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I have mentioned in my recent posts that I'm studying Ideal-convergence. So the thing is I am expected to make a small presentation on this topic in two weeks on what I have learnt so far and understood and stuff. And in that presentation I have to first make an introduction to this topic discussing the origins of this theory or say how it first came into existence and so on. So where can I find the history of this? Also any advice on how to make this presentation a good one like what theorems to start with after introduction and how to proceed further, are most welcome.

Following are the papers I have read thus far:

$[1]$ Pratulananda Das, Sanjoy Ghosal: When I-Cauchy nets in complete uniform spaces are I-convergent, Topology and its Applications, Volume 158, Issue 13, 15 August 2011, Pages 1529–1533, DOI:10.1016/j.topol.2011.05.006

$[2]$ Pratulananda Das and Ekrem Savas: On I-convergence of nets in locally solid Riesz spaces, Filomat 27:1 (2013), 89–94, DOI:10.2298/FIL1301089D

$[3]$ B. K. Lahiri and Pratulananda Das: $I$ and $I^*$-Convergence of Nets, Real Anal. Exchange, Volume 33, Number 2 (2007), 431-442; projecteuclid.

$[4]$ Pratulananda Das and Sanjoy Kr. Ghosal: Some further results on I-Cauchy sequences and condition (AP), Comp. Math. Appl., 59 (2010), 2597-2600, DOI:10.1016/j.camwa.2010.01.027.

$[5]$ Ekrem Savas: *$\mathcal I_\lambda$-statistically convergent sequences in topological groups, Acta et Commentationes Universitatis Tartuensis de Mathematica, Vol 18, No 1 (2014), DOI: 10.12697/ACUTM.2014.18.04.

$[6]$ Amar Kumar Banerjee, Apurba Banerjee: A note on $I$-convergence and $I^{\star}$-convergence of sequences and nets in topological spaces, Matematicki Vesnik, Vol. 67, No. 3, pp. 212-221 (2015).

$[7]$ Martin Mačaj, Martin Sleziak: $\mathcal I^{\mathcal K}$-converence, Real Analysis Exchange, 36(1) (2010/2011), 177-194 arxiv, projecteuclid.

$[8]$ Benoy Kumar Lahiri; Pratulananda Das: $\mathcal I$ and $\mathcal I^*$-convergence in topological spaces , Mathematica Bohemica, Vol. 130 (2005), No. 2, 153–160 MathBohem

If this is not fine I'm ready to read study more stuff.

I am very very sorry for I know this not precisely a mathematical question but I did not know where else to go for advice. It is related to mathematics though.

Martin Sleziak
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    I will just mention that in the joint paper with Martin Mačaj (item [7] in your list gives arxiv link, here is also projecteuclid link) we have tried to give an a brief overview of ideal convergence (or dually filter convergence). It was used by Cartan, Robinson, Bernstein, Katětov and probably many others. – Martin Sleziak Aug 15 '16 at 14:09
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    These posts might also be of the interest: http://math.stackexchange.com/questions/420538/ultrafilters-when-did-it-start and http://mathoverflow.net/questions/19285/how-do-you-axiomatize-topology-via-nets/31443#31443 – Martin Sleziak Aug 15 '16 at 14:12
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    Having a list of "this" forces whoever looks at this question to open each paper to know what's inside. How about proper citations? – Asaf Karagila Aug 15 '16 at 14:24
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    @MartinSleziak, it seems you are in a good position to give an accessible answer here :-) I would be curious to see if the ultralimits populirized by Terry Tao fit in this framework; see e.g., this post. – Mikhail Katz Nov 11 '16 at 08:02
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    You may also like http://www.sciencedirect.com/science/article/pii/S0022247X07014291 – Tomasz Kania Nov 11 '16 at 10:39

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