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I wanted to test myself to see if I could begin to comprehend the math used in astronomy, whats the most basic advanced math I should look into?

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I'd suggest get to grips with trigonometry first and then move onto differentiation. Trig, as you probably know, is all to do with angles whereas differentiation will lead you into how fast things are moving etc.

This next bit is 1st/2nd year university physics, understand this lot and you will then be in a good position to at least understand what it is you're reading about cosmology/astronomy. May take a while to understand this first though! http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion

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Pssssst, by the way, we says Maths...

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Did I attend an unusual school? Is my memory defective?

I remember Newtons laws of motion, and Keplers 'oval orbits' from 'O' level physics.

Basic differentiation, and integration were also covered in 'O' level math(s).

All of these subjects were covered in more detail at 'A' level.

As I didn't study physics at University, I must have leant this at school. The math(s) I studied at university had nothing to do with astronomy.

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Perhaps linear algebra too (vectors and matrices)?

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Pssssst, by the way, we says Maths...

"Two great peoples separated by a common language."

I try to use UK terms and spellings when I post here, but one of the things I've discovered is that the spell checker seems to prefer American spelling on those words in which a 'u' is inserted in that is not used in the US, eg, behaviour vs behavior.

We Americans learned that the shortened version of the word 'mathematics' - which is a plural noun - is singular, 'math' while our British cousins never forgot that it was plural.

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We say tomatoes you say tomato's etc etc

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But we are all joined by our love of Astronomy.

phillc

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I'd say scientific notation for starters. Counting the zeros. In many branches of astronomy that is the only number that counts.

Olly

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We say tomatoes you say tomato's etc etc

we say potato and they say potatoe (well, their ex vice president does, anyway)

to the OP - I'd take it from a historical perspective -ie what maths did the ancient greeks have when they worked out the circumference of the earth and moon etc and then what did kepler have etc etc and how did the dutch guy (forget his name) work out the speed of light in the 18th(?) century... (but that's just me)

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Rather than just look at mathematics why not try "The Road Reality" by Roger Penrose. It's a mega book but he introduces the mathematics as he goes along. If you get stuck then go back at a math’s book.

Regards Andrew

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it seems HARD to remember what sort of Math(s) I was studying at each stage now. Sadly I was... indifferent at Math(s) in school. ISTR the ubiquitous PC101 at University covered "Mechanics and Special Relativity"? The former interesting, and presumably rather relevant to astronomy. The latter impressive but, if I remember rightly, my "Lorenz contractions" were just as likely to end up as "expansions"...

As an extreme (a curiousity, even?) Roger Penrose delivers a fairly ab-initio "Maths Course" in his "Road to Reality" book - Probably commensurate with current theoretical Ph.D. particle / astro physics? I was impressed, but not necessarily much the wiser tho'! Thank heavens science still requires (and required) "hardware guys"?

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I wanted to test myself to see if I could begin to comprehend the math used in astronomy, whats the most basic advanced math I should look into?

Best thing is to have a specific problem you want to understand, then you'll learn the appropriate maths as you go along. For example, try understanding the stellar magnitude system (which involves logarithms) or celestial co-ordinates (spherical trigonometry), or orbits (calculus). Or try and work out how many stars you would expect to see down to a particular magnitude limit: that involves fractional powers.

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If you ever start imaging then it is statistics that comes in handy. It's all about handling noise.

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I have a good many years of experience with sports statistics would that be any help in astronomy?

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We say tomatoes you say tomato's etc etc

About the only thing I recall from the Muppet Show:

"Do you pronounce it 'tomayto' or 'tomarto'?"

"Do I pronounce what 'tomayto' or 'tomarto'?"

But back to the OP: For a basic understanding, simple trig & Euclidean geometry will do (also answers @kniclander's Q). Then progress to simple calculus, 3-D trig (what is in a decent A level/IB syllabus will take you a long way). If you can still manage more, progress to non-Euclidean geometry, tensor calculus (no, I can't! ), and stuff of that ilk.

