At this document one can find a collection of problems that have been discussed the last two years on several mathematical magazines throughout the world.

Some of them are solutions I had submitted to proposed problems and others are proposals I had made for the magazines.

I hope you will find it interesting.

I’ve just uploaded a draft of my work on the Unified Substitution Method (USM) for integrating functions with radicals and inverse trig expressions. Unlike traditional approaches—where you pick from Euler substitutions, trig/hyperbolic substitutions, or ad hoc tricks—USM merges everything into one systematic framework. Here’s what it does that others often do not:

1. Comprehensive Unification: Covers integrals involving , , , and even forms like —all with the same strategy.

2. Rigorous Sign & Domain Handling: No more guesswork about or intervals for . USM systematically determines how to treat each domain so you can reduce complicated integrals to rational or polynomial forms with confidence.

3. Incorporation of Euler-Type Subs: Some classic Euler substitutions (for ) appear as natural special cases, but USM goes further—especially useful in certain inverse-trig integrals where standard methods or CAS may fail.

4. Original Elements:

- New “Euler-like” Identities that tie together half-angle tangent and exponential approaches.

- Explicit Theorems explaining why each substitution works and how each domain interval is handled.

- Extended Scope beyond typical Euler/trig/hyperbolic methods.

If you’d like to see the details, including worked examples and proofs, check out my draft article here.

There is an article in American Mathematical Monthly Magazine on Jacobi's Triple Product identity, Jacobi's Two, Four and Six or Eight Square theorem proof. Please give that article

Ah the beginning of a possibly [logically] messy thread (Mathematical spaghetti code).

Proof there are infinitely many primes. Suppose were the only primes and WLOG let be the largest prime. Let b equal the product of all listed primes. Let and let . Note all primes divide b. Thus, all primes divide or c. This means all primes divide or d (as they all divide c). Consider . Since all primes divide they do NOT divide . So is a prime greater than . Contradiction.

Will post more later, perhaps.

I put three very good articles of C.Krattenthaler about determinants

see here
https://artofproblemsolving.com/community/c7h2233883_find_determinant_of_matrix_obtained_by_two_permuations

Hello to everyone,
Those interested and looking for set theory notes can find it here :
http://euclid.colorado.edu/~monkd/m6730.html

Can anyone recommand me a good article or handout or anything about P-adic integers,P-adic number , Hensel lemma.

In the discussion around the creation of the Articles forum I mentioned that I had a supply of classroom handouts from my years of teaching. None of these are in the slightest bit original. I haven't bothered with specific bibliographical references; consider the source to be the common shared body of wisdom of the mathematical community. In most cases, they weren't in the particular textbook I was using at the time, but I have a tendency to adopt "skinny" textbooks that don't have everything and then supplement them with the particular stuff I like.

The largest number of those handouts are for an undergraduate real analysis course. Our university has a fairly slow-paced two-semester sequence. (The specific course numbers are MATH 361A and 361B, in case I mention a course number in the middle of the text.) This particular handout concerns doubly-indexed series and belongs in the second semester of that two-semester undergraduate course. Note that while the subject matter belongs to the MCT/DCT/Fubini/Tonelli family of theorems, my intent is to teach this in the course before the course that first considers Lebesgue measure and integral. In other words, this should be the first approach to the idea of switching orders of summation.

In writing it, I was assuming only real-valued series. I did rely on that as a crutch in proving Theorem 4; if you wanted to do this for complex-valued series, you'd have to modify the proof of that particular theorem.

I included a couple of modest exercises at the end. It probably should have more than that, and I invite the readers here to suggest additional exercises.

I wrote this 15 or more years ago, as an MS Word document; some time in the last year or so I ported it over to It's a little long as a file to be posted in forum code (and I'd lose some formatting that way), so I'll post it as a .pdf file, which formats to 7 pages.

Hi,

Anywhere undergrads can publish expository articles? some sort of student journal? It wouldn't appeal to math contest buffs so yeah. More of an applied math but not original enough for real paper kinda deal.

I guess this discussion is worth linking here for posterity..,.