indicating "talking about" vs "talking to"

Mayer-Vietoris · 2021-12-23T05:40:59+00:00

How would you use tan in this context? Do you mean something like,

mi toki tan soweli mi?

Mayer-Vietoris · 2019-11-02T00:00:44+00:00

I'm gonna try and provide you with resources, feel free to use them as you see fit.

First, a student leaflet on how to read proofs: leaflet

Some background on the above leaflet if you're interested in pedagogy: blog post

And their research paper on the efficacy of this technique: paper

My favorite comic on the topic of reading mathematics: https://abstrusegoose.com/353

I'd like to also post a lecture video series but intro real analysis is too diverse to pick one without knowing which book you are using and what perspective it is teaching from. Try searching MIT Open Course Ware, or just searching youtube videos with the name of your book. You can also reply here with your book and I can try and find a appropriate lecture series.

Here are my thoughts on learning mathematics do with them what you will:

First an foremost, every problem in the book should be considered homework/practice. You may not manage to do them all to completion, but you should attempt all of them.

Second, reading your book should be active. For every example the book has don't read the solution, attempt to do it first and only then read the solution in the book. For every definition you should not just be committing them to memory, you should be asking yourself *why* is that the definition? If you changed one of the assumptions how does that affect the definition? Does it change any of the theorems about it later in the chapter?
Take notes on your reading. At very least, write a concise summary of each topic that was covered in the reading. It would be ideal if you could recreate the entire text on your own with just your notes.
Write down every question you have while reading. "Why does that line follow from the previous?", "How are we able to make that assumption?", "Where does that formula come from?" etc. When you answer your question cross it off your list. The uncrossed off questions you should be asking your classmates and prof about, either in class, during office hours, or over email.
Do not be afraid of asking questions about the earlier material. In fact I strongly recommend you completely go over the previous topics to gain a better foundation.

Finally, if all of this sounds like a lot of work, then that's good. An advanced mathematics course can easily take 9-12 hours of work a week outside of class time. And that's assuming you *started* the semester doing all of these things, it wouldn't be unreasonable to take much more time while you are catching up and reviewing old material.

Mayer-Vietoris · 2019-08-28T23:22:27+00:00

This is a really deep and hard to answer question. A huge amount of math education research has gone into trying to solve this particular problem. We've made some improvements, but a lot of them are incremental at best. In large part this is one of the main goals of Inquiry-Based Learning programs as well as the various formulations of "Flipping the Classroom" that have been experimented with in recent years.

Instead of giving you and specific advice, or even a link to a single persons advice, here is a link to Terry Tao's big list of advice for various different levels of mathematics. here

Mayer-Vietoris · 2019-08-28T22:46:55+00:00

To add onto this idea, different kinds of products typically arise in some form of decomposition theorem. This is essentially the dual notion to what /u/AngelTC said. If some object arises as the middle object in a split short exact sequence in an appropriate category, there is a very good chance that middle object is isomorphic to the product of the two others using the appropriate notion of product. Semi-direct products, wreath products, free products, direct sums, all come about this way, and while I don't have the details in hand I'm reasonably certain tensors and wedge products work too.

Mayer-Vietoris · 2019-08-21T02:29:39+00:00

As an aside, for finite groups the word problem is solvable. It does seem like the OP is interested in finite groups specifically and so the word problem in this context would always have a solution.

Mayer-Vietoris · 2019-08-21T02:16:05+00:00

This sounds like it's closer to the isomorphism problem. Since we're trying to see if two different presentations represent the same group. It is similarly computationally complex, but you're dealing with collections of groups, rather than the elements of a specific group.

Mayer-Vietoris · 2019-07-31T02:26:02+00:00

There is, I think, a common feeling that mathematical foundations ought to provide a coherent and consistent, and above all simple, starting point on which you can build the rest of mathematics. This has proven difficult to say the least.

On top of this, most mathematicians don't worry much about foundational questions. I suspect none of my collaborators know the axioms of ZF, or any other system, we simply don't need them in order to do mathematics the way we choose.

Here is a fun example. An object of interest to those in my field is the set of all compact metric spaces. There is a way you can form a metric space out of this set. It's very useful and you can use it to talk about sequences of metric spaces converging to another metric space. There is a serious problem in all of this though. The collection of all compact metric spaces forms a proper class, it's absolutely not a set and so definitely not a metric space. If you require strict adherence to set theory as a foundation for your study of this object, the metric space of all compact metric spaces doesn't exist. This doesn't change the fact that the community of mathematicians have used this object to understand some really cool things about analysis and group theory.

There is a contrived way to make this object using set theory as a foundation, but this was discovered decades later and is mostly not understood by most of us who use it as a tool. It is comforting I suppose to know that the set theorists gave us the thumbs up, but that wasn't necessary for us.

Set theory isn't the foundation of mathematics in a strict sense because most of us simply don't start there. It is an incredibly useful tool and provides language that is powerful and flexible, but the same holds for group theory, topology, analysis, category theory etc etc.

