Bookmark | Chris Aldrich

Bookmarked Fundamentals of Point-Set Topology by Michael Miller (UCLA Extension)

Point-set topology is the branch of mathematics that deals with collections of points endowed with sufficient structure to make meaningful the notions of closeness, separation, and convergence. Beginning with familiar notions concerning open sets, closed sets, and convergence on the real number line and Euclidean plane, this course systematically develops the theory of arbitrary topological spaces. Topics include bases and subbases, separation axioms (Hausdorff, regular, and normal spaces), countability (first- and second-countable spaces), compactness and compactification, connectedness, and convergence (nets and filters). Instruction emphasizes examples and problem solving. The course appeals to those seeking a better understanding of the algebraic and geometric underpinnings of common mathematical constructs.

September 24 - December 3 on Tuesday 7:00PM - 10:00PM PT
Fee: $453.00
Location: UCLA, Math Sciences Building, Room 5127

Mike Miller’s fall math class at UCLA has been posted. I’m registering and hope to see you there!

As usual, there’s no recommended textbook (yet), and he generally provides his own excellent notes over a required textbook. I’d suspect that he’ll recommend an inexpensive Dover Publication text like those of Kahn, Baum, or Gamelin & Greene.

If you’re curious about what’s out there, I’ve already compiled a bibliography of the usual suspects in the space:

Armstrong, M. A. Basic Topology. Undergraduate Texts in Mathematics, 3.0. Springer, 1983.
Conover, Robert A. A First Course in Topology: An Introduction to Mathematical Thinking. Reprint. Dover Books on Mathematics. Mineola, N.Y: Dover Publications, Inc., 2014.
Conway, John B. A Course in Point Set Topology. Undergraduate Texts in Mathematics. Springer, 2015.
Crossley, Martin D. Essential Topology. Corrected printing. Springer Undergraduate Mathematics Series. 2005. Reprint, Springer, 2010.
Gaal, Steven A. Point Set Topology. 1st ed. Pure & Applied Mathematics 16. Academic Press, 1964.
Gamelin, Theodore W., and Robert Everist Greene. Introduction to Topology. 2nd ed. Dover Books on Mathematics. 1983. Reprint, Mineola, N.Y: Dover Publications, Inc., 1999.
Kahn, Donald W. Topology: An Introduction to the Point-Set and Algebraic Areas. Dover Books on Mathematics. Mineola, N.Y: Dover Publications, Inc., 1995.
Kasriel, Robert H. Undergraduate Topology. Dover Books on Mathematics. Mineola, N.Y: Dover Publications, Inc., 2009.
López, Rafael. Point-Set Topology: A Working Textbook. 1st ed. Springer Undergraduate Mathematics Series. Springer, 2024.
Mendelson, Bert. Introduction to Topology. 3rd ed. Dover Books on Mathematics. Dover Publications, Inc., 1990.
Morris, Sidney A. Topology Without Tears, 2024. [.pdf]
Munkres, James R., 1930-. Topology. 2nd ed. 1975. Reprint, Prentice-Hall, Inc., 1999.
Shick, Paul L. Topology: Point-Set and Geometric. 1st ed. Wiley-Interscience, 2007.
Sierpinski, Waclaw. General Topology. Translated by C. Cecilia Krieger. Repring. Dover Books on Mathematics. Mineola, N.Y: Dover Publications, Inc., 2020.
Viru, O. Ya., O.A. Ivanov, N. Yu. Netsvetaev, and V.M. Kharlamov. Elementary Topology: Problem Textbook. American Mathematical Society, 2008.
Waldmann, Stefan. Topology: An Introduction. Springer, 2014.
Willard, Stephen. General Topology. Dover Books on Mathematics. Mineola, N.Y: Dover Publications, Inc., 2004.

AI generated featured photo courtesy of Glif Alpha

Bookmarked Topics in Ring Theory and Modules by Michael Miller (UCLA Extension)

Topics to be discussed include the isomorphism theorems; ascending and descending chain conditions; prime and maximal ideals; free, simple, and semi-simple modules; the Jacobson radical; and the Wedderburn-Artin Theorem.
Ring theory is a branch of abstract algebra that deals with sets—for example, the collection of all integers—that admit both additive and multiplicative operations. Modules generalize the notion of vector spaces, but with scalars drawn from a ring rather than a field. Beginning with a survey of the basic notions of rings and ideals, the course explores some of the elegant algebraic structuring that defines the behavior of rings—both commutative and non-commutative—and their associated modules. Topics to be discussed include the isomorphism theorems; ascending and descending chain conditions; prime and maximal ideals; free, simple, and semi-simple modules; the Jacobson radical; and the Wedderburn-Artin Theorem. Theory will be motivated by numerous examples drawn from familiar realms of number theory, linear algebra, and real analysis.

Mike Miller has announced this fall’s math course at UCLA.

Bookmarked Return to Blogging by Christopher Long (cplong.org)

A new year brings new calls for a return to personal blogging as an antidote to the toxic and extractive systems of social media.

Bookmarked Indxd (indxd.ink)

Filling up notebooks is great - but what happens when you need one obscure factoid that's stashed somewhere among dozens of notebooks? Searchability is Analog's Achilles heel.

Introducing Indxd
I wanted a simple, searchable index of all the topics in all my notebooks. So I built it, and you can use it too. Indxd lets you quickly enter notebooks and their topics, then search and browse everything.

INDXD is a digital, web-based index tool for your analog notebooks.

Ostensibly allows one to digitally index their paper notebooks (page numbers optional). It emails you weekly text updates, so you’ve got a back up of your data if the site/service disappears.

This could potentially be used by those who have analog zettelkasten practices, but want the digital search and some back up of their system.

ᔥ sgtstretch in @Gaby @pimoore so a good friend of mine makes INDXD which is for indexing analog notebooks and being able to find things. I don’t personally use it, but I know @patrickrhone has written about it before. (10/27/2022 17:59:32)

Bookmarked Tools for Thinking: a Conference and a Camp by John Borthwick (https://render.betaworks.com/)

Start with a conference: On August 16th we will host a conference at betaworks, bringing together makers and thinkers in this space: Tools for thinking Render Conference. Join us if you are interested, and if you are building something in this space, tell us because we will give you an access code to join for free. The Camp or accelerator program will start in mid September, details on the program are here, and the application form is here.

You had me at “networked commonplace books”…

Independently-hosted web publishing

Bookmarked Independently-hosted web publishing by

Daniel Villar-Onrubia & Victoria I. Marín (Internet Policy Review Volume 11, Issue 2 DOI: 10.14763/2022.2.1665)

The term independently-hosted is used here to describe online publishing practices that utilise the World Wide Web (hereafter the Web) as a decentralised socio-technical system, where individuals and communities operate as the owners or controllers of the online infrastructures they use in order to share content. Such practices may be adopted as an alternative of, or as a complement to, the use of centralised content-sharing systems that belong to and are entirely operated by third parties. The term “publishing” is used here in a rather inclusive way and refers to the act of making content available online, rather than being restricted to the editorial processes that characterise, for instance, academic publishing.
DOI: 10.14763/2022.2.1665

Great to see IndieWeb.org cited in the academic literature.

Bookmarked I Like Index Cards by

Aegir (Aegir.org)

I've been meaning to do some kind of index card style template for the site for ages and never got round to it. Now I have. I’m quite pleased with it. CSS repeating gradient lines and all that. ❧

An absolutely beautiful design for short notes. This is the sort of theme that will appeal to zettelkasten users who are building digital gardens. A bit of the old mixed in with the new.

ᔥ Pete Moor in // pimoore.ca (12/24/2021 18:02:15)