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<HTML><HEAD> <TITLE> Keith Conrad's Home Page </TITLE> <base href="https://kconrad.math.uconn.edu"> </HEAD> <BODY text="#000000" link="#0000EE" vlink="#551A8B" bgcolor="#FFFFFF" alink="FF0000"> <CENTER><H1>Keith Conrad</H1> </CENTER><P> <P><HR> <figure> <center> <img src="lajolla20.jpg"> </center>  </figure> <p> <TR> <TH WIDTH=269 ALIGN=right> <H2><FONT COLOR="black">Job coordinates</FONT></H2> </TH> Address: <br> Math Dept. UConn, <br> 341 Mansfield Road Unit 1009 <br> Storrs, CT 06269-1009 </TR> <p> Office: MONT 234 <p> <TD ALIGN=right> E-mail: kconrad at math dot uconn dot edu. </TD> </B></TD> <p> How to reach the UConn math department by <a href="travel" target="_blank">car</a>. <P> <HR> <TABLE WIDTH=620 CELLSPACING=1 BORDER=0> <TR><TD> <H2><FONT COLOR="black">Some mathematics</FONT></H2> </TABLE> <H3><A HREF="articles" target="_blank"> Published papers </A><BR></H3> <P> <H3><A HREF="blurbs" target="_blank"> Expository papers </A><BR></H3> <P> <H3><A HREF="https://mathclub.math.uconn.edu" target="_blank"> UConn Math Club </A><BR></H3> <P> <h3><a href="http://www.ams.org/mathscinet" target="_blank">MathSciNet</a><br></h3> <H3><A HREF="http://www.numbertheory.org/ntw/web.html" target="_blank"> Number theory web </A><BR></H3> <p> <h3><a href="http://www.jstor.org/" target="_blank">JSTOR</a><br></h3> <p> <h3><a href="http://www.numdam.org/?lang=en" target="_blank">Numdam</a> </h3> <p> <H3><A HREF="http://math.jhu.edu/~savitt/GTM.html" target="_blank"> The GTM test</A> <BR></H3> <p> <h3>Greek alphabet review for <a href="greekwords.pdf" target="_blank">reading</a> and <a href="greekchart.pdf" target="_blank">writing</a> in math (a <a href="greek-letters.pdf" target="_blank">practice sheet</a>) </h3> <p> <H3> A <a href="SamIAm.pdf" target="_blank"> parody</a> of Green Eggs and Ham by Kevin Wald <BR></H3> <H3> A parody of a (once) popular <a href="song" target="_blank"> song</a>. <BR></H3> <H3> Another song parody, about <a href="elementsupdated" target="_blank"> chemical elements</a>. <BR></H3> <p> <p> <H3><a href="mathquotes.pdf" target="_blank"> Analysis</a> in popular media <BR></H3> <P> <H3>Read very carefully the course description of MAT 311 <a href="stfrancis.pdf" target="_blank"> here</a>. (This is not made up.) <BR></H3> <P> <H3> An interesting lesson in <a href="lotterynewyork.pdf" target="_blank">probability</a>. The start of <a href="https://higherlogicdownload.s3.amazonaws.com/AMSTAT/56c109df-f1a1-45e2-bb2b-a6880c16f76a/UploadedImages/v7n1.html#Lock" target="_blank">this page</a> indicates the story is not made up. </H3> <P> <H3> Another lesson in <a href="jaialai.jpg" target="_blank">probability</a>. (The event described there took place on March 3, 1983. Go to the end of <a href="http://www.cs.sunysb.edu/~skiena/jaialai/excerpts/node5.html" target="_blank">this page</a> for more.) </H3> <P> <HR>   <P> <TABLE WIDTH=620 CELLSPACING=1 BORDER=0> <TR><TD> <H2><FONT COLOR="black">Summer program courses and talks</FONT></H2> </TABLE> <H3> <a href="https://www.youtube.com/watch?v=rfVSX0lykxE" target="_blank">Prime Factorization from Euclid to Noether (Number Theory Day, March 1 2023):</a> <a href="noether-dedekind-domains-no-pause.pdf " target="_blank"> Slides</a> <H3> <a href="https://www.mccme.ru/dubna/2017/courses/kconrad.html" target="_blank"><i>L</i>-functions and the Riemann Hypothesis (Dubna, Summer 2018):</a> Lecture <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=21484" target="_blank">1</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=21485" target="_blank">2</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=21486" target="_blank">3</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=21487" target="_blank">4</a> <H3> <a href="https://ctnt-summer.math.uconn.edu/schedules-and-abstracts-2018/" target="_blank"> <i>L</i>-functions and the Riemann Hypothesis (CTNT, Summer 2018):</a> Lecture <a href="https://www.youtube.com/watch?v=lyf9W2PWm40" target="_blank">1</a>, <a href="https://www.youtube.com/watch?v=9wBWyiqQEVk" target="_blank">2</a>, <a href="https://www.youtube.com/watch?v=39hr0T3j31M" target="_blank">3</a>, <a href="https://www.youtube.com/watch?v=j7HEJG6o4UI" target="_blank">4</a>. A separate lecture: <a href="https://www.youtube.com/watch?v=-IWn5TA81MI" target="_blank">Largest Known Prime Number</a>. <BR></H3> <H3> <a href="https://www.mccme.ru/dubna/2017/courses/kconrad.html" target="_blank">The Loss and Rescue of Unique Factorization (Dubna, Summer 2017):</a> Lecture <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=17710" target="_blank">1</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=17721" target="_blank">2</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=17722" target="_blank">3</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=17723" target="_blank">4</a> <H3> <a href="https://www.youtube.com/watch?v=64gHPOXCH8I" target="_blank">Prime Numbers: What is Known and Unknown (Number Theory Day, March 30 2017):</a> <a href="primeknownunknown-no-pause.pdf " target="_blank"> Slides</a> <H3><A HREF="ross2016" target="_blank"> Patterns in Primes (Ross program, Summer 2016) </A><BR></H3> <H3> <a href="https://ctnt-summer.math.uconn.edu/schedules-and-abstracts-ctnt2016/" target="_blank"> Introduction to Modular Forms (CTNT, Summer 2016):</a> Lecture 1 <a href="https://www.youtube.com/watch?v=LolxzYwN1TQ" target="_blank">part 1</a> and <a href="https://www.youtube.com/watch?v=mPycIhlPbZo" target="_blank">part 2</a>, Lecture 2 <a href="https://www.youtube.com/watch?v=QpLlzps1X_E" target="_blank">part 1</a> and <a href="https://www.youtube.com/watch?v=DH4pfe18XGo" target="_blank">part 2</a>, Lecture 3 <a href="https://www.youtube.com/watch?v=uWKK-LI5Kts" target="_blank">part 1</a> and <a href="https://www.youtube.com/watch?v=kjYodVqjeAE" target="_blank">part 2</a>, Lecture 4 <a href="https://www.youtube.com/watch?v=0niomY89EC8" target="_blank">part 1</a> and <a href="https://www.youtube.com/watch?v=lMD556X4cW4" target="_blank">part 2</a>. <BR></H3> <H3> <a href="http://www.mccme.ru/dubna/2016/courses/kconrad.html" target="_blank">Modular Forms (Dubna, Summer 2016):</a> Lecture <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=14541&option_lang=rus" target="_blank">1</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=14568" target="_blank">2</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=14625" target="_blank">3</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=14637" target="_blank">4</a>. <BR></H3> <H3> <a href="http://www.mccme.ru/dubna/2015/courses/kconrad.html" target="_blank">Primality tests (Dubna, Summer 2015):</a> Lecture <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=12091" target="_blank">1</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=12092&option_lang=rus" target="_blank">2</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=12093&option_lang=rus" target="_blank">3</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?presentid=12094&option_lang=rus" target="_blank">4</a>. <br> (In