#realanalysis — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #realanalysis, aggregated by home.social.
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Keeping busy with Sudoku, Wordle, Crosswords, and mining textbooks for statements to practice proving in #Metamath ...
Inspired by this video playlist on #RealAnalysis #Math
https://www.youtube.com/playlist?list=PLYPU-RArkLZNwMZ55-y8FZZEeY7zCJX59
Which was created from https://www.jirka.org/ra/ _Basic Analysis:
Introduction to Real Analysis_ by Jiří Lebl. #JiříLebl a #CreativeCommons (4.0) free #math #textbookIn Metamath's compressed format, my proofs of strong induction over the natural numbers took 316 bytes, well-ordering of the natural numbers: 376 bytes, 2ⁿ⁻¹ ≤ n! : 1204 bytes, formula for finite sum of geometric series: 2566 bytes. The last has 147 steps, some of which are reused and some of which depend on up to 8 prior steps and on a truncated library of 30477 statements of syntax, axioms, definitions, and theorems from the wider world of Metamath.
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The #MathReviews math review of my latest joint paper 🐘 in analysis has appeared! 📙
link for subscribers=
https://mathscinet.ams.org/mathscinet/article?mr=4929931
#RealAnalysis #PDE #PurdueFortWayne -
The #MathReviews math review of my latest joint paper 🐘 in analysis has appeared! 📙
link for subscribers=
https://mathscinet.ams.org/mathscinet/article?mr=4929931
#RealAnalysis #PDE #PurdueFortWayne -
A FORGOTTEN EPISODE in French-occupied Naples in the years around 1800—just after the French Revolution—illustrates why it makes sense to see mathematics and politics as entangled. The protagonists of this story were gravely concerned about how mainstream mathematical methods were transforming their world—somewhat akin to our current-day concerns about how digital algorithms are transforming ours. But a key difference was their straightforward moral and political reading of those mathematical methods. By contrast, in our own era we seem to think that mathematics offers entirely neutral tools for ordering and reordering the world—we have, in other words, forgotten something that was obvious to them.
In this essay, I’ll use the case of revolutionary Naples to argue that the rise of a new and allegedly neutral mathematics—characterized by rigor and voluntary restriction—was a mathematical response to pressing political problems. Specifically, it was a response to the question of how to stabilize social order after the turbulence of the French Revolution. Mathematics, I argue, provided the logical infrastructure for the return to order. This episode, then, shows how and why mathematical concepts and methods are anything but timeless or neutral; they define what “reason” is, and what it is not, and thus the concrete possibilities of political action. The technical and political are two sides of the same coin—and changes in notions like mathematical rigor, provability, and necessity simultaneously constitute changes in our political imagination.
#Mathematics #Math #Analysis #MassimoMazzotti #LAReviewOfBooks #Epistemology #Revolution #RealAnalysis #HistoryOfMath #HistoryOfMathematics
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A FORGOTTEN EPISODE in French-occupied Naples in the years around 1800—just after the French Revolution—illustrates why it makes sense to see mathematics and politics as entangled. The protagonists of this story were gravely concerned about how mainstream mathematical methods were transforming their world—somewhat akin to our current-day concerns about how digital algorithms are transforming ours. But a key difference was their straightforward moral and political reading of those mathematical methods. By contrast, in our own era we seem to think that mathematics offers entirely neutral tools for ordering and reordering the world—we have, in other words, forgotten something that was obvious to them.
In this essay, I’ll use the case of revolutionary Naples to argue that the rise of a new and allegedly neutral mathematics—characterized by rigor and voluntary restriction—was a mathematical response to pressing political problems. Specifically, it was a response to the question of how to stabilize social order after the turbulence of the French Revolution. Mathematics, I argue, provided the logical infrastructure for the return to order. This episode, then, shows how and why mathematical concepts and methods are anything but timeless or neutral; they define what “reason” is, and what it is not, and thus the concrete possibilities of political action. The technical and political are two sides of the same coin—and changes in notions like mathematical rigor, provability, and necessity simultaneously constitute changes in our political imagination.
#Mathematics #Math #Analysis #MassimoMazzotti #LAReviewOfBooks #Epistemology #Revolution #RealAnalysis #HistoryOfMath #HistoryOfMathematics
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A FORGOTTEN EPISODE in French-occupied Naples in the years around 1800—just after the French Revolution—illustrates why it makes sense to see mathematics and politics as entangled. The protagonists of this story were gravely concerned about how mainstream mathematical methods were transforming their world—somewhat akin to our current-day concerns about how digital algorithms are transforming ours. But a key difference was their straightforward moral and political reading of those mathematical methods. By contrast, in our own era we seem to think that mathematics offers entirely neutral tools for ordering and reordering the world—we have, in other words, forgotten something that was obvious to them.
