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<h2 class="hd hd-2 unit-title">Acknowledgments</h2>
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<p><span style="font-family: book antiqua, palatino;">This MOOC originated as a series of columns I wrote for <a href="https://www.scientificamerican.com/espanol/author/investigacion-y-ciencia/" target="[object Object]">Investigación y Ciencia</a>, which is the Spanish edition of <em>Scientific American</em>. I am most grateful to Gabriel Uzquiano, for getting me involved in the project and for improving the drafts I would send him every couple of months, to my editors, J.P. Campos and Ernesto Lozano, for years of advice and encouragement, to Puri Mayoral, for her unfailing efficiency and kindness, and to Laia Torres, for arranging for <em>Prensa Científica S.A.</em> to grant me the rights to use this material, which in some cases appears almost in its entirety. (<em>Prensa Científica S.A</em>. owns the intellectual and industrial property of all contents published in <em>Investigación y Ciencia</em>.) A list of references to my columns is included below.<br /> <br />Over the years, the columns were transformed into lecture notes for my class, also called <em>Paradox and Infinity</em>. The lecture notes then became the basis for the first version of this MOOC, which ran in the summer of 2015, with generous funding from MIT's Office of Digital Learning. A number of people were involved in that project. Damien Rochford worked as a postdoctoral fellow for MIT's Office of Digital Learning and was the heart of our operation. He enhanced existing materials in countless ways and added materials of his own. Descendants of many of Damien's materials are included here. Dana Doyle managed the project, Shira Fruchtman offered technical support and Jessica Kloss led the audio-visual efforts, in collaboration with Damien. <br /></span></p>
<p><span style="font-family: book antiqua, palatino;">The residential version of <em>Paradox</em> has created all sorts of opportunities to improve on the material. My TAs are responsible for countless improvements. Many thanks to David Balcarras, Nathaniel Baron-Schmitt, David Boylan, Nilanjan Das, Samia Hesni, Cosmo Grant, Matthias Jenny, Rose Lenehan, Milo Philips-Brown and Kevin Richardson. I am also grateful to my students, who were not only filled with helpful suggestions but also identified a number of embarrassing mistakes. I am especially grateful to Evan Chang, Anthony Liu, Pedro Mantica, Patrick McClure, Marcos Pertierra, Aleksejs Popovs, Matt Ryback, and Josephine Yu. Thanks are also due to Alejandro Pérez Carballo and Steve Yablo. Alejandro created some beautiful problem sets when he taught <em>Paradox</em> and allowed me to use them in my version of the class. I have drawn from some of those materials in preparing the book. Steve introduced me to the joys of <em>Paradox and Infinity</em> when I was a graduate student and has been a constant source of inspiration since. </span></p>
<p><span style="font-family: book antiqua, palatino;">My lecture notes eventually became a book, <em>On t</em><em>he Brink of Paradox</em>, which is published by MIT Press. The present version of the MOOC is based on the book manuscript. I am grateful to Ryan Doody and to Shira Fruchtman and her team for their careful work in transferring the material from one format to the other, and for all sorts of improvements.<br /></span></p>
<p style="text-align: right;"><span style="font-family: book antiqua, palatino;">Agustín Rayo</span></p>
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<p><span style="font-family: book antiqua, palatino;">The MOOC makes use of the following columns, which Agustín wrote for <a href="https://www.scientificamerican.com/espanol/author/investigacion-y-ciencia/" target="[object Object]">Investigación y Ciencia</a>:<br /></span></p>
<p><span style="font-family: book antiqua, palatino;"><strong>Lecture 1</strong></span></p>
<ul>
<li><span style="font-family: book antiqua, palatino;">"El infinito: Es posible razonar con precisión acerca del infinito, y cuando lo hacemos nos encontramos con un mundo de resultados sorprendentes'' (December 2008 )</span></li>
</ul>
<p><br /><span style="font-family: book antiqua, palatino;"><strong>Lecture 3</strong></span></p>
<ul>
<li><span style="font-family: book antiqua, palatino;">"El juego del diablo: cómo perderlo todo sin equivocarse nunca" (October 2010)</span></li>
<li><span style="font-family: book antiqua, palatino;">"Sombreros e infinitos: Cómo garantizar resultados en una situación aleatoria" (April 2009)</span></li>
<li><span style="font-family: book antiqua, palatino;"> "Los prisoneros y María" (August 2009)</span></li>
</ul>
<p><br /><span style="font-family: book antiqua, palatino;"><strong>Lecture 4</strong></span></p>
<ul>
<li><span style="font-family: book antiqua, palatino;">"Viajes a través del tiempo: ¿Qué nos enseña la ciencia ficción acerca del determinismo y el libre albedrío?'' (October 2009) [The article was inspired by a lecture given by my colleague Brad Skow at MIT.]</span></li>
<li><span style="font-family: book antiqua, palatino;">"¿Cómo sería el mundo si pudiéramos viajar al pasado?'' (February 2016)</span></li>
</ul>
<p><br /><span style="font-family: book antiqua, palatino;"><strong>Lecture 5</strong></span></p>
<ul>
<li><span style="font-family: book antiqua, palatino;">"El problema de Newcomb: Cómo proceder en un mundo en el que se recompense a la irracionalidad'' (September 2008)</span></li>
</ul>
<p><br /><span style="font-family: book antiqua, palatino;"><strong>Lecture 6</strong></span></p>
<ul>
<li><span style="font-family: book antiqua, palatino;">"¿Qué es la probabilidad? O de cuánta información podemos extraer al cuantificar nuestra ignorancia'' (June 2011)</span></li>
<li><span style="font-family: book antiqua, palatino;">"La paradoja de los dos sobres: un misterio probabilístico'' (June 2012)</span></li>
</ul>
<p><br /><span style="font-family: book antiqua, palatino;"><strong>Lecture 7</strong></span></p>
<ul>
<li><span style="font-family: book antiqua, palatino;">"Colecciones no medibles: El conjunto de Vitali: una introducción a la teor\'ia de la medida'' (October 2012 )</span></li>
</ul>
<p><br /><span style="font-family: book antiqua, palatino;"><strong>Lecture 9</strong></span></p>
<ul>
<li><span style="font-family: book antiqua, palatino;">"P=NP: Problema del milenio'' (April 2010)</span></li>
<li><span style="font-family: book antiqua, palatino;">"El duelo de los números grandes: ¿Cuál es el número más grande que puede escribirse en una pizarra?'' (August 2008)</span></li>
</ul>
<p><br /><span style="font-family: book antiqua, palatino;"><strong>Chapter 10</strong></span></p>
<ul>
<li><span style="font-family: book antiqua, palatino;">"Gödel y la verdad axiomática: por qué el conocimiento matemático es menos certero de lo que quisiéramos'' (February 2014)</span></li>
</ul>
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