On the first anniversary of launching my serialized book, I reflect on what I've learned — including the pros and cons of my pivot from Substack newsletter to indie website.
Bookmarks
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
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
s p a r k l e s
Hannah Arendt papers, 1898-2006
Why information is the unifying principle that allows us to understand the evolution of complexity in nature
At least the press is saying Jan 16, 2024 now. Tough luck for those doing their holiday shopping for me.
Happy to announce that @PrincetonUPress will be publishing “Evolution of Biological Information”. Look for it in 2022. @AlisonKalett pic.twitter.com/EkEpMyMROs
— Chris Adami (@ChristophAdami) November 12, 2021
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.
As Prince of Wales, Charles was always ready with an opinion. Now, with his coronation at hand, his job is to have none. https://www.newyorker.com/magazine/2023/05/08/can-charles-keep-quiet-as-king-coronation
A new year brings new calls for a return to personal blogging as an antidote to the toxic and extractive systems of social media.
🔖 How to add your blog to Mastodon
How do I add my WordPress blog to Mastodon?
We often think of scientific ideas, such as Darwin's theory of evolution, as fixed notions that are accepted as finished. In fact, Darwin's On the Origin of Species evolved over the course of several editions he wrote, edited, and updated during his lifetime. The first English edition was approximately 150,000 words and the sixth is a much larger 190,000 words. In the changes are refinements and shifts in ideas — whether increasing the weight of a statement, adding details, or even a change in the idea itself.
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.
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 @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. ()
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A summary of the history of philosophy showing the positive/negative connections between ideas
Interestingly it has not only a spatial interface and shows spatial relationships between people and ideas over time using a timeline, but it also indicates—using colored links—the ideas of disagreement/contrast/refutation and agreement/similarity/expansion.
What other (digital) tools of thought provide these sorts of visualization affordances?
Here’s a surprisingly useful thinking tool for anybody interested in the history of Western philosophy: a sort of garden of forking paths of argument. https://t.co/AH1ophVXH8
— Daniel Dennett (@danieldennett) October 9, 2018
Gotthard Deutsch (1859–1921) taught at Hebrew Union College in Cincinnati from 1891 until his death, where he produced a card index of 70,000 ‘facts’ of Jewish history. This article explores the biography of this artefact of research and poses the following question: Does Deutsch’s index constitute a great unwritten work of history, as some have claimed, or are the cards ultimately useless ‘chips from his workshop’? It may seem a curious relic of positivistic history, but closer examination allows us to interrogate the materiality of scholarly labor. The catalogue constitutes a total archive and highlights memory’s multiple registers, as both a prosthesis for personal recall and a symbol of a ‘human encyclopedia’. The article argues that this mostly forgotten scholar’s work had surprising repercussions: Deutsch’s student Jacob Rader Marcus (1896–1995) brought his teacher’s emphasis on facticity to the field of American Jewish history that he pioneered, catapulting a 19th-century positivism to the threshold of the 21st century. Deutsch’s index was at an inflection point of knowledge production, created as historians were shifting away from ‘facts’ but just before new technologies (also based on cards) enabled ‘big data’ on a larger scale. The article thus excavates a vision of monumentality but proposes we look past these objects as monuments to ‘heroic’ scholarship. Indeed, Deutsch’s index is massive but middling, especially when placed alongside those of Niklas Luhmann, Paul Otlet, or Gershom Scholem. It thus presents a necessary corrective to anointing such indexes as predecessors to the Internet and big data because we must keep their problematic positivism in perspective.
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.