Given a function f(x) which is continuous on an interval [a,b] & differentiable on its interior, the Mean Value Theorem guarantees there exists a value c in that interval such that the line tangent to the function when x = c is parallel to the line drawn between ( a , f(a) ) and ( b, f(b) ). (GIF Description: A function f(x) is plotted from x = a to b, and a red line is drawn b/w its endpoints at ( a , f(a) ) & ( b , f(b) ). A point tracing f(x) carries a compass that records the tangent’s slope relative to the red line. When their slopes are equal, x is labeled c. In the first GIF, the function has a single maxima. In the second GIF, the function has multiple extrema.)
The Intermediate Value Theorem guarantees that for every real number “y” between two outputs of a real continuous function f(x) there exists at least one value “c” between the corresponding inputs such that y = f(x) when x = c.
(GIF Description: The graph of a function f(x) as it ranges from x = a to x = b. Per frame, an output value y between f(a) and f(b) is shown to intersect the curve f(x) for some x = c. As the GIF animates, y sweeps across the range of f(x) and indicates a value of c for every y.)
(GIF Description: Like the first GIF, except now the function leaves the range defined by the endpoints of the domain.)
icavein
Thank you clam man
trueautisticaquarius
Reblog the encouraging clam man to boost someone’s motivation. You know you wanna.
encouraging clam man is always there for me in my time of need. may he be there in yours as well.
If Clam Man can harvest Asiatic clams in -10 degree weather, I can survive 2020.
me hyping myself up before entering any public area: i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal
2020 edition:
me hyping myself up before logging in to start the zoom meeting: i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal i’m normal
When people found out I was a math major they were always like, ‘Oh, I bet you can calculate numbers super fast!’ I would always tell them, 'Dude, I haven’t seen numbers in years.’
Transitions to Higher Math professor (via mathprofessorquotes)
So, when I have nervous breakdowns, I stay indoors for days and do projects. This is my most recent thing. I borrowed a copy of Folland’s Real Analysis from my guy. It’s over 100 bucks to purchase from Wiley & Sons, and the binding is SO BAD that all the pages start falling out immediately. Also, it’s free as a PDF. But, anyway, this one was already purchased, and my guy gave me permission to do this to it:
And this:
And a little bit of this and this:
So that it would be like this now:
I’m waiting for the corner protectors to come in to cover up some not-quite-excellent corner work, but all in all I’m very happy about this new hobby. Rebinding books is a seriously valuable skill for a person in academia. I’m about to make some printed, older-edition-of-textbooks-that-are-out-of-copyright PDFs look SO GOOD, heck yes.
Oops I did the thing again to My New Favorite Book
Reblogging with the latest addition to my ‘math books as ancient grimoires’ collection, because bookbinding is my official 2020 coping hobby.
So, when I have nervous breakdowns, I stay indoors for days and do projects. This is my most recent thing. I borrowed a copy of Folland’s Real Analysis from my guy. It’s over 100 bucks to purchase from Wiley & Sons, and the binding is SO BAD that all the pages start falling out immediately. Also, it’s free as a PDF. But, anyway, this one was already purchased, and my guy gave me permission to do this to it:
And this:
And a little bit of this and this:
So that it would be like this now:
I’m waiting for the corner protectors to come in to cover up some not-quite-excellent corner work, but all in all I’m very happy about this new hobby. Rebinding books is a seriously valuable skill for a person in academia. I’m about to make some printed, older-edition-of-textbooks-that-are-out-of-copyright PDFs look SO GOOD, heck yes.
LAST SEMESTER SUCKED, YO. I’M BACK ON MY ART N CRAFT SHIT
And, yes, that’s the mock up for the coverplate of the TDA book in the lower right corner.
You know, people think mathematics is complicated. Mathematics is the simple bit. Its the stuff we can understand. Its cats that are complicated. I mean, what is it in those little molecules and stuff that make one cat behave differently than another, or that make a cat? And how do you define a cat? I have no idea.
— John Horton Conway
There’s really nothing like a pandemic in which nobody listens to medical science to get a person to second-guess their career choice in interdisciplinary medical research.