In this essay, I’ll use the case of revolutionary Naples to argue that the rise of a new and allegedly neutral mathematics—characterized by rigor and voluntary restriction—was a mathematical response to pressing political problems. Specifically, it was a response to the question of how to stabilize social order after the turbulence of the French Revolution. Mathematics, I argue, provided the logical infrastructure for the return to order. This episode, then, shows how and why mathematical concepts and methods are anything but timeless or neutral; they define what “reason” is, and what it is not, and thus the concrete possibilities of political action. The technical and political are two sides of the same coin—and changes in notions like mathematical rigor, provability, and necessity simultaneously constitute changes in our political imagination.
#Mathematics #Math #Analysis #MassimoMazzotti #LAReviewOfBooks #Epistemology #Revolution #RealAnalysis #HistoryOfMath #HistoryOfMathematics
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A FORGOTTEN EPISODE in French-occupied Naples in the years around 1800—just after the French Revolution—illustrates why it makes sense to see mathematics and politics as entangled. The protagonists of this story were gravely concerned about how mainstream mathematical methods were transforming their world—somewhat akin to our current-day concerns about how digital algorithms are transforming ours. But a key difference was their straightforward moral and political reading of those mathematical methods. By contrast, in our own era we seem to think that mathematics offers entirely neutral tools for ordering and reordering the world—we have, in other words, forgotten something that was obvious to them.
In this essay, I’ll use the case of revolutionary Naples to argue that the rise of a new and allegedly neutral mathematics—characterized by rigor and voluntary restriction—was a mathematical response to pressing political problems. Specifically, it was a response to the question of how to stabilize social order after the turbulence of the French Revolution. Mathematics, I argue, provided the logical infrastructure for the return to order. This episode, then, shows how and why mathematical concepts and methods are anything but timeless or neutral; they define what “reason” is, and what it is not, and thus the concrete possibilities of political action. The technical and political are two sides of the same coin—and changes in notions like mathematical rigor, provability, and necessity simultaneously constitute changes in our political imagination.
#Mathematics #Math #Analysis #MassimoMazzotti #LAReviewOfBooks #Epistemology #Revolution #RealAnalysis #HistoryOfMath #HistoryOfMathematics
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A FORGOTTEN EPISODE in French-occupied Naples in the years around 1800—just after the French Revolution—illustrates why it makes sense to see mathematics and politics as entangled. The protagonists of this story were gravely concerned about how mainstream mathematical methods were transforming their world—somewhat akin to our current-day concerns about how digital algorithms are transforming ours. But a key difference was their straightforward moral and political reading of those mathematical methods. By contrast, in our own era we seem to think that mathematics offers entirely neutral tools for ordering and reordering the world—we have, in other words, forgotten something that was obvious to them.
In this essay, I’ll use the case of revolutionary Naples to argue that the rise of a new and allegedly neutral mathematics—characterized by rigor and voluntary restriction—was a mathematical response to pressing political problems. Specifically, it was a response to the question of how to stabilize social order after the turbulence of the French Revolution. Mathematics, I argue, provided the logical infrastructure for the return to order. This episode, then, shows how and why mathematical concepts and methods are anything but timeless or neutral; they define what “reason” is, and what it is not, and thus the concrete possibilities of political action. The technical and political are two sides of the same coin—and changes in notions like mathematical rigor, provability, and necessity simultaneously constitute changes in our political imagination.
#Mathematics #Math #Analysis #MassimoMazzotti #LAReviewOfBooks #Epistemology #Revolution #RealAnalysis #HistoryOfMath #HistoryOfMathematics
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My photos from the Oct. 10-12 Midwestern Workshop on Asymptotic Analysis :gauss: , here at #PurdueFortWayne 🐘
https://www.flickr.com/photos/coffmanadam/albums/72177720329689718
#NSFfunded #math #MathConference #RealAnalysis #ComplexAnalysis -
My photos from the Oct. 10-12 Midwestern Workshop on Asymptotic Analysis :gauss: , here at #PurdueFortWayne 🐘
https://www.flickr.com/photos/coffmanadam/albums/72177720329689718
#NSFfunded #math #MathConference #RealAnalysis #ComplexAnalysis -
I recently dumped my notes on modulus of convergence for hypergeometric functions on my website. I also had some thoughts on numerical accuracy. Not very valuable thoughts, but thoughts nonetheless.
