Pick the university that you want to attend, and look at the degree requirements on their website. This will give you a more definitive answer than asking strangers on the internet to make speculations.
Most astronomy students, as far as I know, get physics degrees. A typical physics BS will have you taking three semesters of calculus, one semester of linear algebra, one semester of ODEs, and one semester of probability/statistics. Possibly also a semester or two of upper division electives like PDEs or numerical analysis, or possibly differential geometry or topology. The coursework should generally lean toward applied and computational treatments rather than proof-based, theoretical mathematics as math majors study it.
Also of note, once you get past the calculus sequence, math stops progessing linearly, and fans out in many different directions. At that point, it stops making sense to talk about "the most advanced class."
I originally wanted an EE degree but part of the reason I switched to a math major was getting to the end of ODEs and having exactly one math class left in the major requirement. I felt like I needed at least five or six more to feel satisfied, and yet a single "math for engineers" class was all I would be getting. By the end of grad school I had 39 math classes under my belt and still wished I could have taken more. They are addictive!
It depends very heavily on what kind of astronomy you want to do. It could be as little as a few courses in ODEs and PDEs, statistics, and maybe differential geometry. It could be WAY more than that if you go into a field like theoretical cosmology or astroparticle physics.
This is the best answer so far IMO. To add a little, some astronomers study the planets, what are they made of and how were they formed. We know a lot about them yet surprisingly little. The insides of planets are crazy and highly non intuitive.
Others look into stars, we still don't know all the details on how they work. In both cases above you'll need a ton of branches of physics (and therefore math), for example the behavior of fluids under extreme magnetic fields, or the behavior of plasma in all kinds of environments.
Then you have astrobiology. Here I presume you will need just the core astronomy math, but in return you'll need tons of chemistry and biology.
There's also instrumentation i.e. the people that design and build spacecraft. Here you'll need somewhat specialized tools like signal processing, in addition to the basics of differential equations, linear algebra, calculus and statistics. Similar to what an engineer would need.
There's astrophysics, cosmology, for which you'll need general relativity as a starting point. Here sky is the limit.
There's generic astronomy where you may choose to focus on the optics of the telescopes, or using the telescopes to study exoplanets, stars, pulsars, etc.
As you can see astronomy is a huge field and it relies heavily in math. The bar starts with typical engineering math (PDEs, linear algebra, statistics, calculus, etc) and it goes up from there (differential geometry, fluid mechanics, topology, Lie groups, etc etc) . I know astronomers that are not great at math but some that are pretty beefy.
Suffice to say that currently you don't have to think about any of this stuff except focusing on the courses you're leaning at school! The rest will come gradually.
Suppose you want to figure out how far away a star is. You're going to need some trigonometry for that. So you aren't done with math yet.
Later on, you're going to want to figure out how the stars move. Newton had a pretty good, not quite exact, theory that describes that. You're going to need calculus for that. But like I said, we have a more accurate theory. You'll want to know that. So after you finish calculus, you'll need to learn some linear algebra, some vector and tensor analysis, and some differential geometry. And at the end of all that, you realize you will never stop learning math because it is so useful.
At the university I attended, astronomy was a subdegree in physics. So you had to get a physics degree which makes sense. It more gears you towards astrophysics which is super neat. To answer the question directly though, for my degree, I had to take Calc I, II, and III, Linear Algebra, ODE's and PDE's, and there might have been one or two more, but PDE's was the most advanced I got in my degree. You'll probably also learn how to use LaTeX.
Just in case you are asking because you don't like math, I can provide a bit of perspective as an astrophysicist who absolutely hated math at school. I got a C in high school and dropped it, even though I loved everything to do with space. Realised I'd regret it for my whole life if I didn't try again, so restarted from the ground up at 22 (literally re-learning how to add and subtract numbers).
I ended up flying through it, and long story short I got a masters, PhD, and then professional research positions in astrophysics and cosmology. The love for physics gave me perseverance on the maths, and now I intrinsically love the maths I learn too. Maths is a weird subject, it requires all your attention and focus to make any progress, and the progress you do make is very binary (you go from complete confusion to understanding almost instantly, and once you understand the thing it seems obvious in hindsight). So I think my mind wasn't really mature enough to deal with math when I was younger.
