mathematicians in the United States is actually the NSA (National Security Agency). There's also a lot of people who go into math who also learn some statistics and computer programming. If you learn languages like Python or R, you can go into data science. However, data science degrees themselves are starting to become offered and I'm not sure how viable this option will be in the future as more and more people get actual data science degrees. But I know several people who went into data science after they were in math.
There's also other companies that employ mathematicians as "problem solvers." It's in general difficult to find these jobs but usually they are called things like "data analyst, research scientist, etc." But sometimes these jobs want a Ph.D., not a master's.
Some labs also hire math people to help contribute with their research. So like Fermilab, etc hire mathematicians for that as well. I'd have a hard time saying what works with a master's and what doesn't though as I'm mostly familiar with Ph.D. opportunities because that's what I paid attention to.
Best advice is to find someone who did make it into that sort of job and ask them. If you go to big math conferences, there are usually sessions on finding a career in math outside of academics. There's a lot of people there who would be great resources to find out about all this more so than what I could say.
Hope that helps.
Maybe its just me but why don't you just learn Pure Math for fun on the side and just do a major that has a better chance of landing you a job
@@Ecoi1 Hi I'm interested in doing Applied Mathematics and I have some few questions that needs someone who is informed and on the job market
Would you help me with answering them?
I'd rather be a Mathematician or a Physicist than be a toilet cleaner.
Wait what 👀
I wonder if I need these classes for a physics minor
AAAH THERE IS SO MUCH TO LEARN
Nah bro it's easy if you love it i learned the college math in high school
You did not mention the most popular thing: data science and machine learning.
Ok now prove that you can prove a proof with a proving proof proof.
It's called the neutral element. Not the identity element.
How do you compute the V - E + F for a sphere lol
Which math major goes well with a minor in CS?
applied math
Linear algebra
Where is the "The Math Major (Part 1)" video ?
When I was in college, I had the misfortune to take Modern Algebra, probably now called Abstract Algebra. This was during the Vietnam era and colleges were hotbeds of protests and student activism. In that class a student asked what we would DO with this stuff. Clearly the prof had never been asked, let alone even considered such a question. It was a deer in the headlights moment.