Resources for learning mathematics

Nick · 2016-05-23, 23:24

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

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:
https://www.lms.ac.uk/sites/lms.ac.u...reprint%29.pdf

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.

http://www.maths.ox.ac.uk/events/pub...LecturesOnline

Nick · 2018-06-25, 22:10

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

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:
http://www.maths.ox.ac.uk/node/30464

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:
https://www.math.brown.edu/~jhs/frint.html

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.

Complex Numbers
Introductory Calculus
Dynamics
Integration
Differential Equations
Quantum Theory

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.

2016-05-23, 23:24	#1
Nick Dec 2012 The Netherlands 2×5×181 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

2018-11-11, 15:53	#7
pinhodecarlos "Carlos Pinho" Oct 2011 Milton Keynes, UK 7·733 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 2018-11-11 at 15:55

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2016-05-24, 01:15	#2
Dubslow 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.

2016-05-24, 09:58	#3
Nick Dec 2012 The Netherlands 2·5·181 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 3-dimensional geometry is illuminating: https://www.lms.ac.uk/sites/lms.ac.u...reprint%29.pdf

2016-05-26, 21:29	#4
Nick Dec 2012 The Netherlands 3422₈ 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 non-specialist audience. http://www.maths.ox.ac.uk/events/pub...LecturesOnline

2018-06-25, 22:10	#5
Nick Dec 2012 The Netherlands 2·5·181 Posts	Introduction to surfaces (no expert knowledge required): http://www.maths.ed.ac.uk/~v1ranick/surgery/zeeman.pdf

2018-11-11, 13:34	#6
Nick Dec 2012 The Netherlands 2·5·181 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

2019-04-01, 20:12	#8
Nick Dec 2012 The Netherlands 2·5·181 Posts	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: https://www.math.brown.edu/~jhs/frint.html

2019-04-01, 23:38	#9
Uncle Lumpy Mar 2017 17₈ Posts	Thank you so much for these links...fascinating material! Lumpy

2019-12-22, 13:27	#10
Nick Dec 2012 The Netherlands 2×5×181 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

2019-12-22, 13:48	#11
pinhodecarlos "Carlos Pinho" Oct 2011 Milton Keynes, UK 7×733 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.