Math/science sequence up to Astrophysics?

[dreamer17]

Hi,

I'm new to PhysicsForums.
I am a sophomore in high school and currently in Geometry/Honors Chemistry. I am fascinated with astrophysics, and I really want to learn everything about it. I will be teaching all of this to myself, so I'd just like the sequence. I think it goes like this..

Trig --> Calculus --> Multivariable Calculus --> Linear Algebra --> ? ..Then what?

I'll take Honors Physics next year and AP Chem. by senior year.

So far, I understand the basics of trig and a little calculus. I don't want to wait... I am so inspired and want to learn everything about black holes, worm holes, galaxies...EVERYTHING!

PS: Don't tell me to wait or anything! I really want to do this!

Thanks! :)

- Brooke

 

[Nabeshin]

Well, most astrophysics will get by with just the mathematics you have listed here, with the addition of a course in differential equations (and perhaps partial differential equations).

Slightly more advanced mathematics is necessary to learn about General Relativity (the theory of black holes, worm holes, and cosmology), but likely if you're approaching the subject from an astrophysics perspective, you can learn everything you need to know in the class (or book).

 

[dreamer17]

Ok, thanks. So if I do this:

- Self-study AP Calculus AB/BC - which I heard covers up to Calc II
- MIT Opencourseware up to Physics II
- and my science sequence

Will I be good for astrophysics?

Thanks!

 

[Nabeshin]

Ok, thanks. So if I do this:

- Self-study AP Calculus AB/BC - which I heard covers up to Calc II
- MIT Opencourseware up to Physics II
- and my science sequence

Will I be good for astrophysics?

Thanks!

You'll likely want more physics than that. You'll probably want a good course in quantum mechanics, electrodynamics, and thermodynamics and statistical physics, all of which are important in astrophysics.

Chemistry isn't really important at all in astrophysics (although it does become important in some areas under the broader envelope of astronomy), as the name suggests, it's really just applied physics.

 

[dreamer17]

Thanks! So as of today, should I start with Physics I (MIT Courseware) and then move up from there? What order should I go in?

 

[Nabeshin]

Thanks! So as of today, should I start with Physics I (MIT Courseware) and then move up from there? What order should I go in?

Seems reasonable, good luck.

 

[twofish-quant]

So far, I understand the basics of trig and a little calculus. I don't want to wait... I am so inspired and want to learn everything about black holes, worm holes, galaxies...EVERYTHING!

Once you get to multivariable calculus and linear algebra, you should have enough for most astrophysics. You can get a feel for how much you need to know by going to http://adswww.harvard.edu/ and looking at some of the papers. Once you have PDE's and linear algebra, most physics papers outside of particle physics will be comprehensible at least as far as the math goes.

 

[twofish-quant]

Thanks! So as of today, should I start with Physics I (MIT Courseware) and then move up from there? What order should I go in?

You might want take things in same order that MIT students do...

http://web.mit.edu/catalog/degre.scien.physi.html

The typical sequence is

8.01 - classical mechanics
8.02 - e&M
8.03 - springs and things
8.04 - quantum
8.044 - thermo
8.05 - more quantum
8.06 - more classical mechanicsAlso keep checking for MITx.

http://web.mit.edu/newsoffice/2011/mitx-education-initiative-1219.html

One other thing is that you'll probably do better if you arrange some sort of study group. Let me know if you find anything.

 

[mal4mac]

It will take ten years working flat out at the hardest maths/physics courses in school/university just to gain a professional level of knowledge about one area of astrophysics.

You can't learn "everything", even if you spend ten years becoming a top string theorist. I just read this in Weinberg's "Dreams of a final theory":

"String theory is very demanding; few of the theorists who work on other problems have the background to understand technical articles on string theory, and few of the string theorists have time to keep up with anything else in physics, least of all with high-energy experiments." p.174

If you fancy being an expert in black holes, try reading:

Black Holes and Time Warps: Einstein's Outrageous Legacy by Kip S. Thorne

Then try reading all the technical references in his bibliography, then go onto his website and read everything he's done since this book was published (and then everything he's read.) Then you will be close to knowing as much as Kip Thorne about black holes - which still isn't "everything", but as close as you are going to get... and as for galaxies... well, sorry, you've only one life!

 

[Nabeshin]

It will take ten years working flat out at the hardest maths/physics courses in school/university just to gain a professional level of knowledge about one area of astrophysics.