the fourth lecture a team of videographers appears a little after the 43:00 mark and then sporadically through the rest of the lecture. They filmed me and the students on behalf of one of the sponsors of the summer school.) <BR></H3> <H3> <a href="http://www.mccme.ru/dubna/2014/courses/kconrad.htm" target="_blank">Introduction to <i>p</i>-adic Numbers (Dubna, Summer 2014):</a> Lecture <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=9425" target="_blank">1</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=9426" target="_blank">2</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=9427" target="_blank">3</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=9428" target="_blank">4</a>. <BR></H3> <H3> <a href="http://www.mccme.ru/dubna/2013/courses/kconrad.htm" target="_blank">The <i>ABC</i>-Conjecture (Dubna, Summer 2013):</a> Lecture <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=7258" target="_blank">1</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=7313" target="_blank">2</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=7348" target="_blank">3</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=7357" target="_blank">4</a>. <BR></H3> <H3> <a href="http://www.mccme.ru/dubna/2012/courses/conrad.htm" target="_blank"> Analogies between integers and polynomials (Dubna, Summer 2012):</a> Lecture <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=5143" target="_blank">1</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=5144" target="_blank">2</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=5145" target="_blank">3</a>, <a href="http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=5146" target="_blank">4</a>. <BR></H3> <H3><a href="http://bogomolov-lab.ru/SHKOLA/talks/conrad.html" target="_blank"> What is a Reciprocity Law? (Yaroslavl, Summer 2011):</a> Lecture <a href="http://www.youtube.com/watch?v=cS8DYLxtUo4" target="_blank">1</a>, <a href="http://www.youtube.com/watch?v=ivR_21DCFCw&feature=related" target="_blank">2</a>, <a href="http://www.youtube.com/watch?v=NV-F2xZmkY4&feature=related" target="_blank">3</a>, <a href="http://www.youtube.com/watch?v=NTJDb2zUkXw&feature=related" target="_blank">4</a> <BR></H3> <H3><A HREF="https://www.math.tecnico.ulisboa.pt/~ggranja/Talentos/school2011/lectures.html" target="_blank"> Number Theory in Quadratic Fields (Lisbon, Summer 2011) </A><BR></H3> <H3><A HREF="ross2008" target="_blank"> Diophantine Equations (Ross program, Summer 2008) </A><BR></H3> <H3><A HREF="ross2007" target="_blank"> Elliptic Curves and Arithmetic Progressions of Squares (Ross program, Summer 2007) </A><BR></H3> <H3><A HREF="mathcamp2005" target="_blank"> Sums of squares (USA/Canada Mathcamp, Summer 2005) </A><BR></H3> <H3><A HREF="ross2004" target="_blank"> Quaternion algebras (Ross program, Summer 2004) </A><BR></H3> <H3><A HREF="ross2003" target="_blank"> Analogies between integers and polynomials (Ross program, Summer 2003) </A><BR></H3> <H3><A HREF="promys2000" target="_blank"> Zeta and <i>L</i>-functions (PROMYS program, Summer 2000) </A><BR></H3> <P> <HR> <HR> <TABLE WIDTH=620 CELLSPACING=1 BORDER=0> <TR><TD> <H2><FONT COLOR="black">Some pictures</FONT></H2> </TABLE> <UL>  <LI> Mesmerized by a <a href="lenstraconf.jpg" target="_blank"> magic</a> trick. </LI> <LI> <a href="dogsitting" target="_blank">Dogsitting</a>. </LI>  <LI> <a href="factorials" target="_blank">Old factorial notation</a>. </LI> <LI> The <A HREF="gardenofconstants.jpg" target="_blank"> garden</A> of constants. (5 seems a