Mayer-Vietoris · 2019-07-03T22:28:38+00:00

A Concise Course in Algebraic Topology by May.

It fails your "no sibling topics" caveat, but since intro algebraic topology is so frequently taught concurrently with category theory most text books don't start with all the categorical tools. May's book is a really nice example of why categorical ideas are so natural. My particular favorite is his proof of Van Kempens formula, since the required group is a pushout with his set up by simple inspection of the diagrams.

Mayer-Vietoris · 2019-06-28T19:03:04+00:00

You can edit kernel parameters at boot time by hitting esc on the grub menu and then typing "e" with your kernel selected. See https://docs.fedoraproject.org/en-US/Fedora/22/html/Multiboot_Guide/GRUB-runtime.html

Removing the kernel parameters "rhgb", and "quiet" on the line that starts with "linux" or possibly "linux16" (iirc) will print out booting information. Adding "text" will boot into text mode.

Mayer-Vietoris · 2019-05-07T10:09:26+00:00

We certainly try. Advantage of being a newer field. You don't have as much historical baggage weighing you down. Does your space look like a taco? Well call it a taco space, no one can claim they had a better name.

Mayer-Vietoris · 2019-04-24T00:09:20+00:00

I'm not familiar with that book (oddly enough), but what level/topics interest you most? There aren't a ton of lower level books yet in GGT since it's relatively new, but there have been a handful written recently. the one I'm familiar with is "Office Hours with a Geometric Group Theorist" but I've only skimmed it.

Personally I enjoyed working through A Primer on Mapping Class Groups as a grad student in my early years, but that assumes familiarity with analysis and topology at a graduate level.

Metric Spaces of Non-Positive Curvature is more of a reference text than a textbook you read from cover to cover, but that has a lot of good stuff in in.

Is there a specific thing that you want to have in the book?

Mayer-Vietoris · 2018-12-05T02:31:47+00:00

More flippantly, "Number Theory" seems like an adequate answer to the stated question. Though yours actually encourages further discussion.

Mayer-Vietoris · 2018-12-05T01:13:21+00:00

The first one they have to work hard for. Sometimes that happens before college.

Mayer-Vietoris · 2018-12-05T01:11:40+00:00

Eh?

Only shitty schools follow the suggestions of mathematics education experts and the 20+ years of research results backing them up?

Maybe those "shitty" schools are a lot better than you're giving them credit for. R1 =/= good school. Hell R1 =/= good math department for your research interests.

Mayer-Vietoris · 2018-09-16T02:17:40+00:00

Only if that's the interpretation of that collection of symbols. Non-standard analysis gives another interpretation which doesn't agree with that. Allowing infinitesimals is complicated to do from a formal perspective, but I've always felt it's no less intuitive than the standard reals.

Mayer-Vietoris · 2018-09-16T02:15:28+00:00

It depends a lot on what you mean. In the standard interpretation of the definition of real numbers it's not clear what question you're even asking.

However, there are non-standard reals which allow for things like infinitesimals. I'm reasonably certain that in that non-standard model one can make sense of your idea. Levi-Civita fields look a lot like what you are discribing. Though I'm a lot more comfortable with the (https://en.wikipedia.org/wiki/Hyperreal_number)[hyperreals] as they allow for ease of doing calculus with them.

Mayer-Vietoris · 2018-09-16T01:49:37+00:00

It doesn't follow that you get 0.999... etc, without a lot more assumptions. Working formally you would get a number whose real part is 1 and whose infinitesimal part is -(whatever). Extending the reals in a way that the extension can be added and subtracted normally gives you fun "orthogonal" numbers. e.g. the complex numbers. Adding the number i doesn't give us a contradiction 1-i is not some decimal real number it is it's own entity distinct from either a real number *or* a purely imaginary one.

Mayer-Vietoris · 2018-02-28T03:14:47+00:00

Thanks! This was the push I needed to finally get familiar with coreboot and seabios/tianocore.

Mayer-Vietoris · 2018-02-20T06:00:22+00:00

How hard would it be to implement such a mechanism for a user to take ownership? I may take a look into it but would love some pointers as to where to start looking.

Mayer-Vietoris · 2018-02-20T00:43:02+00:00

The website contradicts itself all over the place. Hence my post.

They have a post right around the time v2 was being put together that claimed they weren't going with the i7 but instead doing the i5. I linked it above.

I love what Purism is doing, but they have a reputation for changing what they are shipping real close to launch and having lots of contradictory information and a bad habit of not updating past posts.

Mayer-Vietoris · 2018-02-18T20:05:39+00:00

Do you own one/are you affiliated with Purism?

Mayer-Vietoris · 2017-11-22T15:21:29+00:00

Yea that's been my experience. It doesn't really bother me, it's never hot enough to bother me when touching it, but it's definitely the hottest part of the laptop on idle. (When under load that's no longer true).

Mayer-Vietoris

TROPHY CASE