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Featured Publication

New Series!  IAS/PCMI and the AMS present:
the Teacher Program Series
Books in this series are designed for mathematics teachers, grades 3–12, to improve knowledge through a problem-based approach.


Experimental Mathematics
V. I. Arnold
This book presents several open hypotheses resulting from experiments conducted by the author ranging from geometry and topology to combinatorics to algebra and number theory.


Winding Around: The Winding Number in Topology, Geometry, and Analysis
Joh Roe
The winding number is one of the most basic invariants in topology. This book is dedicated its applications.

The Scholarly Kitchen

Image by Kabir Bakie via Wikimedia CommonsA Social World: Society Membership, Social and Economic Rewards and Human Behavior
How do shifts in cultural and economic views on social behavior affect a student or researcher's decision to join a relevant academic society? Robert Harington delves into a fascinating report from the World Bank titled World Development Report 2015: Mind, Society and Behavior. Read more at the Scholarly Kitchen.

Bulletin of the AMS

Bulletin of the AMS $L^p$ theory for outer measures and two themes of Lennart Carleson united
( view abstract )
$L^p$ theory for outer measures and two themes of Lennart Carleson united
We develop a theory of $ L^p$ spaces based on outer measures generated through coverings by distinguished sets. The theory includes as a special case the classical $ L^p$ theory on Euclidean spaces as well as some previously considered generalizations. The theory is a framework to describe aspects of singular integral theory, such as Carleson embedding theorems, paraproduct estimates, and $ T(1)$ theorems. It is particularly useful for generalizations of singular integral theory in time-frequency analysis, the latter originating in Carleson's investigation of convergence of Fourier series. We formulate and prove a generalized Carleson embedding theorem and give a relatively short reduction of the most basic $ L^p$ estimates for the bilinear Hilbert transform to this new Carleson embedding theorem.

Browse the archive 1891 - 2015.

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