Hey everyone, be aware that if you go to grad school, especially in a theoretical physics field, you WILL see those pure math concepts (topology, abstract algebra, and plenty more). And if you do go into a theoretical field, although you may not be required to take those classes in undergrad, you should consider taking as many as you can because it will be important to have that strong foundation.

Kinda funny, I'm a physics student and my computer background was the right picture in the thumbnail.

Damn it I want to learn it all

Just a random English major floating by...

As a physics graduate, I would personally recommend majoring in Mathematics if you enjoy them a lot. Mathematics is a lot more versatile in terms of career and job options than physics, and it can also serve as a pathway to areas such as mathematical physics or theoretical physics, giving you a better grounding than physics will. I find the main issue (and this is true among most physics students) is that if you want to do some serious physics, the main thing holding you back will be all the math you need to learn and use on a regular basis (unless you do purely experimental stuff, but even then you will need exposure to certain topics). Even to learn very old physics like the theory of classical electromagnetism and classical mechanics you need a good grasp of things like differential equations, vector calculus and complex analysis. In most physics undergraduate courses, the math you learn is simply insufficient to keep up with all the other things you learn where you are meant to apply all those skills. Hence, my recommendation is this: if you like physics more than math, then you might consider doing something like mechanical or electrical engineering, which have a good balance between both and plenty of jobs available. If you enjoy math more, then go for a mathematics or statistics degree, which will give you more career options. Physics is only good if you do it at the postgraduate level, and you have a pretty good grasp of mathematics. The concepts are easy to grasp once you get through all the difficult math. Just something to consider.

You have no idea how helpful this channel is to students. Thank you and keep up the good work!

Physics vs math: which major to choose according to an engineering major. Gold

Some Subjects, I learnt in Pure Mathematics During my MSc : 1. Measure Theory 2. Functional Analysis 3. Topolgy 4. Manifold Theory 5. Field & Galois Theory 6. Differential Geometry 9. Graph Theory 10. ODE & PDE 11. Algebric Topolgy 12. C - Programmimg 13. Fourier Analysis (Optional) 14. Harmonic Analysis(Optional) 15. Linear Algebra 16. Complex Analysis 17. Real Analysis II etc

Great video. My path was bachelor's in pure mathematics, master's in applied maths and now I'm finnishing phd in theoretical physics.. so I kinda went through the whole spectrum and it was really enjoyable! (most of the time)

Major in physics,but learn mathematical physics in parallel with books like mary l boas.You'll have solid basics in math and also you'll get to see how beautifully math fits into physical phenomenon.That makes you love physics and mathseven more.

This channel is so much better than the larger ones (Engineered truth etc) Instant sub!

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I can tell your a physics major from this video. The one thing I do have to add because I’m seeing a lot of comments about how math majors are purely interested in math and teaching it, while true, is that you can be a mathematician and still make a real World impact. Alan Turing was very important in inventing the modern computer and formalizing the underlying theory that allowed the computer to be invented and built. This was all math. Fields like theoretical CS are pure math fields that have real world impacts. Even pure math work like geometry has impact theories like the Big Bang. It’s not all about the equations and constants, and it’s definitely not only about teaching for those confused

Jobs: Applied maths, plenty. Physics, plenty. Pure maths.... um, you weren't really hoping to get a job were You? Well that's a shame.

*The most FAQs* *Engineer: How does it work?* *Economist: How much will it cost?* *Mathematician: How can it be further optimized?* *Physicist: Would you like some ketchup?*

If you really like physics, chances are you'll like a good chunk of math as well. Maybe not so much the proofs but knowing more tools that can be used to describe very interesting things. As you go up the math you need becomes more and more intertwined with the physics you're doing.

