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 , 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

$1^{st}$ 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

$0^{th}$ announcement (save the date) for the 2024 Midwestern Workshop on Asymptotic Analysis - October 11 - 13 at #IndianaUniversity Bloomington.
New web site URL, including the 2024 list of speakers:
http://mwaa.math.indianapolis.iu.edu/
Coming soon (pending final approval from NSF): registration information
#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.

My photos from the Oct. 13-15 Midwestern Workshop on Asymptotic Analysis , at #IUPUI
https://www.flickr.com/photos/coffmanadam/albums/72177720312019555
#NSFfunded #MathConference #RealAnalysis #ComplexAnalysis

Some of my photos from today's poster sessions and talks at the 2023 Midwestern Workshop on Asymptotic Analysis at #IUPUI
https://photos.app.goo.gl/qsZQEQsBGw4NxjKe7
#MathConference #NSFfunded #RealAnalysis #ComplexAnalysis #Indianapolis

Some of my photos from today's Colloquium talk at #IUPUI which kicked off the 2023 Midwestern Workshop on Asymptotic Analysis (continuing Sat./Sun.)
https://photos.app.goo.gl/bJ18CE97i5GZ2h2p8
#MathConference #NSFfunded #RealAnalysis #ComplexAnalysis #Indianapolis

$1^{st}$ announcement for the 2023 Midwestern Workshop on Asymptotic Analysis - October 13 - 15 at #IUPUI . All participants including graduate students are welcome to contribute a research poster.
Online registration (free!) and schedule of speakers now posted at:
http://mwaa.math.iupui.edu/
#NSFfunded #MathConference #ComplexAnalysis #RealAnalysis #Indianapolis

$0^{th}$ announcement (save the date) for the 2023 Midwestern Workshop on Asymptotic Analysis - October 13 - 15 at #IUPUI
Coming soon: web site update with more information and the list of speakers
http://mwaa.math.iupui.edu/
#MathConference #ComplexAnalysis #RealAnalysis #Indianapolis

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

GAUTSCHI'S INEQUALITY:

$\bullet$ Let $x\in {\mathbb{R}}^{+}$ and $s\in (0,1)$. Then, an inequality for ratios of gamma functions known as Gautschi's inequality:
$$x^{1-s}<{\displaystyle \frac{\mathrm{\Gamma }(x+1)}{\mathrm{\Gamma }(x+s)}}<(x+1{)}^{1-s}$$
$\bullet$ Asymptotic behaviour of the ratios of gamma functions:
$${\displaystyle \underset{x\to \mathrm{\infty }}{lim}{\displaystyle \frac{\mathrm{\Gamma }(x+1)}{\mathrm{\Gamma }(x+s)x^{1-s}}}=1}$$
#GammaFunction #GautaschiInequality #Inequality #RealAnalysis #AsymptoticBehaviour #mathematics #analysis #lowerbound #upperbound

I really only have a cursory understanding of the broad strokes of foundational #mathematics - like I did my undergrad #RealAnalysis and #AbstractAlgebra stint but I didn't get to take #Topology and while the joy of getting to engage with #Mathstodon is so real it just makes me wish I could even figure out how to go to #GraduateSchool because #Algebra gives me so much joy, but I'm pretty sure my grades aren't good enough even if I could #ExecutiveFunction some applications. It hurts.

I always struggle with epsilon-delta style proofs

what are some things people do to make these more palatable? #calculus #realanalysis

Here is a #math question from a line of my #economics research:

There are functions which are discontinuous everywhere (Dirichlet function) and non-monotonic continuous but non-differentiable everywhere functions (Weierstrass function). Can a monotonic function be continuous but non-differentiable everywhere? Can the Lebesgue integral of a non-negative discontinuous everywhere function yield a continuous but non-differentiable everywhere function?

I would like to study Real Analysis.
Any #book suggestions?
I started studying from the Principles Of Mathematical Analysis by #Rudin in order to move to Real And Complex analysis. From baby to papa, one would say. I am also aware that there exists Introductory Real Analysis by #Kolmogorov, who I've heard was a great Mathematician. Has anyone studied his book?Any thoughts?Which book would be more preferable to follow?

#math
#mathematics
#realanalysis

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