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Good maths books/Textbooks

13

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  • Registered Users Posts: 3,038 ✭✭✭sponsoredwalk


    The Road to Reality
    Has more math in it than you can shake a stick at,
    and it's classed as a laymans book :eek:
    Math! Encounters with High School Students
    Math Talks for Undergraduates
    What is Mathematics?
    Concepts of Modern Mathematics
    Mathematics: From the Birth of Numbers
    Basic Mathematics
    God Created the Integers
    Euclid's Window
    The Drunkard's Walk

    Godel Escher Bach & Fermat's Last Theorem are both recommended,
    but haven't finished GEB yet. There's a good documentary on google
    videos on Fermat's Last Theorem which gives you a flavour of the book.
    Fremen wrote: »
    "The Cauchy-Schwarz Master Class" by Steele is supposedly very readable even without a grounding in calculus.

    Yeah, it looks good, and reading the first page having the author telling
    you to make up your own proof of Cauchy-Schwarz sets the tone for
    something good. It's been on my list for a while for the future, which
    draws ever-closer.


  • Closed Accounts Posts: 27 Fr.Ebula Conundrum


    Thanks a million for all the replies guys :) Well just to give you some background Im doing the leaving cert course in school at the moment so i'll be covering basic calculus and all that, as well i'm doing enrichment courses for the olympiad, so I guess that rules out anything rather simple... I suppose I'm looking for something in supplement to what I'm already but at the same time something kind of new, if that refines the list of books suggested?


  • Closed Accounts Posts: 6,151 ✭✭✭Thomas_S_Hunterson


    Godel Escher Bach & Fermat's Last Theorem are both recommended,
    but haven't finished GEB yet.
    There's a full series of lectures freely available from a course in MIT on GEB. Notes, videos, audio are all provided.

    http://ocw.mit.edu/high-school/courses/godel-escher-bach/video-lectures/

    O/t but I'm very impressed by how much material is available online for free. Big universities making entire modules available for free is certainly a positive development for academia.


  • Closed Accounts Posts: 27 Fr.Ebula Conundrum


    Disappointing really that although there are quite a few people quite interested and good at maths and yet we're like one of the worst countries when it comes to the olympiad :/


  • Registered Users Posts: 4,838 ✭✭✭DapperGent


    It's very difficult to overcome demographics to be honest.


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  • Closed Accounts Posts: 27 Fr.Ebula Conundrum


    Well when we're significantly behind countries like new zealand, estonia and luxembourg we kinda have to ask questions :/


  • Closed Accounts Posts: 11,148 ✭✭✭✭KnifeWRENCH


    If anyone is doing a module on Functional Analysis in college, make sure to check if your library has a copy of Introductory Functional Analysis with Applications by Erwin Kreyszig. I had to study it this year, and while the module itself was extremely difficult, I found this book to be a lifesaver.

    Alternatively, you could buy it if you feel like forking out ~$100 plus postage and packing. Can't find a cheap copy anywhere, unfortunately.


  • Registered Users Posts: 2,481 ✭✭✭Fremen


    Yeah, Kreyszig's pretty good alright. You can grab a copy at abebooks.com for peanuts. Be careful about buying international editions though. They're printed on low-grade paper and they smell a bit funny.

    I'm trying to read Peter Lax's book on functional analysis at the moment. He has an irritating habit of writing things like

    "Proof: This is trivial",

    when it really isn't.


  • Closed Accounts Posts: 11,148 ✭✭✭✭KnifeWRENCH


    Yeah, bought an international edition of a physics book on eBay recently (from India) and when my friend he saw it he said "That looks photocopied". :pac: So long as the actual material is all there though, I don't mind the aesthetics of it so much! Thanks for that site though, I'll have a look anyway.

    I hate when "proof: trivial" is used - there's very little trivial in functional analysis! Karen Saxe's book on functional analysis was the other one I used other than Kreyszig; it was ok but she leaves a lot of important results as exercises, which irritates me when I want a quick fix to prepare for exams! She also spends a lot of the book talking about the history of the subject and the people involved which, while interesting, doesn't exactly help when preparing for exams.


  • Posts: 0 ✭✭✭ Kara Short Range


    Principles of Mathematical Analysis by Walter Rudin is a good book. It's available as a free ebook at several places online, including several University hosted pages, which leads me to believe that it's out of copyright or in the public domain.

    It's a bit more advanced than most introductory analysis courses, and I guess it provides a bridge between a first college course in real analysis and courses in Topology, Complex Analysis and other areas.

    I'd like to find solutions to the excercises though, as a lot of them are quite challenging. For example, after introducing the Least Upper Bound property of the Real Numbers, one of the exercises involves proving the existence and uniqueness of logs.


