Here are the notes from a basic course on category theory. Unlike the Fall 2015 seminar, this tries to be a systematic introduction to the subject. A good followup to this course is my Fall 2018 course. If you discover any errors in the notes please email me, and I'll add them to the list of errors. You can get all 10 weeks of notes in a single file here:You can get the LaTeX files created by Nelson and García Portillo here. Their typeset version was based on these handwritten versions:
- Lectures notes typeset by Michael Nelson and Marco Aurelio García Portillo.
Bookmarks
Interesting Links/bookmarks for personal use or sharing with others
👓 Category Theory Course | Azimuth | John Carlos Baez
I’m teaching a course on category theory at U.C. Riverside, and since my website is still suffering from reduced functionality I’ll put the course notes here for now. I taught an introductory course on category theory in 2016, but this one is a bit more advanced. The hand-written notes here are by Christian Williams. They are probably best seen as a reminder to myself as to what I’d like to include in a short book someday.
🔖 Introduction to Category Theory | UCLA Continuing Education
This course is an introduction to the basic tenets of category theory, as formulated and illustrated through examples drawn from algebra, calculus, geometry, set theory, topology, number theory, and linear algebra.
Category theory, since its development in the 1940s, has assumed an increasingly center-stage role in formalizing mathematics and providing tools to diverse scientific disciplines, most notably computer science. A category is fundamentally a family of mathematical obejcts (e.g., numbers, vector spaces, groups, topological spaces) along with “mappings” (so-called morphisms) between these objects that, in some defined sense, preserve structure. Taking it one step further, one can consider morphisms (so-called functors) between categories. This course is an introduction to the basic tenets of category theory, as formulated and illustrated through examples drawn from algebra, calculus, geometry, set theory, topology, number theory, and linear algebra. Topics to be discussed include: isomorphism; products and coproducts; dual categories; covariant, contravariant, and adjoint functors; abelian and additive categories; and the Yoneda Lemma. The course should appeal to devotees of mathematical reasoning, computer scientists, and those wishing to gain basic insights into a hot area of mathematics.
January 8, 2019 - March 19, 2019
Tuesday 7:00PM - 10:00PM
Location: UCLA
Instructor: Michael Miller
Fee: $453.00
The new catalog is out today and Mike Miller’s Winter class in Category Theory has been officially announced.
Oddly, it wasn’t listed in the published physical catalog, but it’s available online. I hope that those interested in mathematics will register as well as those who are interested in computer science.
🔖 Unsplash | Beautiful Free Images & Pictures
Beautiful, free images and photos that you can download and use for any project. Better than any royalty free or stock photos.
🔖 Surreal number | Wikipedia
In mathematics, the surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field.[a] If formulated in Von Neumann–Bernays–Gödel set theory, the surreal numbers are a universal ordered field in the sense that all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, can be realized as subfields of the surreals.[1] The surreals also contain all transfinite ordinal numbers; the arithmetic on them is given by the natural operations. It has also been shown (in Von Neumann–Bernays–Gödel set theory) that the maximal class hyperreal field is isomorphic to the maximal class surreal field; in theories without the axiom of global choice, this need not be the case, and in such theories it is not necessarily true that the surreals are a universal ordered field.
🔖 Racial Equity Institute
We are an alliance of trainers, organizers, and institutional leaders who have devoted ourselves to the work of creating racially equitable organizations and systems. We help individuals develop tools to challenge patterns of power and grow equity. Join us today.
🔖 My White Friends by Myra Greene
A photo series of Myra Green's white friends. A study of whiteness in America.
hat tip: Seeing White on Scene on Radio
🔖 reveal.js – The HTML Presentation Framework
A framework for easily creating beautiful presentations using HTML. Check out the live demo. reveal.js comes with a broad range of features including nested slides, Markdown contents, PDF export, speaker notes and a JavaScript API. There's also a fully featured visual editor and platform for sharing reveal.js presentations at slides.com.
🔖 Splotpoint
A Wordpress-theme SPLOT for presenting the SPLOT Way (on the web) - cogdog/splotpoint
Hat tip: Greg McVerry in IndieWeb chat
🔖 Microformats Reader | Michael Beaton
A browser extension that brings the Indieweb to the surface!
