Ah yes, I remember buying that textbook
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@lcamtuf, Chapter 1 defines numbers, some common mathematical notation, and a few other things that give you hope that you can read this book.
You might get through Chapter two.
By Chapter 3, you,put it on the shelve with all your other Springer textbooks.
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@jpgoldberg @lcamtuf Springer books are like the math entries on Wikipedia. They’re both places where people are in a competition to make themselves as baroque and not just esoteric, but practically occult as possible.
Now excuse me, I have to finish replacing the word “one”with“unity”
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@jonathankoren - they're actually not trying to be baroque, they are just mathematicians talking the only way they know how. I know: I'm a mathematician, and I find these entries generally quite clear. The problem is, it's hard to get mathematicians to write in ways that nonmathematicians can understand. At least the first paragraph should be aimed at everyone.
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@johncarlosbaez
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@jonathankoren - sums to unity, adds to one - same thing to us weirdos. Feel free to change it to "sums to one"!
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@johncarlosbaez @jonathankoren I thought the reason for that was that "sums to one" invites the question "sums to one what?"
In some contexts it could be really misleading. "a series of dyadic fractions that sums to one" could mean "a series of dyadic fractions that sums to unity" or "a series of dyadic fractions that sums to a dyadic fraction".
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@mjd @jonathankoren - okay, that's a decent reason for using "sums to unity". I would never dream of interpreting "sums to one" to mean "sums to one of those things I was just talking about", and anyone using it to mean that is really asking for trouble. But I agree that it's good to completely eliminate ambiguity when writing math.
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@johncarlosbaez @jonathankoren I think it dates from a time when grammatical patterns were different: sentences were longer and distant anaphoras were more common. Also a time when the unambiguous "sums to 1" would have looked more uncouth.
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@mjd @johncarlosbaez @jonathankoren
I thought that this goes back to (at least) the Pythagoreans. For them unity was not a number. And it’s only since Frege’s definition of the integers that one is clearly a number.
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@jpgoldberg @johncarlosbaez @jonathankoren The Treviso Arithmetic of 1478 says explicitly that 1 is not a number.
But I find your suggestion of Frege hard to understand. Are you reallly saying that Gauss wouldn't certainly have considered 1 a number? Cauchy? Legendre?
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@mjd @johncarlosbaez @jonathankoren
I never meant to say that Gauss et al wouldn’t consider 1 a number. I wasn’t trying to suggest that Frege is responsible for 1 being considered a number, but I do see how that could follow from what I wrote.
I am ignorant of when 1 became fully accepted as a number, and so I shouldn’t have written something that carries the implicature that it is “only since Frege.”
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@mjd @johncarlosbaez @jonathankoren One thinks it is because 'one' refers to oneself.
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@johncarlosbaez @jonathankoren Donald Knuth’s Concrete Mathematics makes me think that maybe computer scientists are generally better at writing maths textbooks than mathematicians are.
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@benjamingeer @jonathankoren - "Generally", eh? Do you have more than one example?
It's a great book, but Knuth happens to be a great writer, writing about one of the things he knows best. Also, "concrete" mathematics is a lot easier to explain to people who already know calculus than anything like abstract algebra, topology, real analysis, and so on - the main topics in upper-level undergraduate math courses.
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@johncarlosbaez @jonathankoren I’m definitely overgeneralising from a sample size of 1 😄
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@lcamtuf this is the CS unit I keep taking. They change the name every year, but it's always this unit.
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@lcamtuf fuckin lol
so many times
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@lcamtuf I remember a commutative cube like that. I think it was either in Warner’s Foundations of Differentiable Manifolds and Lie Groups or in Bott and Tu’s Differential Forms in Algebraic Topology.
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@lcamtuf They have got me so many times.
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@lcamtuf
[#]Alt4You
A book cover. Titled Introduction to That Thing, subtitled But only for people who already know it.
Second edition, Springer.
It has an incomprehensible diagram and is made in the typical Springer style with their logo.
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@lcamtuf
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@lcamtuf "Category theory for the seasoned category theorist who lost all interest in communicating with non-category theorists but has to pretend like they are to get at least one grant per year to pay for heating and food"
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@lcamtuf @xameer AUTHOR: I will prove to others that I know the thing!
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@lcamtuf
TOC
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@jnpn @lcamtuf
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@lcamtuf Also the number of authors has a linear relation to the shit they throw on you, up to the point when they overflow back to a single author, a dark souls boss.
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@lcamtuf oh, I attended that lecture. Would've been nice to have a written version along with it.
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@lcamtuf
Not Springer, but: Set Theory by Kenneth Kunen. It's even in the same colour.
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@lcamtuf oh hey, it's that meme format I made! This version's by Davide Castelvecchi - https://aperiodical.com/2022/05/didnt-graduate-texts-in-mathematics/
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@lcamtuf @christianp oof, i was not prepared for how hard that title by Prominent Mathematician hit
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@chrisamaphone @lcamtuf @christianp RIGHT? I literally came back to this thread to say some version of that.
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@chrisamaphone @lcamtuf @christianp It also applies to philosophy, physics, computer science, nursing, modern art, etc etc--highly versatile, that one.