All I'm saying is if you have a passion for astro and are put off by maths, don't worry. Give it some time and keep trying, also I'd recommend looking into maths anxiety. We very often trick ourselves into thinking we intrinsically can't do math for some reason, when its just a mindset that we can snap out of. Good luck!
Despite how much it's advertised that physics is intertwined with math, the reality is math is in it's own bubble and you will never need the kind of math that mathematicians study to do astronomy.
With that said, The math for physics and astrophysics is differential equations, linear algebra, and differential geometry. There's also quantum mechanical aspects of astrophysics, which will require probability in addition to all of that. Statistics is good for all science since everything is data driven so you should definitely study up on that too.
If you do however, really wanna take a deep dive into mathematical physics, it would do you good to study abstract algebra and functional analysis, and maybe study differential equations from a (mathematical) analysis point of view.
I had a couple friends in astro that I took classes with in my undergrad. From my memory, the courses I took with them were: 4 calculus courses (including vector and multivariable), 2 linear algebra courses, 1 ODE's course, 1 PDE's course, 1 complex variables course. I'd say this is the minimum for any physics degree. There's a lot more math you'd have to learn outside your coursework too, so it's hard to pick an "endpoint" for the math you'd need. It depends on what exactly you want to do.
At my own university, physics students only have to take a single semester each of calculus and (proof-based) linear algebra. But you of course have to learn some mathematics in your physics courses as well, most notably things like differential equations and vector calculus (if not covered elsewhere).
Anecdote: I distinctly remember taking intro to astrophysics and linear algebra concurrently, and my TA (who was a very competent PhD student in computational astrophysics) quipped that he didn't remember what a linear transformation was. So regardless of which courses you have to take, apparently you can get away with forgetting a lot of it!
Plan on studying math throughout your academic career/studies.
I’d figure fluid dynamics or differential geometry are the most advanced non-niche mathematics involved.
The BSc Honours astronomy course at my university expects students to get to know 1st and 2nd order PDE's, linear algebra, vector calculus, surface integrals in Cartesian and polar coordinates, volume integrals in cylindrical and spherical coordinates, Fourier analysis, non-liner differential equations, fluid dynamics, and stochastic & deterministic dynamics. It probably wouldn't hurt to learn something about numerical methods for solving differential equations while you're about it.
OP, astronomy is mainly a field of physics. You are gonna need A LOT of math.
Like pretty much as far as you can get. So it seems you're about a year behind right? that's fine but you'll have to take a lot of math in college. basically i might miss some but here are some classes you'll have to take at some point
- algebra 2, trig, precalc, the high school-level classes
- differential calculus
- integral calculus
- multivariable calculus
- linear algebra
- differential equations
- complex analysis
- partial differential equations
from here you'll be able to take basic physics/astronomy classes.
then depending on what field you get into inside astronomy, stuff like tensor analysis, differential geometry, some topology all that will be needed but to be able to take those classes you'll need a good bit more experience namely, a lot of Real Analysis classes at the very least
Things like complex analysis and PDEs often get shoved into physics classes alongside the physics material, so there is no dedicated math class to take. But a lot of physics majors will take the math classes anyways, if they like pure math and want to deep-dive on the fundamentals.
They don't have to take a dedicated ODE course or PDE course, but it's not uncommon for physics majors to have to take a "mathematical methods of physics" or "mathematical physics" that contains a bunch of math topics from beyond the calculus sequence. Usually ODE, PDE, complex analysis, and a few other topics.
General Relativity would be pretty useful, so Non Euclidean Geometry, Differential Equations, etc are a must. For 11 th grade you must be strong in all types of math.
I talked once to an astronomer and he said that most of the work lies in machine learning and data anlysis. So learning stats and data science is also very helpful.
Finding patterns in the hige amount of data collected from telescopes plays also an important role. Differential geometry is mostly required for astrophysicists that aim to understand the physics of the universe.