I'm currently a physics undergraduate and I'm torn because I'm on my fourth semester and I can't decide whether or not to change my major, I comletely love physics and I absolutely adore all the math complexity behind it, when I see the electives I gravitate (no pun intended) more to the more theoretical physics electives and I also can take math electives which I will do, I'm not very fond of the labs so far they all have been nothing but a let down so I don't know what to do, I want to still study physics but I also really really want to study math I would like to do the math in physics instead of the lab work. The one thing I like about my university is that all the math classes I take are very much pure math, I could relate to many of the subjects this video covered in regards of pure math, and I actually love all of those subjects I'm planning to take topology next semester and I've already done my fair share amount of studying so I'm excited. So yeah I love math and physics just not a fan of the lab work, though I think if given the choice again I would pick physics everytime.

In the University of Zurich and ETH Analysis classes are what you call "Real Analysis". Every CS, Physics, Math and even engineering students have to prove Analysis-Basics (and linear Algebra) in the first semester. In Zurich-University Physics and Math students do the same courses. So your categorization seems relative to the institution...

OMG! I have this problem right now and I'm so happy this video was suggested SO HELPFUL!

Thank you so much for this breakdown! I was an English Education Major before but now I am majoring in Mathematics with a concentration in Pure Mathematics and Mathematics Teaching. My plan is to definitely go into mathematical research.

This channel is a treasure for students. Thank you zach.

As a double major in math and physics (math graduate now), I will say physics is all about getting intuition of the reasons of phenomena, and math is all about logic. To put it more precisely, physics has math only as tool, and the meaning of the result is more important. Thus approximation and intuition is the main part that you are learning. The reason being physics is “telling the story of the phenomena in real world and making sense of it”. You can only “approximate” the real world, and can never “derive” the real model of the world. There’s only better model, no best model. Math is all about logic and hence rigor. A class always starts from definitions and moves forward, as how math textbook is written. But that’s the result of the theory. There’s always motivation and reason of defining things as it is to establish the theory. Mathematicians always try to make least assumption possible (you can already see this from the postulate 5 story). And the rigor is more important in math that, at every step, you have to make sure you are making deductive argument (while in physics it is always almost inductive). You always have to consider the most general situation. If you miss any possibility, the proof fails. To conclude this, I will describe how you can expect after you finish the degree. After you finishing physics undergraduate, you can study further as physics graduate student for more specific subject, or you can move to engineering as you will equip yourself with all abilities you need to proceed (still need effort to cover the basics in engineering though). After finishing math undergraduate, you will have finish a hard training of logic, so getting into any science territory will be possible. You will have to learn everything for scratch, but your logical thinking should help you make it faster along the way. As to proceed further in math, I would say you are only at the start point. Analysis (ODE, PDE, functional analysis etc) starts from Lebesgue’s integration theory, and algebra branches starts to have dedicated courses on graduate level.

Instructions unclear - now majoring in theoretically transsexual gender dance theory

This is just the channel I was looking for. Thank you!

I really appreciated the caveat at 17:31, I definitely agree with what you're saying here. I got my Bachelor's almost 3 years ago and am finally realizing the (sometimes) harsh job reality. I've decided to go to Grad School, but I still found this video very helpful with that decision :) Thank you!

Here i am, an engineering student watching a battle between Math and Physics. Great!

Great video! This is exactly what I was wondering about! Hope to see more vids, subbed! :)

Physics and mathematics both are interesting subjects both are my favourite they clear our logic and know everything about the world

Doing a great job man....love you!

Informative video! 😊

A lot of us going more towards theoretical physics see these upper level math classes, or classes in proofs, differential gemoetry, number theory, etc.

Choose a math major. Where if you plan on going into grad school from a math undergrad, you have the option of doing a graduate physics degree but that’s not always an option the other way around. If you choose not to go to grad school, math majors are also a lot more employable than physics majors. Mathematics- and especially areas like abstract algebra, group theory, game theory and number theory are highly applicable in areas like computer science, economics, finance, cryptography etc. which means you can branch off and become an expert in other fields.

In mathematics you can specialize in at least as many fields, not just pure and applied

My major is Mathematics, otherwise, I really love Physics. Both solving problem itself and learn more about Physics are wonderful!