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  • Registered Users Posts: 81 ✭✭luciemc


    Can anyone recommend a textbook that would introduce me to some undergrad concepts/courses? Anything that I could teach myself from? I've just finished my leaving and plan on spending a bit of time working through some new maths this summer.. I'll be studying maths in England (hopefully) and I'm fine with the leaving cert syllabus obviously but I know some of the A-level students might have that extra advantage, would like to get started as soon as possible really!

    Sorry if something suitable has already been mentioned but I did try to read through the thread and well... there were just too many books!


  • Registered Users Posts: 6,798 ✭✭✭doc_17


    vinks wrote: »
    quantum computing - second edition, by mika hirvensalo. its quantum computing for dummies (~100pages) and the rest is quantum mechanics and some number theory (another 100pages or so).

    I found that funny!


  • Registered Users Posts: 5,614 ✭✭✭TheBody


    Reading Visual Complex Analysis by Tristan Needham at the minute. Simply amazing. It almost sad to think that there are so many people out there who will never get to appreciate how simply breathtaking topics like complex analysis is.


  • Registered Users Posts: 156 ✭✭MoogPoo


    just reading Road to Reality by Roger Penrose. Unbelievable... unbelievable...
    Its 1000 pages, the first half pretty much summarises everything in college level maths that would be needed for physics topics like differential geometry( I did a module on this but he introduced tensors and covariant derivatives very simply), riemannian geometry, complex analysis, calculus, lie algebras and groups and stuff. About a chapter on each of this giving a few equations and talking about their importance. Then the second half is a quick introduction to modern physics with general relativity, quantum physics, QFT and EM and others. Good solid intuitive ideas are shown and the basic maths is given. The introduction says its for all audiences but in all honesty you'd probably need a lot of college level maths. I was constantly looking up books and going back to it.

    The level is perfect for someone about to finish an undergrad in maths or physic. Reading the book I had a Eureka moment every half hour or so. Great book, fairly cheap too I got it for 25 in easons but im sure you could find it cheaper. Get this book.


  • Closed Accounts Posts: 11,812 ✭✭✭✭evolving_doors


    There's a full series of lectures freely available from a course in MIT on GEB. Notes, videos, audio are all provided.

    http://ocw.mit.edu/high-school/courses/godel-escher-bach/video-lectures/

    O/t but I'm very impressed by how much material is available online for free. Big universities making entire modules available for free is certainly a positive development for academia.

    Cheers +1


  • Closed Accounts Posts: 25,848 ✭✭✭✭Zombrex


    There's a full series of lectures freely available from a course in MIT on GEB. Notes, videos, audio are all provided.

    http://ocw.mit.edu/high-school/courses/godel-escher-bach/video-lectures/

    O/t but I'm very impressed by how much material is available online for free. Big universities making entire modules available for free is certainly a positive development for academia.

    Second that, I recently came across the OCW stuff from MIT when trying to brush up on my Algebra and Calculus knowledge after I found myself stuck on a problem at work that I knew I should know from leaving cert maths.

    It is amazing what they have up, from full lectures to full text books and revision notes to exam papers. Watching a lecture on introduction to calculus, having the course book right there and then having study notes, it was more than enough to get me back into learning and I've move far beyond the specific area I wanted to brush up on. I could literally spend months going through the lectures and text books.

    Fair play MIT, next pay day you are getting a donation from me to help support his amazing resource. :)


  • Banned (with Prison Access) Posts: 3,455 ✭✭✭krd


    http://www.amazon.com/Disappearing-Spoon-Madness-Periodic-Elements/dp/0316051640

    The disappearing spoon.

    History of the development of the periodic table, with lots in between. Very well written. All killer, no filler.


  • Registered Users Posts: 16 hen93


    TheBody wrote: »
    Most first year college maths courses have a lot of calculus in first year and perhaps some sort of stats course. If you can get your hands on any introductory undergraduate calculus book you can start reading that. They are all more or less the same. PM me if you are near Maynooth and I can give you one (for free). What maths courses have you applied to?

    Ok great, thanks a million for your help but I'm not situated near maynooth, I'm sure I can some pdfs online of undergrad books anyway but thanks again. I have mathematical science in nuig and ul down, aswell as theoretical physics and mathematics in Maynooth actually, but it is not a high preference.


  • Registered Users Posts: 5,614 ✭✭✭TheBody


    hen93 wrote: »
    Ok great, thanks a million for your help but I'm not situated near maynooth, I'm sure I can some pdfs online of undergrad books anyway but thanks again. I have mathematical science in nuig and ul down, aswell as theoretical physics and mathematics in Maynooth actually, but it is not a high preference.

