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Nick 2016-05-23 23:24

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.

[URL]https://www.youtube.com/playlist?list=PLTBqohhFNBE_09L0i-lf3fYXF5woAbrzJ[/URL]

Dubslow 2016-05-24 01:15

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.

Nick 2016-05-24 09:58

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 3-dimensional geometry is illuminating:
[URL]https://www.lms.ac.uk/sites/lms.ac.uk/files/2000%20Recommended%20theorems%20in%203-dimensional%20geometry%20%28preprint%29.pdf[/URL]

Nick 2016-05-26 21:29

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 non-specialist audience.

[URL]http://www.maths.ox.ac.uk/events/public-lectures-events#PublicLecturesOnline[/URL]

Nick 2018-06-25 22:10

Introduction to surfaces (no expert knowledge required):
[URL]http://www.maths.ed.ac.uk/~v1ranick/surgery/zeeman.pdf[/URL]

Nick 2018-11-11 13:34

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:
[URL]http://www.maths.ox.ac.uk/node/30464[/URL]

pinhodecarlos 2018-11-11 15:53

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.

Nick 2019-04-01 20:12

Several chapters of the book "A Friendly Introduction to Number Theory" by the well-known mathematician Joseph Silverman are available free online at his page about it here:
[URL]https://www.math.brown.edu/~jhs/frint.html[/URL]

Uncle Lumpy 2019-04-01 23:38

Thank you so much for these links...fascinating material!


Lumpy

Nick 2019-12-22 13:27

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.

[URL="https://www.maths.ox.ac.uk/node/30464"]Complex Numbers[/URL]
[URL="https://www.maths.ox.ac.uk/node/34054"]Introductory Calculus[/URL]
[URL="https://www.maths.ox.ac.uk/node/31744"]Dynamics[/URL]
[URL="https://www.maths.ox.ac.uk/node/32464"]Integration[/URL]
[URL="https://www.maths.ox.ac.uk/node/34201"]Differential Equations[/URL]
[URL="https://www.maths.ox.ac.uk/node/34349"]Quantum Theory[/URL]

pinhodecarlos 2019-12-22 13:48

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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