20160523, 23:24  #1 
Dec 2012
The Netherlands
3×587 Posts 
Resources for learning mathematics
This thread is for links to high quality resources that are useful for learning mathematics (at any level).
To start, here are the recordings of an introductory course on Topology & Geometry (subtitle: Pictorial Thinking) given by Dr. Tadashi Tokieda of the University of Cambridge (UK) when he visited the African Institute for Mathematical Sciences (South Africa) in 2014. https://www.youtube.com/playlist?lis...f3fYXF5woAbrzJ 
20160524, 01:15  #2 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
If I may, Nick, what exactly is your mathematical background? Over the last year or two you've continually heightened my impression of your skills, but I know hardly anything about what exactly your areas of expertise are.

20160524, 09:58  #3 
Dec 2012
The Netherlands
3×587 Posts 
My main interests at present are algebraic, but good ideas in mathematics often come from new interactions between specialisations, so it is important not to let research become too narrow!
For anyone interested in discovering the correct position from which to view a painting, or how modular arithmetic can help us prove that two knots are genuinely distinct, Christopher Zeeman's introduction to 3dimensional geometry is illuminating: https://www.lms.ac.uk/sites/lms.ac.u...reprint%29.pdf 
20160526, 21:29  #4 
Dec 2012
The Netherlands
1761_{10} Posts 
Here is a list of public lectures in mathematics that have been recorded and made available online by the University of Oxford (UK).
They are intended for a nonspecialist audience. http://www.maths.ox.ac.uk/events/pub...LecturesOnline 
20180625, 22:10  #5 
Dec 2012
The Netherlands
3·587 Posts 
Introduction to surfaces (no expert knowledge required):
http://www.maths.ed.ac.uk/~v1ranick/surgery/zeeman.pdf 
20181111, 13:34  #6 
Dec 2012
The Netherlands
3·587 Posts 
First year bachelor students in mathematics at Oxford University get a couple of introductory lectures on the complex numbers.
The Oxford Maths Institute has recorded the second of these and made it public: http://www.maths.ox.ac.uk/node/30464 
20181111, 15:53  #7 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
11616_{8} Posts 
Not sure if any high school students are around but I remember on my first year at uni when I found out about Piskounov, Apostol or Demidovitch, I was so upset not having known about these resources to have even better grades at math during my high school.
I understand that now with all the internet of things everything is shared faster than before so nowadays people have the advantages of that but the disadvantage of not thinking by themselves. Good stuff Nick. Last fiddled with by pinhodecarlos on 20181111 at 15:55 
20190401, 20:12  #8 
Dec 2012
The Netherlands
3·587 Posts 
Several chapters of the book "A Friendly Introduction to Number Theory" by the wellknown mathematician Joseph Silverman are available free online at his page about it here:
https://www.math.brown.edu/~jhs/frint.html 
20190401, 23:38  #9 
Mar 2017
1111_{2} Posts 
Thank you so much for these links...fascinating material!
Lumpy 
20191222, 13:27  #10 
Dec 2012
The Netherlands
3×587 Posts 
The Mathematics Institute at the University of Oxford (UK) have now followed up on their filmed lecture about Complex Numbers with several other single lectures
(usually the first lecture) from 1st and 2nd year undergraduate courses for mathematicians. Complex Numbers Introductory Calculus Dynamics Integration Differential Equations Quantum Theory 
20191222, 13:48  #11 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
2·2,503 Posts 
I follow Oxford on YouTube and sometimes at night, instead on reading, I’m watching their lecture, my wife thinks I am crazy. Haven’t seen the last one.

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