    Ah your missing out if you don't go to Maynooth!! :D Good luck where ever you end up!!


  • Registered Users Posts: 16 hen93


    TheBody wrote: »
    Ah your missing out if you don't go to Maynooth!! :D Good luck where ever you end up!!
    Haha I was down for the open day and it has a great atmosphere alright but the commute home at the weekends is too much :P Cheers!


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  • Registered Users Posts: 852 ✭✭✭blackdog2


    Hi all,


    It has been a long time since I have looked at anything remotely mathematical. Like my Leaving cert german, it has completely left me. I was wondering if anyone can recommend any maths textbooks that begin from 1st year secondary school type level?

    Thanks all


  • Registered Users Posts: 5,614 ✭✭✭TheBody


    blackdog2 wrote: »
    Hi all,


    It has been a long time since I have looked at anything remotely mathematical. Like my Leaving cert german, it has completely left me. I was wondering if anyone can recommend any maths textbooks that begin from 1st year secondary school type level?

    Thanks all

    You could simply begin by getting your hands on a second level maths book(s). The Text and Tests series are quite good. You should be able to get a second hand copy as there is a new maths syllabus in schools now that require new books.


  • Registered Users Posts: 852 ✭✭✭blackdog2


    TheBody wrote: »
    You could simply begin by getting your hands on a second level maths book(s). The Text and Tests series are quite good. You should be able to get a second hand copy as there is a new maths syllabus in schools now that require new books.

    Excellent, I actually used one of the first editions of that, but it was in Irish. I might try to track down an English copy as it would be easier to supplement with other material online etc!

    Thanks for the reply :D


  • Registered Users Posts: 69 ✭✭matthew2008


    hi all, i decided to opt for pass maths when i was in 5th year in school before i even tried the honours maths course (typical 'couldnt care less, sure when will i ever use this in real life' teenager) and nearly 4 years later, im really regretting it. anyway hoping ill be studying science come september and looking to at least begin to catch up to an honours leaving cert knowledge of maths (before project maths came in). anybody suggest any books (and not the general 'text and tests' or 'new concise maths' please) considering i only have the very very basics, thanks!!


  • Registered Users Posts: 338 ✭✭ray giraffe


    anybody suggest any books (and not the general 'text and tests' or 'new concise maths' please) considering i only have the very very basics, thanks!!

    Maths tutor here.

    This book covers the basics (most of honours junior cert course)

    This book covers most of the Honours Leaving Cert course, except Calculus.

    The GCSE books from England are better written than the Irish books, so more suitable for self-learning! :)


  • Registered Users Posts: 69 ✭✭matthew2008


    Maths tutor here.

    This book covers the basics (most of honours junior cert course)

    This book covers most of the Honours Leaving Cert course, except Calculus.

    The GCSE books from England are better written than the Irish books, so more suitable for self-learning! :)

    cheers ill look into that now, and any advice on a calculus book then as well? i imagine thatll be quite important from me


  • Closed Accounts Posts: 978 ✭✭✭Fudge You


    Can anyone recommend me books on Calculus?

    I have two in mind from this thread already. One is, How to Ace Calculus by adams, thompson, hass. Might go with it.

    Thanks people!


  • Registered Users Posts: 966 ✭✭✭equivariant


    Fudge You wrote: »
    Can anyone recommend me books on Calculus?

    I have two in mind from this thread already. One is, How to Ace Calculus by adams, thompson, hass. Might go with it.

    Thanks people!

    "Calculus Early Transcendentals" by Stewart is a good undergrad calculus book. I use it to teach 1st years and I think that it is excellent. A bit pricey if you buy it but I am sure you can find ways around that ;)

    For a more advanced and rigourous treatment I like "Calculus" by Spivak.


  • Registered Users Posts: 1,147 ✭✭✭.E_C_K_S.


    Looking at picking up a couple of books for xmas, has anyone come across anything new or interesting since?


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  • Moderators, Science, Health & Environment Moderators Posts: 1,846 Mod ✭✭✭✭Michael Collins


    .E_C_K_S. wrote: »
    Looking at picking up a couple of books for xmas, has anyone come across anything new or interesting since?

    I very much enjoyed The Calculus Gallery by William Dunham. It's not exactly a doddle to read - I'd rank it somewhere between a text book and a popular maths book, so not too bad but you might need a pen and paper beside your bed!

    Just picked up Bayes Rule by James V Stone, haven't read much of it yet but the topic is certaintly interesting.

    Another book that shows promise is Music of the Primes by Marcus du Sautoy, I'm sure this is mentioned above so you may already have it.

    Feel free to add some of your own favourites, I can never have enough interesting maths books. The real challenge is getting time to read em...


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