User Profile

This text leaves me with the distinct impression that it was written rapidly in the wake of the election of Trump—and that's not necessarily a bad thing. But it /is/ a /lot/ of information to take in: names, organizations, ideas, movements. If you're not familiar with many of these things in advance, it can be difficult to distinguish between the "blink and you'll miss them" fascist actors and movements, and the ones that have had a deep and lasting impact. Sincerely, it's something of a 300-page infodump.

That said, i still think it's very much a text worth reading. I didn't try especially hard to remember every last detail that i was reading; it was more an impressionistic read-through, but even this was really valuable to me. It makes a few things clear: fascists are /everywhere/, trying at all times to find entry points into other movements in order to recruit and swell their own ranks; fascism is not a single, monolithic entity: there are many distinct currents and flavours of fascism, all of which are in at best uneasy alliances with one another, but just as often at war; fascism tries very hard to be "neither left nor right", as is to be expected from a movement whose chief aim is to gain and wield power over all other considerations (including consistency or cohesion); and, perhaps most important for those of us on what could broadly be called "the left": we are not immune. There is no ideology that is safe from fascist entryism. Given a chance, given space to act, fascists will pull from our ranks, will find ways of seducing us. Fascists and fascism must be actively considered and resisted.

Given its title, i thought this text was going to contain more analysis, more discussion of tactics and strategy, and i'm a little disappointed that it didn't. But its length, even as a fairly shallow dive into the complete history of a movement with so much breadth, variation, and nuance, makes clear that this could not really have been possible; it must be left to others.

Yep. That about sums up the maintenance of hegemony.

Goodness, this is the big one.

I have a long and complicated relationship with Dummit & Foote. This is a text that one can get absolutely lost in, and i absolutely have. For example, i think that at one time i had solved (nearly?) all of the problems in Part I. It's full of excellent examples, it's full of wonderful exercises, and… honestly, one could probably spend the rest of one's life reading it if one wished.

That's both good and bad.

On the one hand, it's wonderful about taking its time, about being complete, thorough, approachable to students at just about any level of post-proofwriting-course experience (or maybe with an elementary number theory course under their belts). It's a text that really tries to bring everything it can to the student, and be a comprehensive guide. And… the student is well-rewarded for their efforts. This text has a lot to teach, and spending quality time with it will yield wonderful rewards.

On the other hand, because it's such a vast forest, one can find oneself lost. At the very least, it can take a /very long time/ to get to some topics, or through others. I also don't know that i find all of its explanations and approaches to be the cleanest or the most crystal-clear. For example, i've long found that the presentation of tensor products is wanting in some way that i have trouble specifying; perhaps it's that it is so general that a student can readily miss the point of the exercise, the goal of the tool. I'm not sure; i've not looked at it in some time. Mostly… i've read better presentations elsewhere.

Still… i think one would be hard-pressed to find a better comprehensive algebra text. I think Lang is probably the other major reference (and/or textbook), and… i've never found Lang's writing especially compelling—he was infamous for completing textbooks in a few months, and i think it shows in his presentation; i often find that he says too little in his texts, or tries to be too slick in his presentation in order to make topics appear simpler than they are. In so doing, he will make certain examples appear wonderfully natural and straightforward, while leaving a reader totally adrift on related problems.

I think that this is a text every student with any serious interest in mathematics should own. Even with its drawbacks, well… my copy's spine has been duct-taped back together because it has seen so much happy use, so i think its kind, gentle, and thorough presentation is well worth taking a good look at.

One of the canonical undergraduate texts, this is my first time opening it, and… i must say, i'm impressed. I've read several undergraduate analysis texts, but this is probably the one i've enjoyed most. Of course, it may be that things look different because of the experience i already have, but, still, i think it's a wonderful read. The presentation is clear and efficient, and there are some stylistic choices that feel right to me. For example, Rudin's definition of the "upper limit" of a sequence (or its "lime superieur," or its "limsup") is in terms of the limit points of said sequence thought of as a set, rather than in terms of the limit of the sequence of suprema of tails of the sequence, which is the usual definition (and which i have /always/ found cumbersome to think about). This definition may be less efficient in terms of actually /calculating/ the upper limit of a sequence, but it is amazingly efficient for writing proofs that utilize this tool. There are myriad other examples present that also feel refreshingly clear to me, but… well, perhaps you get the idea.

I've read nearly the first three chapters of this text, and i look forward to reading more.

Thus far, i've found this an engaging read. The presentation of the material is lean, which has its advantages and disadvantages. I'm mostly reading this text as a review, so its complete lack of formal exercises and its brisk (but, crucially, complete) summary of undergraduate topology is perfect for me. But i think even the novice would find this an excellent companion to something like Munkres, the traditional introductory topology text. Indeed, this text presents a number of examples very clearly, with excellent diagrams and accompanying descriptions. Further, Jänich has a real talent for keeping the reader's eyes on the larger picture, on developing ideas and intuition, and not getting overly bogged down in technical details (which they trust the reader will be able to provide—these tend to serve as the text's exercises).

Perhaps the main thing to bear in mind while reading is that some portions of the text assume a knowledge of some background material that i would think would be unfamiliar to many, if not most, undergraduates. But… i've just been skipping things i've not been exposed to, or that i have only vague memories of. Doing so does not seem to disrupt the overall flow of the text; it merely leaves one with fewer examples to draw from, which is perfectly all right. It also gives one material to return to.

The point is: i like it very much, so far, about three chapters in.

Promised myself i'd read a book on category theory this year. Here goes…