Mathematics/Analysis

Subject Classification

ACM: Mathematics of computing~Mathematical analysis

2025

Kraus Maps

by Dominique Unruh

Jun 26

The Sigmoid Function and the Universal Approximation Theorem

by Dustin Bryant, Jim Woodcock and Simon Foster

May 23

Ultrametric Structure for Restriction Spaces

by Benoît Ballenghien, Benjamin Puyobro and Burkhart Wolff

May 07

Examples of Restriction Spaces

by Benoît Ballenghien, Benjamin Puyobro and Burkhart Wolff

May 07

Restriction Spaces: a Fixed-Point Theory

by Benoît Ballenghien, Benjamin Puyobro and Burkhart Wolff

May 07

2024

The Tensor Product on Hilbert Spaces

by Dominique Unruh

Sep 10

Continued Fractions

by Manuel Eberl

Mar 20

(Extended) Interval Analysis

by Achim D. Brucker and Amy Stell

Jan 21

2023

Lambert Series

by Manuel Eberl

Nov 24

The Polylogarithm Function

by Manuel Eberl

Nov 15

Eudoxus Reals

by Ata Keskin

Oct 29

Standard Borel Spaces

by Michikazu Hirata

Aug 08

2022

Pólya’s Proof of the Weighted Arithmetic–Geometric Mean Inequality

by Manuel Eberl

Jul 11

The Sophomore's Dream

by Manuel Eberl

Apr 10

Constructing the Reals as Dedekind Cuts of Rationals

by Jacques D. Fleuriot and Lawrence C. Paulson

Mar 24

A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent

by Manuel Eberl

Mar 15

Wetzel's Problem and the Continuum Hypothesis

by Lawrence C. Paulson

Feb 18

Young's Inequality for Increasing Functions

by Lawrence C. Paulson

Jan 31

2021

Hyperdual Numbers and Forward Differentiation

by Filip Smola and Jacques D. Fleuriot

Dec 31

Real Exponents as the Limits of Sequences of Rational Exponents

by Jacques D. Fleuriot

Nov 08

Complex Bounded Operators

by José Manuel Rodríguez Caballero and Dominique Unruh

Sep 18

Solving Cubic and Quartic Equations

by René Thiemann

Sep 03

The Theorem of Three Circles

by Fox Thomson and Wenda Li

Aug 21

2020

Irrationality Criteria for Series by Erdős and Straus

by Angeliki Koutsoukou-Argyraki and Wenda Li

May 12

Banach-Steinhaus Theorem

by Dominique Unruh and José Manuel Rodríguez Caballero

May 02

The Lambert W Function on the Reals

by Manuel Eberl

Apr 24

Matrices for ODEs

by Jonathan Julian Huerta y Munive

Apr 19

2019

The Poincaré-Bendixson Theorem

by Fabian Immler and Yong Kiam Tan

Dec 18

Verification Components for Hybrid Systems

by Jonathan Julian Huerta y Munive

Sep 10

Fourier Series

by Lawrence C. Paulson

Sep 06

Laplace Transform

by Fabian Immler

Aug 14

The Transcendence of Certain Infinite Series

by Angeliki Koutsoukou-Argyraki and Wenda Li

Mar 27

2018

Smooth Manifolds

by Fabian Immler and Bohua Zhan

Oct 22

The Budan–Fourier Theorem and Counting Real Roots with Multiplicity

by Wenda Li

Sep 02

Irrational Rapidly Convergent Series

by Angeliki Koutsoukou-Argyraki and Wenda Li

May 23

The Error Function

by Manuel Eberl

Feb 06

An Isabelle/HOL formalisation of Green's Theorem

by Mohammad Abdulaziz and Lawrence C. Paulson

Jan 11

Taylor Models

by Christoph Traut and Fabian Immler

Jan 08

2017

Evaluate Winding Numbers through Cauchy Indices

by Wenda Li

Oct 17

Count the Number of Complex Roots

by Wenda Li

Oct 17

The Hurwitz and Riemann ζ Functions

by Manuel Eberl

Oct 12

Linear Recurrences

by Manuel Eberl

Oct 12

The Euler–MacLaurin Formula

by Manuel Eberl

Mar 10

Bernoulli Numbers

by Lukas Bulwahn and Manuel Eberl

Jan 24

The Transcendence of e

by Manuel Eberl

Jan 12

2016

Expressiveness of Deep Learning

by Alexander Bentkamp

Nov 10

Lp spaces

by Sebastien Gouezel

Oct 05

Stirling's formula

by Manuel Eberl

Sep 01

The Cartan Fixed Point Theorems

by Lawrence C. Paulson

Mar 08

2015

Liouville numbers

by Manuel Eberl

Dec 28

Descartes' Rule of Signs

by Manuel Eberl

Dec 28

Landau Symbols

by Manuel Eberl

Jul 14

The Akra-Bazzi theorem and the Master theorem

by Manuel Eberl

Jul 14

2014

The Sturm–Tarski Theorem

by Wenda Li

Sep 19

Real-Valued Special Functions: Upper and Lower Bounds

by Lawrence C. Paulson

Aug 29

Affine Arithmetic

by Fabian Immler

Feb 07

Implementing field extensions of the form Q[sqrt(b)]

by René Thiemann

Feb 06

Sturm's Theorem

by Manuel Eberl

Jan 11

2013

Computing N-th Roots using the Babylonian Method

by René Thiemann

Jan 03

2012

Ordinary Differential Equations

by Fabian Immler and Johannes Hölzl

Apr 26

2011

Lower Semicontinuous Functions

by Bogdan Grechuk

Jan 08

2010

Executable Multivariate Polynomials

by Christian Sternagel, René Thiemann, Alexander Maletzky, Fabian Immler, Florian Haftmann, Andreas Lochbihler and Alexander Bentkamp

Aug 10

2006

Cauchy's Mean Theorem and the Cauchy-Schwarz Inequality

by Benjamin Porter

Mar 14

2004

Integration theory and random variables

by Stefan Richter

Nov 19