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@lcamtuf Tbh I was disappointed about this book. While I wholeheartedly agreed with everything in it, it felt like one of those book where everything was obvious in hindsight, but without any actual hindsight needed. I made a review saying that this book is excellent but aimed at novice readers.
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@lcamtuf because the post is popular please add an alt-text
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@lcamtuf
Hey, sorry to interrupt, but as a non-professional mathematician, I can confidently tell you that you're overcomplicating things.
What you're actually looking at is just a trivial crystallographic Simple Cubic system of Argon, Boron, Carbon, Potassium, Lithium, Magnesium, Phosphorus, Quarks (obviously!), and Radon under elastic constraint. Naturally!
Unless it's a plastic deformation...
Or? wait, what's that? there two types of forces?
Let me kindly ask my colleague Dunning-Krugger: He knows everything on the subject.
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@stphrolland @lcamtuf I am a crystallographer and I approve this message.
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@DanielEriksson @lcamtuf
I was a bit ashamed for the "Quarks" part, and the totally inert Argon and Radon...
But maybe given super extreme high-pressure Argon and Radon could organise themselves anyway ? I have no idea
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@lcamtuf I always felt like Weil's Basic Number Theory was the quintessential example of that book. The thing is, it was also great to read!
I just wouldn't want to be the person who just got excited about quadratic reciprocity and picked it up in the library because the title sounded friendly. Cheeky french number theorists!
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@lcamtuf
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@lcamtuf in college I bought the previous edition; it was a lot cheaper than the current edition, and how much really changes in that thing from year to year?
I spent the $26 I saved on beer.
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@lcamtuf I swear it's still on my bookshelf somewhere.
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@lcamtuf the most difficult courses at my university were ones that began with "Introduction to ..." or "Fundamentals of ..."
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@PizzaDemon @lcamtuf
Advanced … - elementary school level
Intermediate … - high school level
Basic … - college undergrad level
Fundamentals of … - graduate level
An Introduction to … - postgrad level
One of the classes I took in college was titled “An Introduction to Counting”. It was deep number theory from a professor familiar with the joke.
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@lcamtuf Yeah, my linear algebra text is that one.
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@lcamtuf I remember assisting the writer of such a book with LaTeX drawings
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@lcamtuf @TheBreadmonkey When the iPhone was new and I was younger and more ambitious, I bought several books with titles like “iPhone App Development for Absolute Beginners.” All of them, every last one, had a sentence in their first chapter along the lines of, “You should already be experienced with object-oriented programming,” or, “iOS apps are written in Objective-C (Objective-C programming is beyond the scope of this book).”
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@lcamtuf
Oh, yeah. Got several of those, for various values of "that thing".
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@lcamtuf "The obvious proof for this theorem is left as an exercise to the reader", moving on you uneducated swine
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@lcamtuf I feel this hard.
Gave myself a crash course in the matrix algebra used in mechatronics to understand the source code of a library some students wanted to use for FIRST Robotics. It's a library to predict how a 2-wheel robot will drive. Naively, I'd have just suggested to them "your forward speed should be the average of your wheel speeds and your turn speed should be the difference of your wheel speeds," but they wanted to use the library.
So after reading about forty pages of explanatory material and a half-dozen Java classes, I discovered the core of the library was a matrix algebra encoding of... "Your forward speed is the average of your wheel speeds and your turn speed is the difference of your wheel speeds."
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@lcamtuf every time I buy a springer book. Every time.
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@lcamtuf Every time
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@lcamtuf
"solution left as exercise for the student"
quote from one of my least favorite textbooks that indeed had this attitude.
didn't help that it was a $55 book at a time when my rent was $200/mo...
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@lcamtuf Oh look, I bought the green version!
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@lcamtuf @marble have 2 or 3 written by people in my team. Still proud.
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@lcamtuf That reminds me of this Springer meme.
Original (?) source: https://www.reddit.com/r/mathmemes/comments/uz8twg/its_funny_because_its_true/
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@kenshirriff @lcamtuf my least favorite textbook in undergrad was a topology book that would fit in the pocket of baggy jeans. No examples, discussion really, just a list of definitions and things you could prove with topology. Might have learned a lot from it if I had nothing else to do in my life at the time.
The funny thing to me was that a Springer book like this saved the day, as I found one that was probably 4x the thickness and bigger pages, so had a lot more content. A few examples and diagrams made all the difference. But even it had moments where it said, "This will make more sense later...so trust us, you need this to learn more but it won't make sense till you learn."
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@lcamtuf
Theorem 3.14 Every P*[T(\pi)_k] coadjoint solipsistic injection has an \epsilon-complete inverse P[t_j] coupling which is trivially homomorphic to T(\pi)**
Proof: Follows trivially from Theorem 2.34 and Lemma 4.20 by defining P_k = \mu(T*k).
Example 1: C^0 is an example of this.
Example 2: L_\infty is not.
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@lcamtuf
OMG rings true.
My complex analysis course had two texts. The Springer book was full of errors/bugs. It was unusable. The other one (by Henri Cartan) was very good but extremely dense, possibly theost challenging textbook I used in undergrad.
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@lcamtuf
and you have to sell all your organs to buy one
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text/gemini