Shopping for groceries late at night, the grad student minimizes his exposure to other people.
victoriousvocabulary
TORUS
[noun]
1. Architecture: a large convex molding, more or less semicircular in profile, commonly forming the lowest molding of the base of a column, directly above the plinth, sometimes occurring as one of a pair separated by a scotia and fillets. and column.
2. Geometry: a) a doughnut-shaped surface generated by the revolution of a conic, especially a circle, about an exterior line lying in its plane. b) the solid enclosed by such a surface.
3. Botany: a) the receptacle of a flower. b) a thickening of the wall membrane in the bordered pits occurring in the tracheid cells of the wood of many conifers.
4) Anatomy: a rounded ridge; a protuberant part.
Etymology: from Latin, literally, strand, thong, raised ridge.
-
Original: by Daniel Martin Diaz
Jonathan Gleason was my friend who committed suicide just over a month ago… and I just found out that he wrote this 800+ page analysis textbook. By himself. Because he was teaching analysis and he was dissatisfied with the textbook he was assigned so he just…. wrote his own.
Even if you haven’t done any math… please just take a look at this. Scroll through it as fast as you like. It’s incredible that he put so much work and so much free time into this… I’m still in awe and I really want everyone to see it. In particular, if you want a good laugh, look at chapter 5 of the analysis textbook. The opening paragraph is SO Johnny.
He also wrote a linear algebra textbook, here.
I really want to thank everyone who has reblogged/liked this, and even anyone who just clicked on the link to check it out. I wasn’t expecting more than a handful of notes on this, so knowing that his hard work gets shared and even appreciated by a few strangers really means a lot.
I’ve taken some of the best/easiest to follow snippets and provide them here, I hope you enjoy them as much as I have:
“Da fuq”.
Oh thank god.
At least he admits when he’s being sloppy.
God, I wish more math textbooks read like this.
And last but not least, my absolute favorite part, the opening to the chapter on integration.
There are so many more tidbits like this and I wish literally all of my textbooks could be written like this.
Jonothan Gleason died Jan 16th, 2018 and it means so much to me that so many people got a kick out of the little pieces of him that are in this book. Thanks for all of the rb’s and likes, I’m so happy that even just a few hundred people got to enjoy his writing and hard work.
I emailed Jonny’s parents and linked them to this post so they can know that total strangers are appreciating his work. It’s been 2 years now and I still think of him every day; thank you to everyone for sharing this and for all of the kind words, every single one means so much
the real numbers: more real than the real world itself™
What the fuck does that even mean
to put it back in context, this is from a book on synthetic differential geometry in an appendix where some sheaf semantics for the notions are developed; I interpret this line as the author ribbing people for the fact that to an extent people can’t just take new synthetic axioms seriously on their own without some semantics towards real-number based analysis or whatever system, like those are somehow more “real” than whatever new system you can come up with
This interesting thing has happened where I think I’ve finally absorbed the fact that no state is permanent- I mean if I’m sad about something or stressed about something I take it a lot more on stride and remind myself that everything ends eventually, I won’t always feel like this, and sadness is just a state of being
So instead of feeling like a useless moron that can’t do any mathematics whatsoever
I can be like oh ok so I’m a useless moron that can’t do any mathematics whatsoever but I can change that
Same with not being a good person. Ok so I’m not “good enough”. I’m constantly trying to be better and do better by others & myself and realistically? That’s all I can expect from myself so ¯\_(ツ)_/¯
I don’t even pretend to be ‘modest’ or undercut my hard work anymore. Whenever someone in real life tells me they’re impressed or that they’re proud of me I respond like this:
BECAUSE HONESTLY IM TRYING SO GODDAMN HARD AND IF I DONT GIVE MYSELF CREDIT FOR THAT IM GOING TO GO INSANE
Anyway lads that’s what I’m reflecting on less than 3 hours before the new decade, happy new year and all that
I feel this way all the time when it comes to exams. I endeavor to embody this positive outlook going forward. All we can do is our best, and it’s okay for that to be good enough. It is good enough. It is the only victory that matters. I should not allow the more arbitrary distinctions of ‘good enough’ to matter so much.