For those who are wondering why anyone would care, many math libraries such as GSL, boost, and so on, suck. If you are trying to do intense calculations with any sort of decent accuracy, these libraries have dusty corners that fail. And they don't document where those corners are. Or they don't have routines for complex arguments. I write my own routines for these cases.
#Math #RealAnalysis #NumericalComputing
https://www.skewray.com/articles/numerical-accuracy-of-generalized-hypergeometric-series
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A few years ago (mid 2023), I wrote up some research notes regarding the modulus of convergence of the generalized hypergeometric functions. This month I wrote up and posted a series of articles that are those notes, cleaned up a bit, and this article is the wrap-up of the series.
#Math #RealAnalysis #NumericalComputing
https://www.skewray.com/articles/modulus-of-convergence-for-generalized-hypergeometric-functions
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We all get the feeling that, day by day, the world is converging towards disaster. But what tells us how fast? The Modulus of Convergence does!
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In mathematics, we say that a function is bounded if can restrict its image. Oddly, we never seem to 'bind' a function, though. I can find bounds on the the remainder of generalized hypergeometric functions, and I never used the word 'bind' either. Maybe 'bounding' refers to bunnies and deer?
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The generalized hypergeometric series are ubiquitous in the world of computing special functions, for certain amounts of ubiquity. Turns out the speed of convergence is related to the obscure Conway-Maxwell-Poisson distribution, which no one has ever heard of - pretty much the opposite of ubiquity.
#math #RealAnalysis #NumericalComputing
https://www.skewray.com/articles/bounding-the-remainder-of-generalized-hypergeometric-series
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\(1^{st}\) announcement for the 2025 Midwestern Workshop on Asymptotic Analysis - October 10 - 12 at #PurdueFortWayne 🐘 .
Participant registration is now open (through Sept. 21 to be considered for travel support), follow the instructions on the web site:
http://mwaa.math.indianapolis.iu.edu/
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana -
\(1^{st}\) announcement for the 2025 Midwestern Workshop on Asymptotic Analysis - October 10 - 12 at #PurdueFortWayne 🐘 .
Participant registration is now open (through Sept. 21 to be considered for travel support), follow the instructions on the web site:
http://mwaa.math.indianapolis.iu.edu/
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana -
Accurately computing generalized hypergeometric functions is hard. How many terms do we need? Guess we need a general expression for the size of the terms in the series. Oh, wait, I've got one right here!
#math #RealAnalysis #NumericalComputing
https://www.skewray.com/articles/estimating-the-terms-of-generalized-hypergeometric-series
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\(0^{th}\) announcement for the 2025 Midwestern Workshop on Asymptotic Analysis - October 10 - 12 at #PurdueFortWayne 🐘 .
The web site has a preliminary list of 2025 speakers including our keynote speaker Alexandre Sukhov 🇫🇷 . Online registration and the request form for travel support will be available soon on the web site:
http://mwaa.math.indianapolis.iu.edu/
Students are encouraged to display a poster!
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana -
\(0^{th}\) announcement for the 2025 Midwestern Workshop on Asymptotic Analysis - October 10 - 12 at #PurdueFortWayne 🐘 .
The web site has a preliminary list of 2025 speakers including our keynote speaker Alexandre Sukhov 🇫🇷 . Online registration and the request form for travel support will be available soon on the web site:
http://mwaa.math.indianapolis.iu.edu/
Students are encouraged to display a poster!
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana -
Making Magic with MCP: From Data Retrieval to Real Analysis and Insights
https://jellyfish.co/blog/how-ably-makes-magic-with-jellyfishs-mcp/
#HackerNews #Making #Magic #with #MCP #DataRetrieval #RealAnalysis #Insights #Innovation
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Our #PurdueFortWayne 🐘 #math department colloquium talks this semester, on #RealAnalysis #ComplexAnalysis #GraphTheory
https://photos.app.goo.gl/tQaqPeZXf3nMHKzP9 -
Our #PurdueFortWayne 🐘 #math department colloquium talks this semester, on #RealAnalysis #ComplexAnalysis #GraphTheory
https://photos.app.goo.gl/tQaqPeZXf3nMHKzP9 -
My colleagues and I have started the process of applying for a grant from #NSF. This is a strange time for such things here ( 🇺🇸 ) but if anyone is interested I can "live-blog" the process here to document any surprises or changes from our past experience. Specifically we are applying for a "conference grant" to support travel for graduate students and postdocs to an annual regional conference series on mathematical analysis. The conference organizers, including myself, have successfully applied for this grant approximately every year since 2015 - last year it was at Indiana University in Bloomington and for 2025 the location will rotate here to #PurdueFortWayne. So - stay tuned, either for good news or an informative fail-in-public anecdote!