This is a pretty good video!

Hey MajorPrep, awesome video. I was wondering if you could talk about theoretical physics, because I enjoy the math part of physics and would like to know more. Thanks!

Study Integral Equations: Laplace, Fourier Transforms, Green Functions, are all examples of either Volterra or Fredholm Equations. There's a nice (short) classical text, "Integral Equations" by F. Tricomi. It's a big eye opener to study the above in a more generalized and abstract context.

I think doing a pure maths course would work for me as I love doing calculus and integrals instead of doing force and acceleration etc, from studying but math and physics in my leaving Cert, I would prefer maths 100%

Particle physics and general relativity require the undergrad abstract algebra. Also most universities at least here in the UK, require physics students to do at least an introduction module in pure math in order to permit them to study quantum mechanics and electrodynamics (special relativity applied to Maxwell's theory), while math students don't need need anything more than a weekend to see some elementary application of their second year material. On the other hand, experimental physics and engineering is the reverse, multivariate calculus and a little complex analysis is more than enough for physics students, but for the math students having to deal with all the physical models is simply not possible.

I needed this video.

Thanks so much I really appreciated it and thank you again 😁😁

I love calculus and I'm obsessed with the subject. I wish I was a physics major instead of math since it consists of heavily applied calculus. However, I am content with the education I have. I do plan to study physics further into my career.

Excellent channel!

Do you have anything in your channel related to Engineering Physics? I couldn't find any. Thanks for the great video btw!

*IS MATH RELATED TO SCIENCE*

Basic Complex Analysis is covered in many physics curriculums in "Advanced Math for Engineers and Physicists" courses.

Thank you for the video.

Just want to add that having some education in more than one area is a plus. A person I know had a data processing degree. Couldn’t find a job because he could get a computer to do anything, but didn’t know what to get the computer to do. Took some business administration classes and got a job as a systems analyst for a major utility.

Hi I will stay with physics and just tale what ever I need in math to help me down the road. I will say you were very help full, thank you

Damn.. Physics student here, and i have taken proofs (as part of my analysis 1 class that sounds exactly like the real analysis you described in your video) and abstract algebra (as part of my linear algebra class). And thats only the first semester of Physics bachelor in Germany. I'm fked....

Am a mathematical science student,though I was interested more in Physics,some consepts like linear algebra,calculus 1-3,topology are common in both courses

I enjoyed my first year in Pure Math, but I'm moving to Electrical engineering. I personally deem that besides the proof/reasoning/set theory (math method) class was the most useful one, and the rest of the curriculum is kind of more or less useful. I don't see Pure Mathematics is a worth majoring for me, but I do like studying mathematics casually to explore some structures that can help me categorizing concepts and solve problems. Ultimately, I see mathematics as just a collection of general reasoning patterns and concepts that could be useful for problem-solving. While the symbolic manipulation can be fun at times, I don't see a point investing too much time on it.

Complex Analysis has lots of applications in electricity and magnetism, so I don't know why an applied math major or physics student wouldn't take it. At my college electrical engineering students have to take it.

I'd like to add that this varies from university to university. I had real analysis I and II instead of calc I-III, and complex analysis.

I took Fourier anal Complex anal, tensor calc in addition to calculus, differential eqns, linear algebra.

I'd love to see your take on condensed matter physics vs materials science vs chemistry.

Love ur vids!

I'd just like to point out that as a first year physics student, we are being taught a bit of real analysis as part of our calculus class. (10:30) So at least in my case, this is not unique to math major students.