bit sleepy.) </LI> <LI> <A HREF="kazan" target="_blank">Kazan (2012)</A>. </LI> <LI> <A HREF="myshkin" target="_blank">Myshkin (2012)</A>. </LI> <LI> <A HREF="russianvending" target="_blank">Russian Vending Machines</A>. </LI> <LI> <A HREF="nizhnynovgorod" target="_blank">Nizhny Novgorod(2015) </A>. </LI> <LI> <A HREF="kaliningrad" target="_blank">Kaliningrad (2017)</A>. </LI> <LI> <A HREF="moscow2018/worldcup" target="_blank">World Cup (2018)</A>. </LI> <LI> <A HREF="moscow2018/dubna-sha" target="_blank">Dubna and visiting Shafarevich (2018)</A>. </LI> <LI> <A HREF="moscow2018/suzdal" target="_blank">Suzdal (2018)</A>. </LI> <LI> <A HREF="moscow2018/vladimir" target="_blank">Vladimir (2018)</A>. </LI> <LI> <A HREF="colorado2018" target="_blank">Colorado (2018)</A>. </LI> <LI> A <A HREF="ctcar.jpg" target="_blank">car</A> in Connecticut. </LI> <LI> A <A HREF="QEDOct282011.jpg" target="_blank">car</A> near Boston. </LI> <LI> A <A HREF="abelian.jpg" target="_blank">commuter</A>, not a commutator. </LI> <li> A street I <a href="KeithStrasse.jpg" target="_blank">don't</a> live on in Berlin. And <a href="KeithStreetClemsonSC.jpg" target="_blank">another</a> one in Clemson. And an <a href="KeithAvenue.jpg" target="_blank">avenue</a> in Oakland. </li> <li> <a href="http://en.wikipedia.org/wiki/Keith_number" target="_blank">Numbers</a> I don't use. </li> <LI> Galois theory is a <A HREF="galoiscake.jpg" target="_blank">piece of cake</A>. (I had this made for a student's 21st birthday in my Galois theory class during 2015. Note how nicely the zeta is drawn, frankly better than some students wrote it on the homework.) </LI> <LI> A <A HREF="kubotaLseries.jpg" target="_blank">Kubota <i>L</i>-series</A>, seen near the UConn math department in 2016. You can find out more about the Kubota Standard <i>L</i>-series <a href="https://www.kubotausa.com/products/tractors/compact/l01" target="_blank">here</a>. According to <a href="https://www.kubotausa.com/products/tractors/compact">this page</a> these <i>L</i>-series are compact (who knew?). I think the letter <i>L</i> in "<i>L</i>-series" stands for loader or landscaper, definitely not Langlands. </LI> <LI> An appliction of mathematical logic to <a href=" https://www.google.com/maps/@40.9687093,-72.6951619,3a,75y,245.12h,94.13t/data=!3m6!1e1!3m4!1sUpjUr5r0yTN-FJeIgHkHNQ!2e0!7i13312!8i6656" target="_blank">street signs</a>. If that Google street view link dies, a screenshot is <A HREF="soundavenue.jpg" target="_blank"> here</A> (look in the lower right).</LI> <li> An application of advanced math to <A HREF="spray.jpg" target="_blank">cooking</A>. Read the label carefully. (Taken from Crisco olive oil spray.) </li> <LI> A good example of bad <A HREF="badfonts.jpg" target="_blank">kerning</A>. </LI> </UL> <HR> <TABLE WIDTH=800 CELLSPACING=1 BORDER=0> <TR><TD> <H2><FONT COLOR="black">If you are an amateur and think you solved a famous math problem, look here</FONT></H2> </TABLE> <ul> <li> <a href="http://www.scottaaronson.com/blog/?p=304" target="_blank">Scott Aaronson</a> </li> <li> <a href="http://blogs.discovermagazine.com/cosmicvariance/2007/06/19/the-alternative-science-respectability-checklist/#.UR7Z6vkS7hM" target="_blank">Sean Carroll</a> </li> <li> <a href="http://math.mit.edu/~cohn/Thoughts/advice.html" target="_blank">Henry Cohn</a> </li> <li> <a href="http://mathoverflow.net/questions/6912/6916#6916" target="_blank">Greg Kuperberg</a> </li> <li> math.stackexchange <a