#NSFfunded #math #MathConference #RealAnalysis #ComplexAnalysis -
My colleagues and I have started the process of applying for a grant from #NSF. This is a strange time for such things here ( 🇺🇸 ) but if anyone is interested I can "live-blog" the process here to document any surprises or changes from our past experience. Specifically we are applying for a "conference grant" to support travel for graduate students and postdocs to an annual regional conference series on mathematical analysis. The conference organizers, including myself, have successfully applied for this grant approximately every year since 2015 - last year it was at Indiana University in Bloomington and for 2025 the location will rotate here to #PurdueFortWayne. So - stay tuned, either for good news or an informative fail-in-public anecdote!
#NSFfunded #math #MathConference #RealAnalysis #ComplexAnalysis -
My photos from the Oct. 11-13 Midwestern Workshop on Asymptotic Analysis :hilbert: , at #IndianaUniversity #Bloomington
https://www.flickr.com/photos/coffmanadam/albums/72177720320846162/
#NSFfunded #math #MathConference #RealAnalysis #ComplexAnalysis -
My photos from the Oct. 11-13 Midwestern Workshop on Asymptotic Analysis :hilbert: , at #IndianaUniversity #Bloomington
https://www.flickr.com/photos/coffmanadam/albums/72177720320846162/
#NSFfunded #math #MathConference #RealAnalysis #ComplexAnalysis -
\(2^{nd}\) announcement/reminder for the 2024 Midwestern Workshop on Asymptotic Analysis - October 11 - 13 at #IndianaUniversity #Bloomington.
The web site now has a schedule of talks with abstracts:
http://mwaa.math.indianapolis.iu.edu/
(register by Sept. 15, after which travel reimbursement may no longer be available)
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana -
\(2^{nd}\) announcement/reminder for the 2024 Midwestern Workshop on Asymptotic Analysis - October 11 - 13 at #IndianaUniversity #Bloomington.
The web site now has a schedule of talks with abstracts:
http://mwaa.math.indianapolis.iu.edu/
(register by Sept. 15, after which travel reimbursement may no longer be available)
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana -
\(1^{st}\) announcement for the 2024 Midwestern Workshop on Asymptotic Analysis - October 11 - 13 at #IndianaUniversity #Bloomington.
The web site has an updated list of 2024 speakers, and an online registration form:
http://mwaa.math.indianapolis.iu.edu/
(register by Sept. 15, after which travel reimbursement may no longer be available)
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana -
\(1^{st}\) announcement for the 2024 Midwestern Workshop on Asymptotic Analysis - October 11 - 13 at #IndianaUniversity #Bloomington.
The web site has an updated list of 2024 speakers, and an online registration form:
http://mwaa.math.indianapolis.iu.edu/
(register by Sept. 15, after which travel reimbursement may no longer be available)
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana -
On the first use of decimal points: https://www.npr.org/2024/02/24/1233702474/the-decimal-point-was-in-use-150-years-before-previously-thought-research-shows
My discomfort with the decimal / base 10 system is...it's too popular. For too many people, it's our only conceptual way of understanding real numbers.
I remember taking real analysis as an undergrad, and not really getting it. It took me years until I could pry my brain away from conceiving of real numbers as something different from their representation as decimal expansions.
For example, people say π "is" 3.14159...and that it "goes on forever". Well, no: the sequence of symbols that starts with 3.14159 is one way of *representing* π, and it's only that representation that goes on forever; as a number, π is, well: π.
If I ever get the chance to teach undergrad real analysis, I want to focus the course on showing students just what the real numbers (and functions thereof) *are*, and how unspeakably strange they are.
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So is the only difference between a Darboux sum and a Riemann sum how you choose to calculate the height of a rectangle? I’m thinking there must be more to the story. #ITeachMath #Mathematics #RealAnalysis
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Video lectures for a #RealAnalysis class that I've taught at #UCLA:
Feel free to e-mail me if you are interested in the problem sets and other study materials.
https://youtube.com/playlist?list=PL54Pt_mZzBqjcodJ_GqXxqG1WCCmq433k
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For some reason there's a small, almost trivial early result in #RealAnalysis that I really like:
Every bounded infinite collection of rational numbers has an accumulation point.
Is there a similar, simple, elegant result that you like?