For GCSE higher maths we actually do proofs, like one that I did was prove that the sum of two odd numbers is always even: n=> even k=> even (2k+1)+(2n+1)=2n+2k+2 =2(n+k+1) *Anything multiplied by 2 is even

In my school as a Physics Major, We took Calculus 1 and 2 from the Math department and is proof based. Since we already did compute calculus in high school. Then we also took Linear Algebra, Probability, Complex Analysis, Mutivariable Analysis, and Real Analysis 1( Metric spaces) from the Math department. The Physics department taught two Math classes. MATH METHODS 1 AND 2. Math methods 1 was Vector Analysis, multivables and Intro to Linear algebra. Math methods 2, Linear Analysis, Differential and Partial differential equations.

I've been increasingly under the impression that while Pure mathematics doesn't have any immediately obvious real world applications, these sorts of exercises can explain the very fabric of our reality in ways that we cannot directly observe, and so would end up being very relevant to theoretical or quantum physics where you're now working in that nebulous zone of exploring higher dimensions, etc. It's funny because I thought I hated math if it wasn't something that I could directly apply around me, but I've found I actually love the more abstract, higher mathematics. I'm a newly starting out physics major right now and really want to immerse myself in both so its a tough decision.

Finished up my bachelors in Applied Math last year, it was such an incredibly rewarding and difficult journey but I wouldn't trade that for anything. Plus now that I'm not in university anymore I've been reading through Leonard Susskind's Theoretical Minimum series alongside other texts.

To be honest when you actually spend a week getting into it, a lot of these higher level math concepts are really not as complicated as they're made out to be. Maybe that's just me but tbh it's all just more clever ways to do addition.

Year 4 pure math student, only recommend if you are very very very interested. It just different, the thing with this is that pure math is abstract, you can’t rely on common sense, you just have to guide your self through practice and try to understand. I always love math, and it has been insanely worth it. Real analysis, omg I remember the open set closed set, point-wise vs uniform conversion, definition of integrability, good old times. I think the hardest topic here has to be the proof for mean value theorem. Took me like 2 months to understand that proof, and able to recreate it. Another thing is to define a goal function, and rearranging functions into more useful for by adding zero and such. Very fun good old times, but now I am just doing smooth manifolds and groups and rings.

Constructing proofs in high school geometry turned on the Math lightbulb for me. Eureka!! (Re-)Discovering Physics in my Senior Year set me on my path. As an Undergrad, I got turned-on to Dynamical Systems, Chaos, Collective Phenomena and Condensed Matter Physics. I was going to be a Theory Geek! In Grad School I learned that there is a whole new level to being a good Theory Geek! (There's people who solve extra problems in Jackson "for fun".) I also learned that my knack is really in the lab and data analysis, which has served me well for the past 30+ years. About 15 years ago, I came across the field of System Engineering, which is what I'm predominantly involved with, especially verification and more data analysis.

3:00 this is how I was taught T=Temperature (in Celsius, Fahrenheit or Kelvin) and t=time(in seconds)

Coming back to the mass on the spring, a physic major will learn how to derive the equation. Deriving equations of motion from forces or energy principles is a big part of what physics majors do, especially in the upper level courses. But we do a few in intro physics (such as the mass on a spring). As a physics major, your first differential equation will show up in a physics course, before you learn what they are and how to solve them. Generally, physics majors spend a lot of time solving problems where they are asked to derive the equation that describes the physical situation. Solving is secondary and sometimes not even part of what the problem asks. Often, approximations are made and some sloppy math is used. The emphasis is on understanding and using first principles, and then gauging whether the answer makes sense or not. The solving part is the necessary evil that comes in between.

Hey just curious here. Can I do data science in post grad without having stats as a major in my undergrad? I mean I have done Mathematical Statistics as an elective up to 2nd year and I've heard it's quite important for data analysis

I can't decide,I like both physics and maths. Is it possible to have knowledge in both ? Any way you gave a very clear understanding of both of them.

Best answer: Major in both Math and Physics.

So I could take physics major required classes, and a math elective classes? Could I do this with an Engineering Physics major too? Where I get experience in physics, math, _and_ engineering?