You can't learn "everything", even if you spend ten years becoming a top string theorist. I just read this in Weinberg's "Dreams of a final theory":

"String theory is very demanding; few of the theorists who work on other problems have the background to understand technical articles on string theory, and few of the string theorists have time to keep up with anything else in physics, least of all with high-energy experiments." p.174

If you fancy being an expert in black holes, try reading:

Black Holes and Time Warps: Einstein's Outrageous Legacy by Kip S. Thorne

Then try reading all the technical references in his bibliography, then go onto his website and read everything he's done since this book was published (and then everything he's read.) Then you will be close to knowing as much as Kip Thorne about black holes - which still isn't "everything", but as close as you are going to get... and as for galaxies... well, sorry, you've only one life!

String theory is not astrophysics. As two-fish notes, a good understanding of pde and linear algebra is sufficient for most contemporary astrophysics papers. It isn't too difficult to attain this level of familiarity. Making a research contribution, however, is a much bigger investment, but not really in mathematics so much as in time and depth.

As far as any branch of physics goes, astrophysics is probably the MOST approachable (in my opinion). Just browse through astro-ph, a lot of the papers are simply observational in nature, but even in those developing some particular theoretical model, the math is no more advanced than pde (i.e. no group theory, algebra, diff. geometry, etc.).

Note: One of the most difficult maths in astrophysics comes from error estimation and statistics. As an observer (someone who does not intend to contribute, but rather simply to follow the field), this is almost completely irrelevant, since what you're likely interested in is more the conclusions and model rather than these nitty gritty details.

 

[twofish-quant]

It will take ten years working flat out at the hardest maths/physics courses in school/university just to gain a professional level of knowledge about one area of astrophysics.

I don't think that is true.

I think that most junior level undergraduates are at the point where they can do useful work in most fields in astrophysics. One good thing about astrophysics is that there are so many different problems and fields that it's not hard for someone to develop an expertise in an area and know more than an expert in some other field.

For example, I know a lot about type II supernova. I don't know anything about say interstellar gas clouds or planetary orbital theory. A clever junior level undergraduate could spend two weeks reading articles and know more about the physics of Mercury's orbit than me. With about six months of work, he could probably know as much about Mercury's orbit as anyone else in the world.

"String theory is very demanding; few of the theorists who work on other problems have the background to understand technical articles on string theory, and few of the string theorists have time to keep up with anything else in physics, least of all with high-energy experiments." p.174

And for astrophysics, string theory is totally useless.

Then try reading all the technical references in his bibliography, then go onto his website and read everything he's done since this book was published (and then everything he's read.) Then you will be close to knowing as much as Kip Thorne about black holes - which still isn't "everything", but as close as you are going to get... and as for galaxies... well, sorry, you've only one life!

No. It doesn't work that way.

What you do is to read up on the literature, and then think about a problem that no one is looking at. I'm pretty sure that if you read Kip Throne's books, you'll find something that is interesting about black holes that he hasn't had time to research, and one purpose in going to graduate school is so that you can talk to Kip Throne, and ask him directly "so can you think of some problems that I can work on?"

Everyone in astrophysics tend to be hyper-experts in one thing, while knowing very little about something else. One reason graduate research is different than undergraduate is that as an undergraduate, you are asking the professor "tell me what you know" whereas in graduate school, the question is "tell me what you *don't* know."

 

[twofish-quant]

Note: One of the most difficult maths in astrophysics comes from error estimation and statistics. As an observer (someone who does not intend to contribute, but rather simply to follow the field), this is almost completely irrelevant, since what you're likely interested in is more the conclusions and model rather than these nitty gritty details.

I don't think that the math is particularly difficult. It's just that it's not part of the standard undergraduate physics curriculum which means that most people with physics backgrounds (myself including) are shockingly weak in this area.

 

[Nabeshin]

I don't think that the math is particularly difficult. It's just that it's not part of the standard undergraduate physics curriculum which means that most people with physics backgrounds (myself including) are shockingly weak in this area.

Well, that's why I say it's difficult :) I agree it's probably not any more 'intrinsically difficult' (whatever that means), it's just the math that always has me most outside my comfort zone.

 

[mal4mac]

String theory is not astrophysics. As two-fish notes, a good understanding of pde and linear algebra is sufficient for most contemporary astrophysics papers. It isn't too difficult to attain this level of familiarity.

It might not be astrophysics to you, but it is to these guys:

"Searching for Inflation in Simple String Theory Models: An Astrophysical Perspective"
http://arxiv.org/abs/0709.0002

Anyway, I produced that quote just as an example of how difficult it is to learn "everything".

