Related papers: Hasse theorem -- an elementary approach
We present a proof of the Sturm-Hurwitz theorem, using basic calculus.
We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena
A vector variational principle is proved.
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.
We prove an elementary lemma concerning primitive amalgams and use it to greatly simplify the proof of the Sims conjecture in the case of almost simple groups.
We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"
We give an elementary proof of a Landesman-Lazer type result for systems by means of a shooting argument and explore its connection with the fundamental theorem of algebra.
This paper contains a new elementary proof of the Fundamental Theorem of Calculus for the Lebesgue integral. The hardest part of our proof simply concerns the convergence in ${\rm L}^1$ of a certain sequence of step functions, and we prove…
We give an elementary proof of the reducedness of twisted loop groups along the lines of the Kneser-Tits problem.
We give a one-sentence elementary proof of the combinatorial Fa\`a di Bruno's formula.
We present a short and self-contained proof of the choosability version of Brooks' theorem.
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.
We present a nonstandard simple elementary proof of Szemer\'{e}di's theorem by a straightforward induction with the help of three levels of infinities and four different elementary embeddings in a nonstandard universe.
We give necessary and sufficient conditions for an integral polynomial without linear factors to be the characteristic polynomial of an isometry of some even, unimodular lattice of given signature. This gives rise to Hasse principle…
A Short Course on Frame Theory.
We present a relative form of the Toponogov comparison theorem.