I'd like to add that pure mathematicians can care about physics, look at the analysis of Hilbert spaces for example. There even exists mathematical physics which is taking problems from theoretical physics, rewording them in terms of more general mathematics to make it into a math problem, and then try to solve that in order to help physics :)

I love your videos.

My thoughts on these are: Pure Math made you to think critically And applied maths made you to solve problems by using some available clues that around Meanwhile physics made you to think outside of the box and using your experience from the past to solve your problem

I started with peteoleum engineering, to fall in love with math, which finally took me to love physics. I'm about to become a physicist now, and after that i want to study astrophysics

I am interested to major at math

Couldn't decide. Currently double majoring in physics and math.

Yep, definitely pure maths for me. I love proofs! Real analysis and number theory sound fun😄

Group theory is a "required" course for physics and chemistry students studying physical chemistry, or crystallography.

You can't go into accounting with math/physics degrees. Accounting is a very technical/skills based field. It's not as difficult as math but you need to have the technical background in accounting in order to go into it. Finance only marginally needs technical knowledge so math majors easily fit in.

I had to choose between these two majors 3 years ago. I went with neither, instead I applied for engineering.

Mfw even as a physics major I still took: 2 courses of linear algebra, 1 course of linear geometry, 4 courses of real analysis (2 for 1 variable and 2 for multiple variables), complex analysis, and even functional analysis (even though we never really had a proper topology course and just had the bare bones of the subject from all the analysis we had done before). Heck, I still remember joking about how glad I was I "decided to take a maths major" with my classmates during the first 2 years. I kind of feel like a crossbreed between a physics and a pure math major.

You are the best.

Math is to physics, what linguistics is to literature!

So I want to study physics and do research but I do not find the idea of becoming a professor appealing, can I do more of the theoretical stuff (like astrophysics or particle physics) without being a professor?

0:56 was an eye-opener for me tonight. Doesn't applied physics focus on classical and some modern physics?

You are the best

Note that maths and physics (and also to some degree how they relate) is very different in Europe then in the US

I would recommend to look into the study Of econometrics because it has a lot of these topics in their undergrad program

It is interesting to be thinking between two hardest majors... there are plenty of other "easier" things to learn (though might require more brute-force efforts)

I understand that when it comes to majoring in physics and math, you are able to get a job as a crytographer, engineer, computer scientist, and other neat jobs like that. So will I have to major in applied physics or math to be able to get those types of jobs, and will I still be able to get a job as a teacher/professor with that majors(to keep my options opened)?

In my university in Ireland, the physics and Maths first years are almost completely identical, and can be identiacal depending on what electives you pick. Physics is treated more as maths course than a science. For example the physics and maths students would take courses like Linear Algebra and Calculus, whereas other sciences like chemistry and so on would do something like: Calculus for Scientists, or Numerical Methods for Scientists, which would be a more simplified class leaving out alot of proofs and so on. Interesting to learn that in America, physics is treated more like a science, separate from maths, whereas in europe I think Physics isnt separated as much. For example in Cambridge there is no undergrad option for Physics, only Mathematics. How much maths and/or physics you do depends solely on the individual classes you pick towards the end of the course.

Does this mean I’m screwed if I want to be an electrical engineer after I graduate from Cal? Because I’m majoring in physics. I know I can work in that field, but is it going to be hard for me, since it’s not an engineering degree? I’ve looked up several open positions at various engineering companies, and they all say! “Engineering, physics, computer science, or other related degree,” but will I always be second choice for a typical EE position?

Awesome explanation Thanks

Do you think going from a math undergrad to an engineering masters is a feasible route?

I’m in this position right now. I’ll probably go for maths, has more job prospects and I’m better at it I think

I'll take Physics, thank you very much.

What I do is study physics but visit math lectures when I have time. So far, the math they do is very similar to the math we do, so it's a good way for me to revise.

I am very good in elementary algebra and yet, I suck at doing Coulomb's Law. So I think that physics is harder than elementary algebra and even calculus. Even Ohm's Law is very hard for me to solve.

Just fantastic materials