🔖 Read.as
Matt Baer🔖 The Oxygen of Amplification | Data & Society
New Data & Society report recommends editorial “better practices” for reporting on online bigots and manipulators; interviews journalists on accidental amplification of extreme agendas
This report draws on in-depth interviews by scholar Whitney Phillips to showcase how news media was hijacked from 2016 to 2018 to amplify the messages of hate groups.
Offering extremely candid comments from mainstream journalists, the report provides a snapshot of an industry caught between the pressure to deliver page views, the impulse to cover manipulators and “trolls,” and the disgust (expressed in interviewees’ own words) of accidentally propagating extremist ideology.
After reviewing common methods of “information laundering” of radical and racist messages through the press, Phillips uses journalists’ own words to propose a set of editorial “better practices” intended to reduce manipulation and harm.
As social and digital media are leveraged to reconfigure the information landscape, Phillips argues that this new domain requires journalists to take what they know about abuses of power and media manipulation in traditional information ecosystems; and apply and adapt that knowledge to networked actors, such as white nationalist networks online.
This work is the first practitioner-focused report from Data & Society’s Media Manipulation Initiative, which examines how groups use the participatory culture of the internet to turn the strengths of a free society into vulnerabilities.
🔖 This Is Why We Can’t Have Nice Things: Mapping the Relationship between Online Trolling and Mainstream Culture by Whitney Phillips | The MIT Press
Why the troll problem is actually a culture problem: how online trolling fits comfortably within today's media landscape.
Internet trolls live to upset as many people as possible, using all the technical and psychological tools at their disposal. They gleefully whip the media into a frenzy over a fake teen drug crisis; they post offensive messages on Facebook memorial pages, traumatizing grief-stricken friends and family; they use unabashedly racist language and images. They take pleasure in ruining a complete stranger's day and find amusement in their victim's anguish. In short, trolling is the obstacle to a kinder, gentler Internet. To quote a famous Internet meme, trolling is why we can't have nice things online. Or at least that's what we have been led to believe. In this provocative book, Whitney Phillips argues that trolling, widely condemned as obscene and deviant, actually fits comfortably within the contemporary media landscape. Trolling may be obscene, but, Phillips argues, it isn't all that deviant. Trolls' actions are born of and fueled by culturally sanctioned impulses—which are just as damaging as the trolls' most disruptive behaviors.
Phillips describes, for example, the relationship between trolling and sensationalist corporate media—pointing out that for trolls, exploitation is a leisure activity; for media, it's a business strategy. She shows how trolls, “the grimacing poster children for a socially networked world,” align with social media. And she documents how trolls, in addition to parroting media tropes, also offer a grotesque pantomime of dominant cultural tropes, including gendered notions of dominance and success and an ideology of entitlement. We don't just have a trolling problem, Phillips argues; we have a culture problem. This Is Why We Can't Have Nice Things isn't only about trolls; it's about a culture in which trolls thrive.
🔖 The Ambivalent Internet: Mischief, Oddity, and Antagonism Online by Whitney Phillips and Ryan M. Milner
This book explores the weird and mean and in-between that characterize everyday expression online, from absurdist photoshops to antagonistic Twitter hashtags to deceptive identity play.
Whitney Phillips and Ryan M. Milner focus especially on the ambivalence of this expression: the fact that it is too unwieldy, too variable across cases, to be essentialized as old or new, vernacular or institutional, generative or destructive. Online expression is, instead, all of the above. This ambivalence, the authors argue, hinges on available digital tools. That said, there is nothing unexpected or surprising about even the strangest online behavior. Ours is a brave new world, and there is nothing new under the sun – a point necessary to understanding not just that online spaces are rife with oddity, mischief, and antagonism, but why these behaviors matter.
The Ambivalent Internet is essential reading for students and scholars of digital media and related fields across the humanities, as well as anyone interested in mediated culture and expression.
🔖 Storyful – The world’s social media intelligence agency
Storyful is a social media intelligence agency that sources and verifies insights for media, communications and brand partners by analyzing digital content.