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You should have a look at what is called "Precalculus" in North America. Some texts:

This will allow you to gauge where you stand.

Rather than just look at mathematics why not try "The Road Reality" by Roger Penrose. It's a mega book but he introduces the mathematics as he goes along. If you get stuck then go back at a math’s book.

Regards Andrew

As an extreme (a curiousity, even?) Roger Penrose delivers a fairly ab-initio "Maths Course" in his "Road to Reality" book - Probably commensurate with current theoretical Ph.D. particle / astro physics? I was impressed, but not necessarily much the wiser tho'!

Even though this is a truly amazing book, and

Lord of the Rings is the story that I have revisited most often. The novels I now read are mainly mysteries, and I usually don't reread them.

I have over 500 non-fiction books, some of which I use regularly. As my desert island book, I would choose Roger Penrose's The Road to Reality: A Complete Guide to the Laws of the Universe.

I don't think that Manok101 would find this book useful for acquiring a working knowledge of mathematics. Much more detail is needed, and loads and loads of exercises and problems every step of the way.

Penrose's ambitious book attempts to give an overview to everyone, from interested laypersons to research scientists, of all of fundamental physics, and of all the math (and more) underlying fundamental physics. Even though Penrose advises readers to skip over any and all math not to their liking, I think that readers who don't have math backgrounds will find it heavy going. It's not necessarily meant to be read from cover - a reader should just open it to whatever topic tickles their fancy. If something in one paragraph is not understandable, the reader should try to find some background elsewhere in the book, or go on to the next paragraph or chapter.

My biggest complaint is that, at 1100 pages, the book is too short!

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I have a good many years of experience with sports statistics would that be any help in astronomy?

Quite possibly. You almost certainly are used to concepts like measures of variation, Gaussian distributions, the behaviour of random processes, the Central Limit Theorem, etc in which case a lot should be familiar.

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Honestly I probably would have been better at math had I understood that it would have helped me out one day. Who knows, maybe one day.

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For TOPIC LISTs (at least!), The "50 [subject] Ideas" books are surprisingly good

- Especially for something, often consigned to the £2.99 bins in "The Works" etc.

50 Mathematical Ideas You Really Need to Know: Amazon.co.uk: Tony Crilly: Books

50 Physics Ideas You Really Need to Know: Amazon.co.uk: Joanne Baker: Books

50 Ideas You Really Need to Know: Universe: Amazon.co.uk: Joanne Baker: Books

Get the ones on Philosophy & Psychology. Be "invincible" in internet forum debate.

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"Precalculus" is Merkinese for "Algebra, Trigonometry, Basic Analytical Geometry, and Matrices".

For TOPIC LISTs (at least!), The "50 [subject] Ideas" books are surprisingly good

50 Mathematical Ideas You Really Need to Know: Amazon.co.uk: Tony Crilly: Books

I'm ploughing my way through one of Crilly's books (The Big Questions: Mathematics) and I don't find his explanations that good -- I keep finding myself thinking how much better the book would have been if Marcus du Sautoy had written it!

As regards the OP and astronomy books with maths in them, two of my favouritegeneral astronomy books, van Zyl's Unveiling the Universe, and Karttunen's Fundamental Astronomy, have appendices covering all the maths required in a straightforward manner. The van Zyl book has it to approx A level standard and the Karttunen one to approx 1st year undergraduate level, but both only cover what is useful for the astronomy. Karttunen's appendices also cover relativity, Minkowski space and a few other useful odds and sods.

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Manock101, I would suggest you go to "The Open University" website and go through the self assessment tests working your way up until you fall over. Each set has a reading list appropriate for that subject/level.

A word of warning.. If you self assess M205 then be prepared for a shock. This course is a prerequisite for subjects like Gravity/Relativity/Understanding Space and Time. Even the OU admit this course is a killer.

ray

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