hey can you please cheak out the sylabous of srilankan Advanced level maths sylabous. And make videos out of it for students. There is many students who is looking for online studys these days.
My favorite way of describing the difference between pure and applied math is as follows. Pure math explores the world *of* mathematics, applied math explores the world *with* mathematics.
It does not matter how long you have been out of school. You have also an advantage over the younger kids. You lived and you know that going to bars is not that great.
LunaticSoul first and foremost, are you familiar with the so-called horseshoe technique for insane integration? no but seriously, if youre still in school you can improve your math simply by doing more of it. you dont have to be a genius to get the best grades in math. that and maybe by kissing the teachers arse
LunaticSoul™ I’m not sure if it was obvious or not, but our comments were sarcastic. We were referencing a joke video about an alleged PhD student. So despite my previous comment I’m not actually doing a PhD in Maths. However, I am a Mathematical Physics student so I hope I can offer you _some_ insight. I’m not sure if you’re an undergraduate student like myself or if you’re still in secondary/high school. If you’re an undergrad then you’ll probably know most of what I’m going to say anyway. I’ll give my advice in a followup comment to keep it separate from this cluttered comment.
LunaticSoul™ This may seem obvious, but to improve you need to practice. Whenever you’re given homework in school you need to do it, to the best of you’re ability. Persistence is just as important as ability when it comes to Maths. If you ever get stuck, refer to your book, notes, examples taken down from class etc. Any resource you have, use it. There’ll always be an explanation of what you need to do in there somewhere. You just need to be persistent, and grind it out until you figure what you need. It’s also very important to actually understand what you’re doing. Don’t just memorize how to use a method. Understand (within reason obviously) how and why it works. For example, if you’re doing derivatives in calculus: what does it mean when you take the derivative of f(x)? You’e obtaining a new function, f’(x), that gives the slope of f(x) at any x co-ordinate. But what is a slope? A slope is a measure of the rate of change of a function. The bigger the slope, the bigger the rate of change etc. Understanding is important. If you’ve understood something, rather than just memorized the steps on how to repeat it, you’re work load drops significantly. You actually have to “learn off” a lot less. But more importantly, you can recognize _when_ to use that concept that you’ve understood. You can spot connections more clearly when you understand. (I lack the ability to convey this point properly. I might edit it if I can re-phrase it in a more impactful manner. It’s importance cannot be overstated.) When it comes to understanding, paying attention in class is also vital. It’s so much easier to learn from a teacher than it is trying to figure this stuff out for the first time at home on your own (that’s something I’ve been suffering from recently). _Never_ be afraid to ask a question, despite how ridiculous you think it might seem or how you might think others will react. If you get a better understanding out of it then it’s always worth it. If you happen to be uncomfortable with that though, then ask your teacher your questions at the end of class. You’ll usually get a better explanation then anyway. Another bit of advice, read ahead in your book/notes if you get the chance. Nothing too heavy now, just enough that future topics aren’t completely alien to you. It makes it a hell of a lot easier to digest a new topic for the first time when you recognize some of it already. Last main point when revising/practicing for exams. Speed and the ability to function under pressure are almost as important as what you actually know. You could understand every single thing in you text book, but still not hit you’re potential in an exam because you’re taking too long to put it onto paper. You can beat this by practice obviously. Find out what the recommended time is for a particular question/set of questions, set a timer, and try to complete it in the given time. I think that’s everything. I really hope it’s of some use and that you didn’t know all of this already. I’ll post a TL;DR next. Best of luck in your studies.
Nice video, but there's something I want to add for those who would want to do a math major: there is a huge common core between applied and pure maths, and most of the classes you spoke about will be followed by both applied and pure math students. It's really when you become senior or when you do a masters that the distinction becomes clear. TL;DR applied maths students do proofs and pure maths students do calc
A man walks onto a train and frantically starts yelling, “I’ll differentiate you! I’ll integrate you!” People get scarred and start fleeing the train. The man looks around and sees one man sitting in the corner. “Why are you still here?” He asks. “I’m not scarred of you!” The remaining man replies. He is puzzled and tries to think of why he’s not scarred. And after a short moment of silence and confusion, the remaining man says, “I’m e^x.”
Great video! I am a current senior pursuing my BSc in Math and proving the square root of 2 is irrational just came to mind for my first proof class. It was definitely a challenge for me switching from the usual calculus, differential equations, and linear algebra class to a proof course. Perhaps, it was more so just approaching and looking at a particular problem in a different way. Nonetheless, being able to write QED at the end of a proof was such a great "mic-dropping" experience!
As a third year math major, thank you so much for deciding NOT to run through the proof of sqrt2 being irrational. I’ve seen this proof about ten times over the past year, I can recite it from memory.
I watched this video for the first time 3 years ago, this may I graduate with my applied math degree, it's insane to comeback and see how much of this video I can go into depth now
I’m interested in switching from a computer science major to math major. Is there any advice you have about getting a math degree or making the decision to pursue one?
@@wavez4224 I quit math major, I don't suggest math major but I guess it differs from country to country tho because I am Turkish and in Turkey, science diplomas are not valued. What's worst is you struggle a lot before you can graduate for nothing in return :) I guess computer science can work for your good after graduation more than math diploma so...
Hey guys, so I've already done a math major video on this channel but this video (and part 2) are going to replace that one! Most of the stuff from before is in this video as well but I've added way more on top of it. As I talk to more people in these majors and learn more there's always stuff I want to add to videos that will provide even more important information for you all. Sorry for any repetitiveness but hope it provides even more value. Enjoy!
Already graduated last year in Applied Math with an emphasis in PDEs, loved the major despite the somewhat difficulty in landing a job straight out of undergrad. Wish I did a minor in Computer Science or in Statistics but i ended up learning statistics and programming in python on my own.
Great video! I know a lootttt of math majors who go on to get their masters in engineering in some field, and crush it in their career. math major means "im super smart and can do anything", however, with just a math degree alone, sometimes you get funnelled into teaching or data or research. Math + STEM masters is a pretty wild combo :) Thanks man for another awesome Major Video!!!
Heyyy CodedCuber, thanks for the question. What your master's is will moreso dictate your career vs your undergrad. For example, the same is true with Physics / Chem undergrad majors. Many of these people continue onto a masters in chem engineering or electrical / mechanical engineering. They have a pre-requisites, as you will most likely have all the prerequists for something like a master's in electrical engineering or computer engineers with your CS Degree. I have a FB community with the EE who runs Major Prep (an awesome guy by the way) where we discuss all this stuff with 200+ engineers / STEM majors. Let me know if you want in! facebook.com/groups/1percentengineer/
Jake Voorhees Wait, what?? In which country is that? As far as I know in Canada you need to complete an undergraduate degree in engineering specifically before you get accepted into a graduate program in engineering. But I do agree a math degree would be awesome to have in addition to an engineering one!
Yeah I would never do a math major, you can't really do anything with it but get a higher degree in more math oriented STEM fields and I'm not a big fan of school, so I'm one of the best person's I know in math at least at all the schools I attended but I find math too boring to major in and I also couldn't find a career that a math major would be good for so i decided to go with my love rather than my strength: Science.
Great video and summary of courses. Former math major here. I chose pure math but career wise went into applied (finance + technology, or fintech). Learning double integrals and proof by contradiction was fun, but have to admit never found a practical use. Keep up the great videos!
Apart from the usual platitude that it's the relevant critical thinking and not the advanced skills that are used, it entirely depends on where you go. My first 'real' job after school (physics + maths double major) was in a bank. I basically did freshman lab reports, but instead of describing a block sliding down an incline plane or whatnot, it was stats pertaining to this or that model for clients. It (fallaciously) convinced me that "we require candidates with quantitative science/maths diploma" is corpotalk for "we could train high-schoolers to do it, but they lose interest too quickly to bother." Then, all cocky, I went into modelling for aviation applications and, ho boy, I could barely keep up with the level of maths coworkers casually threw around. It paralleled the same uni workshop that convinced me I didn't want to stay for PhD, and I had to resign because maintaining a serious relationship wasn't congruent with studying PDE for 2-3 hours every day after work. Then I started working as a software developer, and the last time I used any actual maths was to show (this doesn't warrant the word 'prove') our casework is a vector space if we look at the data from a different angle.
9:11 I have another proof: You can factor out a two to get 2(9a-3b)=1. An even number times any integer cannot equal an odd, so the two cannot be equal.
Wow. Sensitive people eh. That is a way but he was just trying to illustrate some different common ways of proving things. In reality theres probably hundreds of ways to prove it.
That feeling when you find a niche meme only a student of your subject would understand completes my life. Until I graduate and the paycheck starts to come in, memes will get me by.
Jake Voorhees not yet but I'm a nanotechnology major student, and will be a future physics and pure mathematician student too. After those degrees I'm double majoring at Purdue university for mechanical engineering and aerospace engineering
Great Eric, you should join my 1% Engineer FB group facebook.com/groups/1percentengineer/, MajorPrep is in there and he has his own too facebook.com/groups/majorprep/
In an early differential equation book, it covered the Heavyside transform and then the new edition showed how similar the Laplace transform was. A newer book covered Laplace transform and didn't even mention Heavyside. The 50s was when the changeover occurred.
I think the most common proof by contradiction is that there are infinite primes, as follows: There are finite prime numbers. Take their product, plus 1. This is not divisible by any of those numbers (for all primes p, remainder mod p is 1) Therefore, the assumption is false.
Just so you know, 5th degree polynomials do have an "exact" solution, just not one using roots of lower degree polynomials. The solutions are expressed using elliptic functions. This is not the case with higher degree polynomials tho.
Numerology and numerical analysis. I quickly learned that a mechanical approach to problem solving, left me, as well as my grades, wanting, for sure. Thinking ' out side the box ' will make proof solving a lot more fun. Super vid. Become a teacher dude - I remember my landlord and I talking in the kitchen one day. I said to him that I love math, but I suck at it. He said to me that, If you love math, you Don't suck at it. He is a math instructor at the university of Cal. I guess I get pissed, when I don't.get the results I am looking for. I feel like a failure. Dumb I guess. Weird maybe, but math gets me excited. Thanks for the look ahead for anyone thinking of life beyond the head-banging of what we can expect with either choosing pure or applied math. 😉
Lots of my peers in my undergrad were math/physics double majors. They loved it (but it was brutal, they say). According to them, the math major curriculum will expose to you just how much physicists butcher mathematics at times lol.
@@pumpernickelstickybottoms5081 what do they cover? The only proofs I've come across are induction, contradiction. When does it start to get hard. I really want to do Maths and I'll start in 2020.
Tripp Roberts I was on the fence about it, but at my school the difference between a physics major and a physics minor is like 2-3 classes. I would rather have a stronger math background then physics background going into grad school because I want my area of expertise to lie more into theoretical astrophysics, which is very math heavy.
I feel your pain Anakin, 6 years for a undergrad major + minor is rough. I was in my final year for a major in Physics with application in Nanotechnology (wordy, I know) but decided to pick up discrete maths + stats units, and now I have a year left to finish with a double major in the aforementioned Physics + Mathematics & Statistics. Good luck with astrophysics, I commend your bravery: I'm tossing up between that dream and aiming for a more profitable (that is, in dollars, not knowledge) career using applied maths/sciences in private industry. Choices are tough when you don't know till you try and a lifespan is only so long.
The examples given for pure mathematics seem very trivial and easy to understand. When I studied the subject 50 years ago, I got totally lost in Elementary Real Analysis. Looking at the subject today, it seems fatally flawed in the way numbers are introduced.
+baldiesarelife haha it's hard to show the difficulty of these classes cause I'm assuming many people watching don't really have a proofs background. But did what I could to show examples and still say they don't do justice for the classes.
Love your videos. I have a deep fascination with stats and you make almost any higher order math accessible, especially with your videos. Thanks. Curious, what is your level of math?
Howdy!! I am a Mathematics Education major! I absolutely love Mathematics!! I’ve taken a lot of Applied and Pure Math classes and I like Applied Math a lot more.
Gosh, I just love math so much I am currently limited by my environment and the school I go to, but I am so excited to have opportunities in the world of mathematics that i just want to learn it alI
Yeah math is awesome honestly, been in uni for 6 weeks now and the biggest struggle is explaining people how math is applied lmao, I honestly don't care how it's applied yet, I just like the math.
XBOX USERNAME Tuskediowa90238 it does. Trust me. If you’re in high school, the math is just basic. College gets more advanced and it’s worst if you don’t know the basics.
My point was its a very general statement that applies to many things. X is easy. You simply need to know the basics because they become advanced as you level up. Replace X with any skill or subject that you find appropriate and it'll hold true.
This video solidified my belief that I don't like abstract "useless-to-me-at-this-time" math and want to just take engineering cuz I want to use them fancy simulation and modelling software, also applied math sounds fun, but certainly not as fun as electrical engineering. Great video btw.
Math has never been my strong suit (hence why I moved from CS upon realizing I would have 3 years of math classes), but this is really interesting! I know a few math majors- mostly CS/math double majors, also a guy double majoring in math and finance with a CS minor. The CS-math students all seem to find the math part hellish. XD
@@azmanmatamin9020 wtf? Only truly geinus person would do that major. You know what a dumb person will major in? Gender studies. And that person appears to be you.
I love my undergrad math degree. It did a lot for me spiritually. But it did very little for me economically. All it did was get my foot into the door for an accounting job, and I still ended up having to go back to school to take accounting classes anyway. The search for truth is very expensive, and it's tough to balance it with the requirements for survival. So if you can stand it, I'd recommend going the engineering or computer science route rather than the pure math route. You're better off studying pure math on your own by going to your college's library and saving yourself some money.
