View Full Version here: : Maths in Astrophysics?

06-08-2009, 04:33 PM
Hi all,

This is my first post here so please excuse any ignorance on my behalf!
I'm interested in astrophysics and would like to understand more about the maths involved. I understand that algebra, calculus and trig are important, however I cant seem to find a good book that covers the Maths needed to understand the maths involved in Astrophysics!

I just bought Astrophysics is easy by Mike Inglis, which has very little Maths and would like to learn more. The problem being that my undergraduate science study was in Biochemistry/Genetics based streams, which after some time my VCE Maths and Physics knowledge has decreased (joy of getting old:)

If anyone knows of either; a good book on maths for astrophysics which starts at a basic level and advances to moderate, or a website then that would be quite helpful.

Even a description of what areas in Maths and Physics that I should cover (ie, so I can edit out what I dont need), would be most appreciated.

Thanks in advance.

06-08-2009, 04:58 PM
Welcome to iceinspace Greg. I look forward to seeing the recomendations as well. Nice to have you here and I hope you can input often.
Are you interested in say...gravity..some here are.


06-08-2009, 04:59 PM
What aspects of Astrophysics are you looking at?

I found the Observational Astronomy from Cambridge Press was pretty good, though maybe it doesn't go into the maths of the maths very far. I haven't done maths for a long time and didn't find it too onerous.

06-08-2009, 05:18 PM
Hi Alex and Paul,

Thanks for your prompt replies.

What aspects am I interested in? Thats a really good question, and one that I am yet to answer myself. Gravity is of interest, as well as Stellar Astrophysics and Relativity. I always found those SBS documentaries about black holes to be of interest. Its hard to answer as I have read quite a bit of theory but whenever I browse academic books on the subjects I get lost quite easily.

Basically I need to brush up on my Maths to have a greater appreciation for the research and findings involved in Astrophysics, however its been quite some time so I'm unaware of where to start.

Any pointers are much appreciated.


06-08-2009, 05:30 PM
Maybe you might consider doing an external maths course like the ones recommended by Swinburne University Astronomy Online.


You can just get the books or actually enroll in Unilearn. I have just the books and it wasn't too bad a slog to get through.

06-08-2009, 05:35 PM
Well, you can get these books at Abbey's Bookshop Online...

http://www.abbeys.com.au/items.asp?id=178041&name=Introduction%20to%20the%20Theo ry%20of%20Stellar%20Structure%20and %20Evolution

http://www.abbeys.com.au/items.asp?id=226642&name=Astrophysics%20Processes:%20Th e%20Physics%20of%20Astronomical%20P henomena


http://www.abbeys.com.au/items.asp?id=234321&name=Facts%20and%20Speculations%20i n%20Cosmology

http://www.abbeys.com.au/items.asp?id=227359&name=Future%20of%20Theoretical%20Ph ysics%20and%20Cosmology

http://www.abbeys.com.au/items.asp?id=126489&name=Introduction%20to%20Galaxies%2 0and%20Cosmology

http://www.abbeys.com.au/items.asp?id=161450&name=Space%20Time%20Relativity%20an d%20Cosmology


They're just a few I can recommend.

Welcome to IIS:D:D

06-08-2009, 05:38 PM
Oh....if you need any help, there's a few of us here who have majors in the Physical Sciences and some of us are presently doing grad work, so we will more than likely know what you need to know:D

06-08-2009, 05:49 PM
Hi there. I'm new too. I was recommended these by a colleague in the US.
--Basic Training in Mathematics by R. Shankar (presumably NOT Ravi)
--Spacetime & Geometry by S. Carrol
--Physical Universe by Frank Shu
ISorry. have no idea of the publishers or ISBNs.

Hope that helps a little.

06-08-2009, 06:27 PM
Maths to the sounds of the sitar:P:D:D

07-08-2009, 10:22 AM
Thanks everyone for your advice and input. It seems as though there is no silver bullet for relearning the maths needed for Astrophysics. Someone could make a nice amount of money if they make a book which bridged the gap from average maths to what is needed for Astrophysics.

Cheers for the suggested titles. I'll look into them for sure. I checked that swinburne site which has a good little section on maths for their courses http://astronomy.swinburne.edu.au/sao/prospective/maths.xml

I'll pull out some of my old texts and try to relearn what is suggested on the swinburne site, then start looking at the more academic texts.

Damn it, I have to re-learn calculus :doh:

07-08-2009, 01:32 PM
If you feel like being extended, you might try Roger Penrose - The Road to Reality - http://www.booko.com.au/books/isbn/9780679776314

It is quite maths-based.

I warn you though, it has the capacity to fry your brain


07-08-2009, 05:36 PM
Hi Pete,

I had a look at that link, and I think that would lead to a stroke at the moment :P I read a few theoretical books on string theory (no maths, just text), after that I bought Polchinski's 2 book series (a nice cheap copy from ebay) and was surprised at how much maths I had forgot. I did specialist maths in VCE, but you know the old saying "if you dont use it....."

Looks like I cant find any shortcuts around it.

Thanks again for everyones input!


07-08-2009, 09:41 PM
I recently did VCE Specialist Maths, Maths Methods & Physics thru distance education Victoria (http://www.distance.vic.edu.au/). At my lesiure.

This is a cheap way of bringing education skills up to date. I did this to help my high school kids...but after all this they didn't want my help...all help given by me ends in tears!

If I could do it anyone can do it.....With the proviso that you need to be reasonably switched on to get a good score for Specialist Maths. I found it's student drop out rate was extremely high.

