#complex-analysis — Public Fediverse posts

This episode reinforces a recurring theme of the series: asymptotics is geometry in disguise. Whether through steepest descent, Laplace’s method, or contour deformation, the dominant contribution always comes from regions where analytic structure forces concentration. Learning to recognize these regions—and to justify why others do not contribute—is the real content of the method.
#NumberTheory #ComplexAnalysis #AnalyticNumberTheory #Mathematics #MathCommunity #STEM #PureMath
🔗 https://cortexdrifter.blogspot.com/2026/04/a-small-taste-from-my-new-book-season-2_25.html

Curious how a simple mapping can transform circles into vertical lines or pencils of parallel lines into circles through the origin? Discover the elegant interplay between formulas and geometric intuition—and see why Möbius transformations are central to modern mathematics.

#ComplexAnalysis #Math #Geometry #MöbiusTransformation #RiemannHypothesis

https://cortexdrifter.blogspot.com/2026/01/a-small-taste-from-my-new-book-episode-9.html

Episode 5 of “A Small Taste from My New Book” is out!
Explore the beauty of asymptotic analysis, Laplace integrals, and contour integration.
https://cortexdrifter.blogspot.com/2025/12/a-small-taste-from-my-new-book-episode-5.html
If you’re passionate about deep mathematical understanding, check out my books:
📘 The Riemann Hypothesis Revealed
📗 The Essential Transform Toolkit
Both are available on Amazon and written to make advanced concepts accessible and rigorous.
Let’s keep the conversation going, what’s your favorite contour trick?
#Mathematics #ComplexAnalysis #Laplace #Asymptotics #MathBooks #AcademicMastodon

A month to go

I’ve been a bit preoccupied these recent weeks so it was with a shock that I realised that we’re into Week 9, which means just four weeks (including this one) until the end of term and just a month before Christmas. Teaching finishes here in Maynooth on Friday 19th December, but I don’t have any lectures on Fridays so in my case it will finish the day before (with a tutorial). I don’t know how many students will be there, but the module concerned is my 4th year Mathematical Physics module and the students are very hard-working, so I think most will attend. After such a busy term I’m sure that they will need a break as much as I will.

I had to rejig the schedule for both modules I am teaching this semester to accommodate the introduction of in-class tests to replace take-home assignments (for reasons I outlined here). I’ve also been handing out voluntary exercises for practice, not counting towards the module mark but for formative reasons. Both modules are mathematical in nature, and I think the best way to learn mathematics is by doing it…

Despite the changes with respect to last year, I am still roughly on track. In my Engineering Mathematics module I’ve just finished Laplace transforms, and will start Fourier methods tomorrow. With the mathematical physicists, I am in the middle of complex analysis, having done complex differentiation and conformal mappings and starting complex integration next week.

I still have a couple more class tests to get through. On the positive side, the students are turning up for them and have expressed approval for the fact that they don’t have compulsory homework to do off-campus. This form of assessment is undoubtedly harder work for the students, it’s also better preparation for the examination that take-home assignments.

We’ve just received the draft examination timetable for January, and I’m pleased that both of the examinations for which I am responsible will take place quite early in the examination period (on 12th and 15th January, respectively) so I should be able to get them corrected in time to have a break for some research before teaching resumes at the start of February.

#complexAnalysis #engineeringMathematics #genai #generativeAi #mathematics #maynoothUniversity

I’ve just published a new post exploring the hidden oscillations behind prime numbers, focusing on the Mertens function, Möbius sums, and their deep ties to the Riemann Hypothesis.
If you’re into analytic number theory or curious about the “structure inside the chaos” of primes, you might enjoy this one.
https://cortexdrifter.blogspot.com/2025/11/the-hidden-oscillations-behind-prime.html
#math #numbertheory #primes #riemannhypothesis #complexanalysis

Amid all the excitement last week, I forgot that it was the sixth teaching week of the Semester. That means that we’re now past the halfway point. Among other things that meant that examination papers were due in on Friday (8th November). That means two papers for each module I’m teaching, one to be sat in January and another for the repeat opportunity in August, so that’s four altogether.

I always find setting examination questions very difficult. In theoretical physics we want to stretch the stronger candidates at the same time as allowing the weaker ones to show what they can do. It’s a perennial problem how to make the questions neither too easy nor too difficult, but it is compounded this time by the fact that I’m teaching two modules for the very first time so judging the right level is tricky.