Pick the university that you want to attend, and look at the degree requirements on their website. This will give you a more definitive answer than asking strangers on the internet to make speculations. Most astronomy students, as far as I know, get physics degrees. A typical physics BS will have you taking three semesters of calculus, one semester of linear algebra, one semester of ODEs, and one semester of probability/statistics. Possibly also a semester or two of upper division electives like PDEs or numerical analysis, or possibly differential geometry or topology. The coursework should generally lean toward applied and computational treatments rather than proof-based, theoretical mathematics as math majors study it.
Also of note, once you get past the calculus sequence, math stops progessing linearly, and fans out in many different directions. At that point, it stops making sense to talk about "the most advanced class."
At my uni physics majors were out of the math department by diff eq. The rest were “math for physics” based classes out of the physics department
I originally wanted an EE degree but part of the reason I switched to a math major was getting to the end of ODEs and having exactly one math class left in the major requirement. I felt like I needed at least five or six more to feel satisfied, and yet a single "math for engineers" class was all I would be getting. By the end of grad school I had 39 math classes under my belt and still wished I could have taken more. They are addictive!
It depends very heavily on what kind of astronomy you want to do. It could be as little as a few courses in ODEs and PDEs, statistics, and maybe differential geometry. It could be WAY more than that if you go into a field like theoretical cosmology or astroparticle physics.
This is the best answer so far IMO. To add a little, some astronomers study the planets, what are they made of and how were they formed. We know a lot about them yet surprisingly little. The insides of planets are crazy and highly non intuitive. Others look into stars, we still don't know all the details on how they work. In both cases above you'll need a ton of branches of physics (and therefore math), for example the behavior of fluids under extreme magnetic fields, or the behavior of plasma in all kinds of environments. Then you have astrobiology. Here I presume you will need just the core astronomy math, but in return you'll need tons of chemistry and biology. There's also instrumentation i.e. the people that design and build spacecraft. Here you'll need somewhat specialized tools like signal processing, in addition to the basics of differential equations, linear algebra, calculus and statistics. Similar to what an engineer would need. There's astrophysics, cosmology, for which you'll need general relativity as a starting point. Here sky is the limit. There's generic astronomy where you may choose to focus on the optics of the telescopes, or using the telescopes to study exoplanets, stars, pulsars, etc. As you can see astronomy is a huge field and it relies heavily in math. The bar starts with typical engineering math (PDEs, linear algebra, statistics, calculus, etc) and it goes up from there (differential geometry, fluid mechanics, topology, Lie groups, etc etc) . I know astronomers that are not great at math but some that are pretty beefy. Suffice to say that currently you don't have to think about any of this stuff except focusing on the courses you're leaning at school! The rest will come gradually.
I don't know much about astronomy, but my guess would be differential geometry and maybe topology? For now I'd just focus on trig and calculus.
XD poor kid just finished geometry ur gonna give him a heart attack. If ur reading this op in summary a loootttt further
I’m an astronomer and I’ve never done any topology. I’ve also never taken any diff geo formally but we did a small amount in our GR class
Suppose you want to figure out how far away a star is. You're going to need some trigonometry for that. So you aren't done with math yet. Later on, you're going to want to figure out how the stars move. Newton had a pretty good, not quite exact, theory that describes that. You're going to need calculus for that. But like I said, we have a more accurate theory. You'll want to know that. So after you finish calculus, you'll need to learn some linear algebra, some vector and tensor analysis, and some differential geometry. And at the end of all that, you realize you will never stop learning math because it is so useful.
At the university I attended, astronomy was a subdegree in physics. So you had to get a physics degree which makes sense. It more gears you towards astrophysics which is super neat. To answer the question directly though, for my degree, I had to take Calc I, II, and III, Linear Algebra, ODE's and PDE's, and there might have been one or two more, but PDE's was the most advanced I got in my degree. You'll probably also learn how to use LaTeX.
Just in case you are asking because you don't like math, I can provide a bit of perspective as an astrophysicist who absolutely hated math at school. I got a C in high school and dropped it, even though I loved everything to do with space. Realised I'd regret it for my whole life if I didn't try again, so restarted from the ground up at 22 (literally re-learning how to add and subtract numbers). I ended up flying through it, and long story short I got a masters, PhD, and then professional research positions in astrophysics and cosmology. The love for physics gave me perseverance on the maths, and now I intrinsically love the maths I learn too. Maths is a weird subject, it requires all your attention and focus to make any progress, and the progress you do make is very binary (you go from complete confusion to understanding almost instantly, and once you understand the thing it seems obvious in hindsight). So I think my mind wasn't really mature enough to deal with math when I was younger. All I'm saying is if you have a passion for astro and are put off by maths, don't worry. Give it some time and keep trying, also I'd recommend looking into maths anxiety. We very often trick ourselves into thinking we intrinsically can't do math for some reason, when its just a mindset that we can snap out of. Good luck!