As far as any branch of physics goes, astrophysics is probably the MOST approachable (in my opinion). Just browse through astro-ph, a lot of the papers are simply observational in nature, but even in those developing some particular theoretical model, the math is no more advanced than pde (i.e. no group theory, algebra, diff. geometry, etc.).

But that's a subset of astrophysics. The guy said he wanted to know "everything" and "black holes" were top of his list - I think for that spec. ten years of hard work is a reasonable estimate...

The least approachable course I had at university was an MSc level course in astrophysics. Ten years were not enough :) Approachability depends on the lecturer/textbook/paper that's in front of you...

 

[mal4mac]

No. It doesn't work that way.

What other way would you learn "everything"? Or get close to it...

Or do you mean - that "a life (in science) doesn't work that way" - if so I'd agree with that...

What you do is to read up on the literature, and then think about a problem that no one is looking at. I'm pretty sure that if you read Kip Throne's books, you'll find something that is interesting about black holes that he hasn't had time to research, and one purpose in going to graduate school is so that you can talk to Kip Throne, and ask him directly "so can you think of some problems that I can work on?"

Yes - that's how to do research, or 'a life in science', or 'a life'. But the OP wanted to "know everything". A Quixotic aim methinks...

 

[Mépris]

How well did you do on Algebra? Don't try to rush into it.

I was at a point where I could integrate ln x^3 but couldn't prove that sqrt2 + sqrt5 is irrational. Actually, I'm still at that point and I'm still trying to learn algebra properly. Once I'm done with that, I will read Euclid and only then will I take on a book like Spivak or Apostol.

I've also observed that class mates of mine had a lot of trouble with calculus, not because they didn't know how to integrate but because their algebra was poor. Poorer than mine in fact, and I suck. Shame AP-like math doesn't really do a good job at teaching. Or at least, that's the impression I get.

MIT uses Apostol for 18.01 - or I think they do, for the "honours" variant of the course - and I guess if you can do that without any difficulties, you should be good to go. I haven't tried myself and I think I could pull through considering I've done monkey calculus before and did well at it but I'd rather learn my algebra well first...

 

[Nabeshin]

It might not be astrophysics to you, but it is to these guys:

"Searching for Inflation in Simple String Theory Models: An Astrophysical Perspective"
http://arxiv.org/abs/0709.0002

Anyway, I produced that quote just as an example of how difficult it is to learn "everything".

I know, this is precisely the kind of thing I intend to do graduate study in next year. Certainly we dream of making strong astrophysical predictions, but we have to be a little realistic about the state of the theory. Anyways, this is a whole different thread :)

But that's a subset of astrophysics. The guy said he wanted to know "everything" and "black holes" were top of his list - I think for that spec. ten years of hard work is a reasonable estimate...

Haha, I suppose. I didn't take the word everything as literally as you did, I suppose. An undergraduate level GR course will give you a lot of knowledge about black holes (you can even study them at a lower level, as in taylor & wheeler). To get to the research frontier on black holes though, you're probably about right (sophomore in HS -> 4th or 5th year of graduate school, ~ 10 years).

The least approachable course I had at university was an MSc level course in astrophysics. Ten years were not enough :) Approachability depends on the lecturer/textbook/paper that's in front of you...

Indeed, preferences...

How well did you do on Algebra? Don't try to rush into it.

I was at a point where I could integrate ln x^3 but couldn't prove that sqrt2 + sqrt5 is irrational. Actually, I'm still at that point and I'm still trying to learn algebra properly. Once I'm done with that, I will read Euclid and only then will I take on a book like Spivak or Apostol.

I've also observed that class mates of mine had a lot of trouble with calculus, not because they didn't know how to integrate but because their algebra was poor. Poorer than mine in fact, and I suck. Shame AP-like math doesn't really do a good job at teaching. Or at least, that's the impression I get.

MIT uses Apostol for 18.01 - or I think they do, for the "honours" variant of the course - and I guess if you can do that without any difficulties, you should be good to go. I haven't tried myself and I think I could pull through considering I've done monkey calculus before and did well at it but I'd rather learn my algebra well first...

Worth stating that formal, abstract algebra (or analysis, as in the case of Spivak) is not really used in astrophysics. The 'monkey' algebra and calculus, however, is ubiquitous.

 

[eumyang]

MIT uses Apostol for 18.01 - or I think they do, for the "honours" variant of the course - and I guess if you can do that without any difficulties, you should be good to go.

Not quite. The text by George Simmons (published by McGraw-Hill) is used for 18.01 & 18.02. The Apostol texts are used for the "Calculus with Theory" courses (18.014 & 18.024).