Other subjects are very educational & quite passable by most people.

07-08-2009, 10:06 PM
How about An Introduction to Modern Astrophysics (http://www.amazon.com/Introduction-Modern-Astrophysics-Bradley-Carroll/dp/0805304029/ref=cm_cr_dp_orig_subj) (second edition). I have the first edition. The Amazon reviews give a good indication of its target audience.

I've even had opportunity to refer to it for some formulas when I was programming some imaging related software :)


07-08-2009, 11:01 PM
Very good book, Eric. It is for advanced undergrad and grad students....I wouldn't attempt it unless you have a fairly good grounding in the maths.

08-08-2009, 03:26 PM
Thanks Eric and wasyoungonce. The book you mentioned is one of the books that I want to understand more. I have a copy but its a bit of a pain to read until I can get my calculus knowledge back.

Mind you, when I did specialist Maths and Math Methods in VCE, that was about 15 years ago. I still have the old text books lying around so I might start again from year 10:lol:

I've found a few websites that are good for dusting off the old cobwebs. I've had a few "Eureka, the hat goes on the head moments" if you know what I mean.

I'm thinking about 1 hour a night (after the kids go to bed), and in a few months I should be up to scratch.

Anybody here done the Swinburne Masters in Astronomy? I've heard that its not that Maths heavy, however some of the units do require tertiary level Maths. I plan on doing this in the long future (many moons down the track, pun intended), so if anyone has done it, could you please let me know what level a students Maths should be at?

Thanks again,

08-08-2009, 04:14 PM
I'm doing my Masters at present, in Astronomy, at JCU. Similar sort of program to Swinburne. Neither program is exceptionally maths heavy, but you do need to know it at tertiary level in order to do the work that does require it. Make sure you have adequate algebra and calculus skills. I try and brush up whenever I can....I'm no maths genius, either, but I get by alright. You'll find you can't remember all the equations anyway, so what I do is have a handy reference of the equations ready when I need them. Actually, just to give you an idea of what sort of maths you're most likely going to encounter, I can send you some of my tutorials. Much of your work will be how well you can assimilate the theoretical and observational side of astronomy and then apply the maths thats needed. If you already have a solid grounding in astronomy, you'll find it quite manageable.

If you can get yourself up to scratch in a few months and can handle the maths well enough, I'd suggest that you might apply to do the Masters starting next year. Don't put it off too long, otherwise life might get in the way and you never end up doing it!!!. You should be able to get funding via the RTS (Research Training Scheme) and FEEHelp....that's very good, as you have up to $100000 to use for your degree(s) and that'll come in handy if you decide to go onto a PhD afterwards.

08-08-2009, 05:31 PM
Thanks renormalised, I'll PM you straight away with a few details. Much appreciated.

I've had a look at the samples from the Swinburne site, but if anyone on this board is involved with that program, I would grealy appreciate any additional material that they can legally share.

Thanks to everyone so far, its good to communicate with like minded people who dont ridicule me for my limited knowledge in this area.

If cyber beers existed, the next round would be on me :thumbsup:


09-08-2009, 05:17 PM
Ok... the first subject you will have to be competent with is spherical trigonometry, then classical (newtonian) orbits. The classic texts are

Spherical Trigonometry by Smart.
Orbital Mechanics by A.E. Roy

You will have to reach the point where you are able with no more than a scientific calculator to confidently and accurately predict and calculate the circumstances for a solar eclipse and get results in agreement with the methods described in the book by Jan Meeus for calculating ephemerides - without using Meeus' book first (which is cheating).

The next will be thermodynamics, statistical mechanics and requiring a solid foundation in differential equations, a solid basis in vector calculus and tensors if you're going into the physics of stellar interiors.

Then gravitation and relativity theory... the standard text is Gravitation by Misner Thorne and Wheeler

Basically this goes beyond the stuff taught in tertiary applied maths courses, and then some.

10-08-2009, 03:20 PM
Hi Wavytone,

Thanks for your information and suggested texts. I've got a bit of work to do, but thank you all so much for informing me on what aspects to tackle first.

Many thanks,

10-08-2009, 03:52 PM
Just remember though that alcohol and Calculus don't go together.
You should never drink and derive.

12-09-2009, 04:17 PM
Here's the first of four maths units required for an Astronomy and Astrophysics BA at mq uni. The text books are all provided on-line, free.


12-09-2009, 05:06 PM
Otherwise you will end up convoluted around the first solid integral you hit!


Ian Robinson
12-09-2009, 06:58 PM
If you are going to do (or have a serious go at) any physics based degree , Maths 1 wont even go anywhere near giving you the mathematical background to handle the theoretical / mathematical aspects of 2nd year or higher level undergrad physics topics , and training in vector calculus is not sufficient.
Nor do the lecturers and tutors giving these topics have time to spoon feed students who don't have the requisit knowledge or to teach students maths they call on or use .

Majority of physics majors I've met were double majors (physics / maths) or came from engineering or maths backgrounds.

You need a least 2 years of linear algebra, analysis and calculus , and probably a good grounding in electromagetism too.

I've done undergrad physics and it's not easy math , the easiest was the year 2 topic in quantum mechanics ( failure rate 70% at my university when I did it ).

No way of avoiding it .... physics is a very hard and difficult science to learn at university level.

12-09-2009, 07:12 PM
MATH135 -- that brings back memories! I did that in 1998 or 1999.


12-09-2009, 08:25 PM
Bert :)

Happy Birthday btw !:thumbsup: