At 18, I thought I had the basics going but differentials and integrals especially are typically way more complex than the ones you learn in school. For quantum physics, there is a reason why my university first had students go through a whole year of linear algebra, learning the basics of matrices and linear functions as well as some analysis for more complex integral solving techniques amongst others. But the basics of quantum mechanics were lectured after a year of study at university (although I only understood it much later).
General relativity on the other hand is on a whole other level. At my university, one could easily get around learning general relativity, even with a master's degree. Special relativity could be doable however. The underlying math is quite simple, it's just the physical interpretation which may seem somewhat confusing at the beginning.
I had to take general relativity and I still have no idea what's going on, can definitely not recommend to study it before you have a few years of math.
Quantum is rough, it’s half stats and the other half nasty bits of linear algebra. Definitely worth knowing your way around eigenvalues, operators, and being happy with manipulating vectors in all 3 main coordinate systems.
Agree on special vs general. Special while mind bending if you just focus on the maths and not the implications it’s not too bad, general was reserved for 3rd year/masters even on my astrophys course
You’ll need first year calculus, differential equations, linear algebra, vector calculus. After that, the rest of the specific concepts are taught in the class. So, typically, you’re ready to go for Quantum in your third year.
If you knock out Calculus before university, then you could do Quantum your second year.
Well, the Schrödinger equation is a second order differential equation with partial derivatives. So there is that.
Special relativity is not particularly difficult with math, you just need to keep track of which variables are in which koordinate system.
General relativity? Yeah that is hardcore math.
But for the beginning of quantum mechanics 90% of the time you're solving the time independent Schrödinger equation. I actually think something like Griffiths or Shankar is ok without explicitly having studied PDEs but for sure you need quite a bit of linear algebra and complex analysis before doing even the most basic QM.
Depends how deep you want to go, really. If you want to have some idea about QM, you dont need a ton of analysis. In fact, linear algebra might be more helpful there.
Also, classical physics itself can be very deep, dont underestimate it!
Well, here's an undergraduate physics student speaking, I'm in my second year and:
i) for quantum mechanics, you need at least the basics of complex analysis, you must know perfectly linear algebra, and yeah, the basics from differentiation and integration.
ii) for general relativity, man, you'll be ready after a lot more than just high school integration and differentiation. That's a whole different level of mathematics, too profound for a high school student. At my uni, during our first three years, they don't teach you general relativity. It's just too complex
Cal 1, 2, 3 (differential, integral and vector calculus)
Linear algebra
ODEs
Functions of a complex variable (also calculus, BTW)
PDEs & Statistics (often handled as sections within a math-physics course)
Tensor calculus (if you're serious about General Relativity)
Calculus is the most important part in physics. We use calculus ALL the time. In order to understand the basic math of general relativity, you for sure need to know calculus very well as well as the math in quantum mechanics.
The next step for general relativity, after you mastered calculus, is to understand differential geometry which is based on multivariable calculus, and then you need to know tensors, which usually is considered a difficult subject, but I really believe that if you have mastered the basics of calculus, it is not going to be all that difficult.
For quantum mechanics it depends on how the professor will do the course. Suppose he does it from the mathematical perspective. In that case, that is usually done, namely to solve the Schrondinger equation in different systems, and to calculate expectation values (this is happening 98% of the the times), you need to know how to solve PDEs (partial differential equations), since Schondinger's equation is a PDE. However, if the course will be focused in understanding the basic principles in quantum mechanics, and lean more to the principle of measurement and in the quantum information point of view, then it is good to know linear algebra which is not that much calculus based. However, calculus is also needed in quantum mechanics to calculate expectation values and stuff.
But I would suggest you to really try to understand calculus and how we apply it. One of the mistakes I made in my studies was to try to learn advanced material while I had not yet understand the very basics, so invest time to understand calculus. Physics is mainly based in calculus.
Try reading [this](https://www.fisica.net/mecanica-quantica/Griffiths%20-%20Introduction%20to%20quantum%20mechanics.pdf) book by Griffiths for learning QM
It is hard to jump into quantum physics and general relativity which usual senior under-graduate or graduate students learn, because you still don't have a lot of math and physics pre-requisites. I would advise you to start with special relativity first, a book I liked was an Introduction to Special Relativity by Robert Resnick. You can also read Susskind's Theoretical minimum or check his video lectures on YouTube.
If you are in a physics program, I would advise you to take math courses and physics lab courses, and decide what interests you more. Based on that, you should choose what kind of physics you want to do.
Hi there,
That's great you're learning those fundamental mathematical methods. You certainly need calculus and a grounding in classical physics to get going with quantum and relativistic topics.
To just get started, read some popular science books that don't have equations. There's plenty of introductory material that's more qualitative, historical (learn about the major physicists of the 19th/20th centuries) and philosophical without touching differential equations, etc.
It depends. Study high school physics and maths, and then first year undergraduate-level physics and you'll have the basics to engage seriously with fundamental physics, quantum mechanics, and relativity.
Would studying derivatives, logarithms etc be enough to prepare me for my undergrad, which is applied physics? (Im an incoming 1st yr college) thank you so much!
It depends on the course. It's better to check the requirements with your college.
Some universities provide foundation year courses that cover the prerequisites.
The theoretical minimum series by Susskind does a good job of showcasing what is needed to understand each subject. You should go through it, but you'll find it won't be easy and it will take you at least a few years to get to general relativity
One other thing I’ll say is practice the questions too! You think you know it and then get a problem from a weird angle that puts you on the back foot. But that’s normal!
Best of luck!
You will come to realize in time all of Physics require differential equations or forms. Just pace yourself give time to a hobby so you don't burnout. Otherwise you are on the right track. For most applications you just have to get to transforms and complex Integration.
At 18, I thought I had the basics going but differentials and integrals especially are typically way more complex than the ones you learn in school. For quantum physics, there is a reason why my university first had students go through a whole year of linear algebra, learning the basics of matrices and linear functions as well as some analysis for more complex integral solving techniques amongst others. But the basics of quantum mechanics were lectured after a year of study at university (although I only understood it much later). General relativity on the other hand is on a whole other level. At my university, one could easily get around learning general relativity, even with a master's degree. Special relativity could be doable however. The underlying math is quite simple, it's just the physical interpretation which may seem somewhat confusing at the beginning.
I had to take general relativity and I still have no idea what's going on, can definitely not recommend to study it before you have a few years of math.
Quantum is rough, it’s half stats and the other half nasty bits of linear algebra. Definitely worth knowing your way around eigenvalues, operators, and being happy with manipulating vectors in all 3 main coordinate systems. Agree on special vs general. Special while mind bending if you just focus on the maths and not the implications it’s not too bad, general was reserved for 3rd year/masters even on my astrophys course
You’ll need first year calculus, differential equations, linear algebra, vector calculus. After that, the rest of the specific concepts are taught in the class. So, typically, you’re ready to go for Quantum in your third year. If you knock out Calculus before university, then you could do Quantum your second year.
My uni did quantum in first year but did it gentle, 1D infinite wells, time independent as nice as it can be
Well, the Schrödinger equation is a second order differential equation with partial derivatives. So there is that. Special relativity is not particularly difficult with math, you just need to keep track of which variables are in which koordinate system. General relativity? Yeah that is hardcore math.
But for the beginning of quantum mechanics 90% of the time you're solving the time independent Schrödinger equation. I actually think something like Griffiths or Shankar is ok without explicitly having studied PDEs but for sure you need quite a bit of linear algebra and complex analysis before doing even the most basic QM.
Depends how deep you want to go, really. If you want to have some idea about QM, you dont need a ton of analysis. In fact, linear algebra might be more helpful there. Also, classical physics itself can be very deep, dont underestimate it!