 

[twofish-quant]

It might not be astrophysics to you, but it is to these guys:

"Searching for Inflation in Simple String Theory Models: An Astrophysical Perspective"
http://arxiv.org/abs/0709.0002

Curiously that paper is about how string theory *isn't* astrophysics. They show that some recent string models don't result in inflation. This is a good paper for explaining how string theory (as of now) is pretty much useless for anything in astrophysics.

Anyway, I produced that quote just as an example of how difficult it is to learn "everything".

You don't really have to. Astrophysics is something of a potluck dinner. When I need nuclear equations of state, I don't know how to calculate them myself, so I go to the experts on that topic, and I get a table that I can put into my computer programs.

The guy said he wanted to know "everything" and "black holes" were top of his list - I think for that spec. ten years of hard work is a reasonable estimate...

An intro book to black holes "Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects: Stuart L. Shapiro, Saul A. Teukolsky" is accessible to an senior undergraduate. One thing about black holes is they are not that complicated if you focus on the simple bits.

The other thing is the research is hard, but not because it's hard to understand. It took me about five years to write my dissertation, but it's something that most junior physics undergraduates can read without any problem. If you are working on an original problem, you will go down blind alleys and have to do a lot of grunt work, and that takes a very long time. Once you've figured it out, then you can just write it up, and someone else can understand what you did in a day or two.

The least approachable course I had at university was an MSc level course in astrophysics. Ten years were not enough :) Approachability depends on the lecturer/textbook/paper that's in front of you...

One reason that I think that the OP is on the right track is that most of the things that you learn in astrophysics is stuff that you teach yourself. If the textbook makes no sense, get another textbook. The other thing about survey courses is that they are survey courses, so if you are doing research then much of that turns out to be not directly useful for the research that you are doing.

 

[twofish-quant]

Certainly we dream of making strong astrophysical predictions, but we have to be a little realistic about the state of the theory. Anyways, this is a whole different thread :)

One thing that is important in research is to research problems that you can get a dissertation out of. String theory is not ready for prime time, and it may not be ready ever. The possibility exists that it's a massive red herring, and the answer is elsewhere.

That's not like things like gas dynamics or E&M. We know that they work, and they are "ready for business."

An undergraduate level GR course will give you a lot of knowledge about black holes (you can even study them at a lower level, as in taylor & wheeler). To get to the research frontier on black holes though, you're probably about right (sophomore in HS -> 4th or 5th year of graduate school, ~ 10 years).

It depends on what you want to study. If you want to study quantum gravity, that will take a lot of time, but that arguably is not astrophysics. If you want to study how accretion disks work, or how black hole magentospheres work, or do dark matter statistics, gravitational lensing, evolution of supermassive black holes, black hole formation, computational general relativity, etc. etc. It's not that hard. One thing about research is that you want to avoid any unnecessary math, and people in those fields work hard to simplify the math to the bare minimum that you need to understand what you are studying.

Using overly complicated math is usually a sure sign that you really have no idea what is going on.

 

[Mépris]

Not quite. The text by George Simmons (published by McGraw-Hill) is used for 18.01 & 18.02. The Apostol texts are used for the "Calculus with Theory" courses (18.014 & 18.024).

Yes, that's the one but at the time, "honours" was the closest word to it I could find. I wonder why they call the .014 and .024 courses "with Theory" but their more "math intensive" variant of their differential equations class is called "honours differential equations".

---

Anyway, I can be a bit obsessive about knowing the "how and/or "why" of things, which may or may not be a good thing. I don't think I'd be able to do the .01 variant (whether via OCW or irl at any uni) when I know that there's an alternative which takes a more thorough approach to the same topic, i.e, .014.

 

[twofish-quant]

Also when people talk about astrophysics, they focus far far too much on things like string theory. Don't worry if you don't know the mathematics of string theory, since most astrophysicists don't understand it either, and if it becomes important, someone will figure out a way of simplifying it for people that are not math uber-geniuses (and most astrophysicists are not).

GR, for example, has been "dumbed down" so that mere mortal astrophysicists can use it. Here's three pages of math, and then the final equation that you can use without thinking about it much.

One thing to remember, is that no string theorist has ever won the Nobel Prize, whereas the last astrophysicists that won the Prize did so for doing some things (accelerating universe) that requires sophomore-level physics math.

Something else that's good news is that it's not as if you have to wait ten years before doing anything productive even for the weird stuff. If you want to get into deep quantum gravity, then you have to learn some more basic stuff first, and once you learn the basic stuff, you can start going useful things. The other good news is that the math and science you'll learn is going to be useful outside of physics. Calculus is useful in a 1000 other places.