Another issue is that I’m once again in a situation in which I have to set examination papers without having taught all the material. At least I’ve covered the first half of the content so I have some idea of what the students found difficult, but that’s not the case for the second half. It should be a bit easier next year once I’ve experience of covering the whole syllabus. Assuming, of course, that I’m teaching the same modules again next year, which is by no means guaranteed…

I’m teaching a module on Differential Equations and Complex Analysis for 4th year students and just about ready to switch to the part that comes after the and. I taught a bit of Complex Analysis when I was at Sussex and I’m quite looking forward to it, although it does pose a particular challenge. Some of the class are doing a Double Major in Theoretical Physics and Mathematics, and have done quite a lot of Complex Analysis before, while others are doing a Single Major in Theoretical Physics and haven’t really done any. I have to somehow find a way to satisfy these two different groups. The only way I can think of to do that is to teach the subject as a physicist rather than a pure mathematician, with an emphasis on examples and real-world applications rather than in the abstract. We’ll see how this works out over the next few weeks.

P.S. On the subject of Complex Analysis, I just remembered this post from a few years ago.

https://telescoper.blog/2024/11/11/midpoint/

#ComplexAnalysis #education #ExaminationQuestions #Examinations #mathematics

Où j'apprends que la formule d'Euler, familière aux ingénieur.es et physicienn.es pour son usage en physique ondulatoire, n'a été acceptée que 50 ans après son introduction et qu'elle est issue du problème de logarithme de nombres négatifs, tel log(-1), débattu par Leibniz et Jacques Bernouilli en 1712

https://www.youtube.com/watch?v=f8CXG7dS-D0

#complexAnalysis #maths #physics #engineering #complexNumber

After getting Bill Tavis' #Mandelmap (https://www.mandelmap.com) I got again interested in the Mandelbrot set and want to know more about it. Is there somewhere a book that explains to a mathematical reader our current knowledge about the set? Or could someone of the experts write such a book and inform me about it in a few years, once it is ready? 🙂

#MandelbrotSet #Fractals #ComplexAnalysis #Books #Mathematics

Five Models for Making Sense of Complex Systems

| by Christina Wodtke
| Medium

Five diagrams are particularly useful for understanding complex systems. This seems more important every day, as we are all complexifying things full time.

🔗 https://cwodtke.medium.com/five-models-for-making-sense-of-complex-systems-134be897b6b3

#complexity #complex #complexanalysis #complexideas #complexsystems #clarifications #tools #ToolsForThought

#realanalysis #complexanalysis #complexnumbers

Is there a "Stop doing complex analysis" meme already?

1/0 is just the point at infinity on the extended complex plane, which is the North Pole of the Riemann sphere

:neofox_googly_shocked:

#maths #ComplexAnalysis

Who needs coffee, when you can evaluate an integral like the one below to wake you up :neofox_googly:
#maths #complexAnalysis

Finished the second assignment for the Complex analysis course, and my brain must have reached the limit… of $$\frac{e^{it}}{t}$$ as $$t \to \infty$$ :neofox_dizzy:
#maths #math #complexAnalysis #ou #m337

I'm doing a review exercise at the end of Book 2 (out of 4) from the Complex analysis, and I got the wrong value of an integral. The given solution uses a different method, so now I'm trying to figure out what I did wrong.

I bet the reason is something along the lines of "oh you can't use method X here, because the foxxo is too floofy to be boopable at eπ" :neofox_googly_shocked:

#maths #math #complexAnalysis #ou #m337

from "Real Proofs of Complex Theorems (And Vice Versa)" by Lawrence Zalcman (1974)

https://www.tandfonline.com/doi/abs/10.1080/00029890.1974.11993518?journalCode=uamm20&utm_source=dlvr.it&utm_medium=mastodon

#math #complexanalysis

The picture in this Wikipedia article about a feature of the planets tidal system
https://en.wikipedia.org/wiki/Amphidromic_point
looks like somebody attempted to do complex analysis on a world map.
#tides #amphidromic #ComplexAnalysis

From "Function Theory in Several Complex Variables" by Toshio Nishino (1996)

https://bookstore.ams.org/mmono-193?utm_source=dlvr.it&utm_medium=mastodon

#math #complexanalysis

A new math bird is posted!

https://fractalkitty.com/2023/07/01/valley-quails-airfoil/

Thanks everyone for the suggestions on curves - I went with the airfoil :)

Just a reminder - I take requests for favorite birbs. I prefer north american ones I have observed, but am open to suggestions.

#mathart #birb #birdwatching #mathbird #joukowski #airfoil #complexAnalysis

Hi guys! Is there someone here doing research in #PDE, #LieGroups, #ComplexAnalysis?

#math #mathematics #maths