I studied Economics, Math and Law as well as History in College and I have to admit the Counting and Operations and concepts associated with most basic math appear to me because they are associated with the concept of truth. I realize Economic data is often aggregated, but issues associated with Poverty, Income Distribution and such are subjective and so far as I can tell there could be several Economic systems in the world that "worked". Whether they would really be different or only appear to be unique is a topic I have studied and spent a lot of time thinking about. But does anyone really want to break the American Economy by changing it? The word Law means "to lie" and so even though it is associated with truth and the legal system is said to be valuable and important I always take definitions seriously. And if counting was my only skill, being a teacher would be just fine with me. And I wouldn't sit up nights worrying about what I had taught students.
With extensive use of tight sigma levels & confidence intervals, sexy symmetric histograms and box-plots, and normally approximated sample distributions.
@@flanagamer No it isn't....lmao. The money is in Finance. Like Investment Banking, Trading, Private Equity, Analysts and Traders at Banks, Hedge Funds and Trading Firms.
idktriple6 yeah but certified actuaries can make upwards of $150k/year in some places! That’s pretty good money, & a lot easier than becoming an investment banker unless you go to an Ivy League school
Yes. And you would be surprised about the amount of people that are actually very passionate about mathematics. Me, for example, I used to love maths and enjoyed my classes ever since I started learning out of love and not force. And after graduating highschool I really wanted to do something I enjoyed such as maths or physics but under parental pressure I had to pursue medicine. I'm a first year now and the thought of this statistics course being the last mathematical course I'll take does feel a bit upsetting. I don't know if I'll regret this choice later on in life but that doesn't matter now, since the question is about passion I did use to hate maths when I was younger (around 5-8th grade) But that was mainly because I did not understand what maths really was; I was only doing what I'm asked to do in class and tried forcing myself to learn the materials just to pass and the fact that everyone complains about maths did not help at all. But once I learnt to actually enjoy doing maths and appreciating the pleasure of knowing how to solve different kinds of problems maths started being a class I actually look very forward to, and it never seemed as complicated ever since. So the thing is: You MUST learn to enjoy maths to truly excel at it in any way.
Z. B. I can’t really say that. I can say that i was never “naturally gifted” and never completely understood everything like some math prodigies do. I still understand it quite well, and If i had to pick a math concept that Ive struggled the most in, it would be Geometry.
Calculus is not applied math. Calculus is math. If you use calculus to solve a problem in the natural sciences (but use all the rigor of mathematics) then you did applied math. Real analysis (advanced calculus) can be a pure math topic. Abstract algebra is consider a pure math subject, but if you use representation theory to express the symmetries of the hydrogen atom, then you are doing applied mathematics. The divide can be subtle (and sometimes artificial).
Oh, I tried proving the product of two odd integers is odd in a different way. Let n ≠ a, where a is even; n = b where b is odd. => b = a + c, where c is odd. Assume the product of two integers is n^2. => n^2 = b^2 If b^2 is odd, then the (a+c)^2 must be odd. => b^2 = (a+c)^2 => b = (a+c) Since b^2 was reduced to b, b is odd, and b^2 is b • b, b^2 must be odd; therefore n^2 must be odd. Ergo, the product of two odd integers is odd. I assumed the question asked me to just use two odd integers, not two odd integers of different values. And when adding an odd and an even value, you do yield an odd number; thus, I used that definition instead.
Hey man I'm currently doing electrical engineering and will have my masters in 2 years. I want to get another degree either in mathematics or physics which would you reccomend? I can do both since they can be combined but you will learn less as opposed to if you did them full.
I don't know about you but I'll rather study pure mathematics than applied mathematics. To me it's just a much more interesting and better way of doing math.
A friend of mine received his degree in mathematics. He's extremely smart, genius level even, but he hasn't found a job and is working for a health agency. Something completely unrelated to his major. He is now back in college going for an accounting/finance degree. Get ready for an extremely difficult time finding a job, unless you're very lucky. Major in something practical and minor in things like math, liberal arts, and history.
Compares maths and liberal arts. TRIGERED!! (Really dude, maths is a much better minor than liberal arts. It will actually complement your major, if you major in something like engineering,computer science or chemistry and minor in mathematics then you will have good problem solving and modelling skills. Even majoring in pure maths and minoring in applied maths means you will have problem solving and modelling skills combined with tools to make them useful which is something every big company looks at nowadays. Also algorithms,statistics and data are becoming more and more relevant each passing day which makes skills that a maths major has even more relavant.)
Also everyone knows that majoring in maths will make you a part of glorious mathematician/phycisist master race that is superior to all of those pesky liberal arts majors,history majors,chem and biology majors and even engineering majors(Engineers are cool and all but still they dont care about rigorousness as long as it works, which makes them inferior to glorious mathematician/phycisist master race)
So let me get this straight, because your one friend, who you mentioned nothing about his job pursuit dedication, internships or intangibles couldn’t get a job, every math major should expect a hard time? Lol
