Maths as a hobby, where to go?

DáireM

Hey guys, hoping some of you could give me a hand with this.

Finished the LC last year and one of my favourite subjects was maths. I wasn't autistically good but managed to get a b1 in higher level. Trouble is, with the course I'm doing I do very little maths. I always enjoyed working through the past papers and, as sad as it sounds, got a thrill from solving a particularly difficult problem .

I've tried reading a textbook and some lecture notes from MIT's OpenCourseware but I found them very tough going. I just get sick of reading through pages and pages of notation and can't concentrate.

I watched some online lectures from MIT on Vector Calculus and from Yale on Game Theory and found them really good but resources like this seem to be few and far between on the web.

Can anyone point me in the right direction?

Thomas_S_Hunterson

Lots of online lectures here: http://lecturefox.com/

Consider moving to a more mathsy course.

Fremen

There are some branches of maths which are more amenable to self-study than others. Some parts of number theory are quite accessible, so that a good LC student could get to grips with it without developing the kind of mathematical sophistication you need in college.
Take a look at Apostol's book on analytic number theory. He derives some nice results without doing anything too crazy. This subject matter would have a very different "feel" to what you did in school. (I might have an electronic copy if you asked nicely. Just for trial purposes though, buy it if you like it.)

Stanford have some good video lectures, too. The lecture series on fourier transforms has some mad stuff in it, definitely worth a look. It's a graduate course, but it's not really that hardcore. As far as I remember, all you need is some basics of trigonometry and complex numbers.

Edit: If you try to just trawl through a textbook, you're going to get bored and burn out any enthusiasm you have pretty quickly. I suggest you pick some "projects" or goals to work towards. For instance, you could start by building up the maths you need to understand the statement of the Riemann hypothesis. That would mean learning enough complex analysis to understand zeros, poles, analytic continuation and complex integration. A big but manageable project for someone working on it as a hobby.

nesf

If you're in a university the college's Maths society should be organising lectures that are open and accessible to the public. Seriously consider going along to them, they can be fascinating and it's great to talk shop with people afterwards, you can learn so much from a conversation etc.

DáireM

Thanks for the help lads, that lecturefox site is really helpful and I'll definitely look into those Stanford lectures. Might see about that Apostol book when I have some time off. I did plan on joining MathSoc but never got around to it .

The idea about the Riemann Hypothesis is quite a good one, actually. I've read the Music of the Primes and found it pretty interesting so that might be a project for the future!

Azelfafage

If you are over the age of 25 you may wish to give up.

New ideas in Maths rarely come from older people.

A bit like sports.

The body fades..the mind fades.

.

LeixlipRed

What rubbish. I know a guy who came back to study maths in his 60s. He's exceptionally talented at it, far much more than me. Age is meaningless, all you need is an open mind.

alan4cult

Azelfafage wrote: »

If you are over the age of 25 you may wish to give up.

New ideas in Maths rarely come from older people.

A bit like sports.

The body fades..the mind fades.

.

Complete Rubbish, i agree with Red. Ever heard of Andrew Wiles. He was too old to receive the Fields medal for his proof of Fermat's last Theorem.

sponsoredwalk

Azelfafage wrote: »

If you are over the age of 25 you may wish to give up.

New ideas in Maths rarely come from older people.

A bit like sports.

The body fades..the mind fades.

.

Andrew Wiles was 42 when he proved Fermat's Last Theorem, he worked on it during his 30's (and since childhood i suppose lol.

Erwin Schroedinger was something like 39 when he formulated the quantum mechanical wave equation.

Einstein was well into his 30's before learning and extending Non Euclidian Geometry in the General Theory of Relativity.

Immanuel Kant was in his 50's when working on his Critique of Pure Reason, very conscious of mathematics.

Thomas Hobbes got into mathematics very late, although he did nothing in math of much worth it influenced his philosophy a great deal.

I think Archimedes was well into old age also when working on math.

This comment really reminds me of the "ethical" question of whether a 40 year old woman should have babies, ridiculous. 2 + 2 = 5 and will continue to do so.

hivizman

DáireM wrote: »

Hey guys, hoping some of you could give me a hand with this.

Finished the LC last year and one of my favourite subjects was maths. I wasn't autistically good but managed to get a b1 in higher level. Trouble is, with the course I'm doing I do very little maths. I always enjoyed working through the past papers and, as sad as it sounds, got a thrill from solving a particularly difficult problem .

I've tried reading a textbook and some lecture notes from MIT's OpenCourseware but I found them very tough going. I just get sick of reading through pages and pages of notation and can't concentrate.

I watched some online lectures from MIT on Vector Calculus and from Yale on Game Theory and found them really good but resources like this seem to be few and far between on the web.

Can anyone point me in the right direction?

Three writers to look out for:

(1) Marcus du Sautoy: he's a maths professor at Oxford and recently took over from Richard Dawkins as Professor for the Public Understanding of Science. Recent books include The Music of the Primes on the Riemann Hypothesis and Finding Moonshine on Symmetry.

(2) Ian Stewart: retired now, but for many years a maths professor at Warwick University. He has written many popular maths books, including Does God Play Dice? The New Mathematics of Chaos. I used Ian Stewart's textbook on Galois Theory when I was a student: a model of clarity.

(2) Raymond M Smullyan: an American maths professor, specialising in logic. He has written several "logical puzzle" books, for example, To Mock a Mockingbird, though he uses the puzzles to derive in an informal way key results of mathematical logic such as Gödel's Incompleteness Theorem. Smullyan has also written textbooks, and his book on Set Theory and the Continuum Problem will be reissued early next year.

Bonzostar

DáireM wrote: »

Hey guys, hoping some of you could give me a hand with this.

Finished the LC last year and one of my favourite subjects was maths. I wasn't autistically good but managed to get a b1 in higher level. Trouble is, with the course I'm doing I do very little maths. I always enjoyed working through the past papers and, as sad as it sounds, got a thrill from solving a particularly difficult problem .

That's not sad at all. I'm exactly the same, and I'm in 5th year.

DáireM wrote: »

I've tried reading a textbook and some lecture notes from MIT's OpenCourseware but I found them very tough going. I just get sick of reading through pages and pages of notation and can't concentrate.

I watched some online lectures from MIT on Vector Calculus and from Yale on Game Theory and found them really good but resources like this seem to be few and far between on the web.

Can anyone point me in the right direction?

The work of the authors mentioned in previous posts and that of Simon Singh is really good. I am a massive fan of Simon. He is big into codes- making and breaking. Very interesting stuff.
The International Mathematical Olympiad publishes problems from previous years on their website. You might want to have a look at them. They are tough though:
http://www.imo-official.org/

Best of luck.