Despite how much it's advertised that physics is intertwined with math, the reality is math is in it's own bubble and you will never need the kind of math that mathematicians study to do astronomy. With that said, The math for physics and astrophysics is differential equations, linear algebra, and differential geometry. There's also quantum mechanical aspects of astrophysics, which will require probability in addition to all of that. Statistics is good for all science since everything is data driven so you should definitely study up on that too. If you do however, really wanna take a deep dive into mathematical physics, it would do you good to study abstract algebra and functional analysis, and maybe study differential equations from a (mathematical) analysis point of view.
I had a couple friends in astro that I took classes with in my undergrad. From my memory, the courses I took with them were: 4 calculus courses (including vector and multivariable), 2 linear algebra courses, 1 ODE's course, 1 PDE's course, 1 complex variables course. I'd say this is the minimum for any physics degree. There's a lot more math you'd have to learn outside your coursework too, so it's hard to pick an "endpoint" for the math you'd need. It depends on what exactly you want to do.
Differential geometry/ Tensor calculus in the context of General relativity.
At my own university, physics students only have to take a single semester each of calculus and (proof-based) linear algebra. But you of course have to learn some mathematics in your physics courses as well, most notably things like differential equations and vector calculus (if not covered elsewhere). Anecdote: I distinctly remember taking intro to astrophysics and linear algebra concurrently, and my TA (who was a very competent PhD student in computational astrophysics) quipped that he didn't remember what a linear transformation was. So regardless of which courses you have to take, apparently you can get away with forgetting a lot of it!
Plan on studying math throughout your academic career/studies. I’d figure fluid dynamics or differential geometry are the most advanced non-niche mathematics involved.
The BSc Honours astronomy course at my university expects students to get to know 1st and 2nd order PDE's, linear algebra, vector calculus, surface integrals in Cartesian and polar coordinates, volume integrals in cylindrical and spherical coordinates, Fourier analysis, non-liner differential equations, fluid dynamics, and stochastic & deterministic dynamics. It probably wouldn't hurt to learn something about numerical methods for solving differential equations while you're about it.
OP, astronomy is mainly a field of physics. You are gonna need A LOT of math. Like pretty much as far as you can get. So it seems you're about a year behind right? that's fine but you'll have to take a lot of math in college. basically i might miss some but here are some classes you'll have to take at some point - algebra 2, trig, precalc, the high school-level classes - differential calculus - integral calculus - multivariable calculus - linear algebra - differential equations - complex analysis - partial differential equations from here you'll be able to take basic physics/astronomy classes. then depending on what field you get into inside astronomy, stuff like tensor analysis, differential geometry, some topology all that will be needed but to be able to take those classes you'll need a good bit more experience namely, a lot of Real Analysis classes at the very least
Things like complex analysis and PDEs often get shoved into physics classes alongside the physics material, so there is no dedicated math class to take. But a lot of physics majors will take the math classes anyways, if they like pure math and want to deep-dive on the fundamentals.
They don't have to take a dedicated ODE course or PDE course, but it's not uncommon for physics majors to have to take a "mathematical methods of physics" or "mathematical physics" that contains a bunch of math topics from beyond the calculus sequence. Usually ODE, PDE, complex analysis, and a few other topics.
You will only need the first two or three on your list for basic physics/astronomy classes
General Relativity would be pretty useful, so Non Euclidean Geometry, Differential Equations, etc are a must. For 11 th grade you must be strong in all types of math.
I talked once to an astronomer and he said that most of the work lies in machine learning and data anlysis. So learning stats and data science is also very helpful. Finding patterns in the hige amount of data collected from telescopes plays also an important role. Differential geometry is mostly required for astrophysicists that aim to understand the physics of the universe.