href="http://math.stackexchange.com/questions/275194/how-does-a-non-mathematician-go-about-publishing-a-proof-in-a-way-that-ensures-i" target="_blank">here</a> and <a href="http://math.stackexchange.com/questions/157250/spotting-crankery" target=_blank>here</a> </li> <li> <a href="http://terrytao.wordpress.com/career-advice/be-sceptical-of-your-own-work/" target="_blank">Terry Tao</a> </li> </ul> <TABLE WIDTH=620 CELLSPACING=1 BORDER=0> <TR><TD> <H2><FONT COLOR="black">Reasons to be Cautious in Mathematics</FONT></H2> </TABLE> <ul> <li> <a href="http://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-wrong" target="_blank">Theorems that turned out to be wrong</a> </li> <li> <a href="http://mathoverflow.net/questions/27749/what-are-some-correct-results-discovered-with-incorrect-or-no-proofs" target="_blank">Theorems with wrong or incomplete initial proofs</a> </li> <li> <a href="http://mathoverflow.net/questions/15444/the-phenomena-of-eventual-counterexamples" target="_blank">Eventual counterexamples</a> </li> <li> <a href="http://mathoverflow.net/questions/52101/longest-coinciding-pair-of-integer-sequences-known" target="_blank">Sequences that initially agree but eventually don't</a> </li> </ul> <hr> <TABLE WIDTH=620 CELLSPACING=1 BORDER=0> <TR><TD> <H2><FONT COLOR="black">Some links</FONT></H2> </TABLE> <ul> <li> Page about <a href="letterwriting" target="_blank">recommendation letters</a> </li> <li> My <A HREF="http://math.stanford.edu/~conrad/" target="_blank"> brother's </A> page</li> <li> Math <A HREF="http://www.themathleague.com" target="_blank"> contests </A></li> <li> An interesting lesson in <a href="http://menmedia.co.uk/manchestereveningnews/news/s/1022757_cool_cash_card_confusion" target="_blank">negative numbers</a>. (If the link is broken, go <a href="http://plus.maths.org/content/news-world-maths-lotto-confusion" target="_blank">here</a>.) <li> A great <a href="opticalillusion.png" target="_blank">optical illusion</a>. (The figures are not really moving. This is due to Akiyoshi Kitaoka. See <a href="http://www.ritsumei.ac.jp/~akitaoka/index-e.html" target="_blank">here</a> for more information.)  </li> <li> Another <a href="http://i.stack.imgur.com/d2OKd.gif" target="_blank">optical illusion</a>. (Partial explanation is <a href="http://i.imgur.com/nA53dlx.gif" target="_blank">here</a>.) </li> <li> A <a href="http://galoisdb.math.upb.de/" target="_blank"> database</a> of field extensions. </li> <li> Some html commands for special symbols, both (Roman) <a href="http://www.w3.org/MarkUp/html-spec/html-spec_13.html" target="_blank"> alphabetical</a> and <a href="http://www.dionysia.org/html/entities/symbols.html" target="_blank"> mathematical</a>. (For a more general site, go <a href="http://webby.free.fr/html/caracteres-speciaux.html" target="_blank">here</a> or <a href="http://www.w3.org/TR/REC-html40/cover.html#minitoc" target="_blank">here</a>.) </li> <li> Figure out LaTeX commands for symbols by drawing the symbol <a href="http://detexify.kirelabs.org/classify.html" target="_blank">here</a>. </li>  </ul> <br> <br>  <script type="text/javascript" language="javascript"> var sc_project=786260; var sc_partition=6; var sc_security="70ddaadd"; var sc_invisible=1; </script> <script type="text/javascript" language="javascript" src="http://www.statcounter.com/counter/counter.js"></script><noscript><a href="http://www.statcounter.com/" target="_blank"><img src="http://c7.statcounter.com/counter.php?sc_project=786260&java=0&security=70ddaadd&invisible=1" alt="website free tracking" border="0"></a> </noscript>  </BODY></HTML>