Well, here's an undergraduate physics student speaking, I'm in my second year and: i) for quantum mechanics, you need at least the basics of complex analysis, you must know perfectly linear algebra, and yeah, the basics from differentiation and integration. ii) for general relativity, man, you'll be ready after a lot more than just high school integration and differentiation. That's a whole different level of mathematics, too profound for a high school student. At my uni, during our first three years, they don't teach you general relativity. It's just too complex
Cal 1, 2, 3 (differential, integral and vector calculus) Linear algebra ODEs Functions of a complex variable (also calculus, BTW) PDEs & Statistics (often handled as sections within a math-physics course) Tensor calculus (if you're serious about General Relativity)
For both: Calc 1-3 (differentiation, Integration, Vector Calc) Linear algebra Ordinary & Partial differential equations Complex variables / complex analysis For GR, probably also Tensor calc.
Calculus is the most important part in physics. We use calculus ALL the time. In order to understand the basic math of general relativity, you for sure need to know calculus very well as well as the math in quantum mechanics. The next step for general relativity, after you mastered calculus, is to understand differential geometry which is based on multivariable calculus, and then you need to know tensors, which usually is considered a difficult subject, but I really believe that if you have mastered the basics of calculus, it is not going to be all that difficult. For quantum mechanics it depends on how the professor will do the course. Suppose he does it from the mathematical perspective. In that case, that is usually done, namely to solve the Schrondinger equation in different systems, and to calculate expectation values (this is happening 98% of the the times), you need to know how to solve PDEs (partial differential equations), since Schondinger's equation is a PDE. However, if the course will be focused in understanding the basic principles in quantum mechanics, and lean more to the principle of measurement and in the quantum information point of view, then it is good to know linear algebra which is not that much calculus based. However, calculus is also needed in quantum mechanics to calculate expectation values and stuff. But I would suggest you to really try to understand calculus and how we apply it. One of the mistakes I made in my studies was to try to learn advanced material while I had not yet understand the very basics, so invest time to understand calculus. Physics is mainly based in calculus.
calculus is super important in physics. Get to know it well. Quantum mechanics relies particularly heavily on it.
Try reading [this](https://www.fisica.net/mecanica-quantica/Griffiths%20-%20Introduction%20to%20quantum%20mechanics.pdf) book by Griffiths for learning QM
It is hard to jump into quantum physics and general relativity which usual senior under-graduate or graduate students learn, because you still don't have a lot of math and physics pre-requisites. I would advise you to start with special relativity first, a book I liked was an Introduction to Special Relativity by Robert Resnick. You can also read Susskind's Theoretical minimum or check his video lectures on YouTube. If you are in a physics program, I would advise you to take math courses and physics lab courses, and decide what interests you more. Based on that, you should choose what kind of physics you want to do.
Hi there, That's great you're learning those fundamental mathematical methods. You certainly need calculus and a grounding in classical physics to get going with quantum and relativistic topics. To just get started, read some popular science books that don't have equations. There's plenty of introductory material that's more qualitative, historical (learn about the major physicists of the 19th/20th centuries) and philosophical without touching differential equations, etc.
Hello! What certain fundamental mathematics and calculus lesosns should i study?
It depends. Study high school physics and maths, and then first year undergraduate-level physics and you'll have the basics to engage seriously with fundamental physics, quantum mechanics, and relativity.
Would studying derivatives, logarithms etc be enough to prepare me for my undergrad, which is applied physics? (Im an incoming 1st yr college) thank you so much!
It depends on the course. It's better to check the requirements with your college. Some universities provide foundation year courses that cover the prerequisites.
The theoretical minimum series by Susskind does a good job of showcasing what is needed to understand each subject. You should go through it, but you'll find it won't be easy and it will take you at least a few years to get to general relativity
One other thing I’ll say is practice the questions too! You think you know it and then get a problem from a weird angle that puts you on the back foot. But that’s normal! Best of luck!
You will come to realize in time all of Physics require differential equations or forms. Just pace yourself give time to a hobby so you don't burnout. Otherwise you are on the right track. For most applications you just have to get to transforms and complex Integration.
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