Daniel E. Otero

Associate Professor
Department of Mathematics
Xavier University.
Cincinnati, OH 45207-4441
(513)745-2012 phone (voice mail available)
otero@xavier.edu email

Courses I'm teaching now (Fall 2017):

      MATH 120-01 Elementary Functions (MWF 1:00-1:50, CRN 90759, ALT 102)

      MATH 120-02 Elementary Functions (MWF 2:00-2:50, CRN 90760, ALT 102)

      MATH 300-01 History of Mathematics (MW 4:30-5:45, CRN 90803, ALT 108)

Students can find detailed information about these courses through Xavier's Canvas learning management services.


         Office hours (Hinkle 104):

                  MW 11:00am - 12:00pm; T 11:30am - 1:00pm; R 1:30pm - 3:00pm; or by appointment.

Courses I have designed:

      MATH 125 Mathematical Perspectives: The Mathematics of Calendars and Timekeeping

      MATH 125 Mathematical Perspectives: Strategies for Cooperation and Competition

      MATH 147 Calculus from an Historical Perspective

Stuff I'm really interested in professionally:

History of Mathematics

      I am cofounder (with Prof. Dan Curtin, Northern Kentucky University) of the Ohio River Early Sources in Mathematical Exposition (ORESME) Reading Group, a biannual seminar in the Cincinnati area that meets to read significant original sources in mathematics.  The ORESME home page is maintained by Prof. Curtin and me. At our last meeting, January 29-30, 2016, at NKU, we read Ideal Theory in Rings, an English translation (by Daniel Berlyne, an undergraduate at the University of Warwick) of the seminal paper Idealtheorie in Ringbereichen [Math. Ann. 83 (1921), 24-66] by Emmy Noether (1882-1935) in which she demonstrated the power of the ascending chain condition on ideals which today bears her name.

      The MacTutor History of Mathematics Archive at St. Andrews, Scotland, is one of the neatest sites that exists on the Web.  It is a substantial compendium of all sorts of information about important mathematics and mathematicians of history.

      David Joyce at Clark University maintains a great page on the history of mathematics.

      Adam Parker (Wittenberg University) and I presented an afternoon workshop, Teaching Mathematics with Primary Historical Sources, after the MAA Ohio Section Fall Meeting at Wittenberg, November 1, 2014.

      David Pengelley (New Mexico State University) and I presented an MAA Minicourse, Study the Masters: Using Primary Historical Sources in Mathematics Teaching, at the Joint Mathematics Meetings in Boston in early January, 2012.

      I co-chaired, with Amy Shell-Gellasch (Beloit College) and David Pengelley, a successful session of papers titled "Treasures from the Past: Using Primary Sources in the Classroom," at the Joint Mathematics Meetings in New Orleans on January 7, 2011.

      I spent three weeks each during the summers of 1996 and 1997 at the Institute on History of Mathematics and Its Use in Teaching (IHMT) at American University in Washington, DC.  The Institute was organized under the auspices of the Mathematical Association of America and was funded by the NSF through their Undergraduate Faculty Enhancement program. I consider this experience a seminal one in establishing me as an historian of mathematics.

      Whenever I teach the History of Mathematics course here at Xavier, I arrange a field trip with my students to visit the Rare Book Collection at the University of Cincinnati. It houses a remarkably large number of old books of historical importance in mathematics. Our visit there is often the high point of the semester!

      One of my distinguished colleagues at the IHMT, Ed Sandifer (Western Connecticut State University), is a founding member of the Euler Society. One of the more exciting goals of the Society is to prepare English translations of as much of the mathematical opus of the great eighteenth century mathematician, Leonhard Euler.  These translations are housed online at the Euler Archive.

      David Pengelley maintains a compendious website listing resources galore for the use of history (and original sources in particular) in the mathematics classroom.

      David Calvis at Baldwin-Wallace College (Berea, OH) has a wonderful page of mathematics history stuff.

      David Wilkins of Trinity College, Dublin, maintains this nice page of historical resources.

       The International Study Group on the Relations Between History and Pedagogy of Mathematics, an affiliate of the International Commission on Mathematics Instruction, has a newsletter and annual meetings.

      The Canadian Society for the History and Philosophy of Mathematics has a very interesting web page.

       Jeff Miller's project on the earliest known uses of many mathematical terms is fascinating and under continuous revision.

Specific resources arranged chronologically

      An article by Don Allen on Babylonian mathematics.

      A very nice bibliography on Babylonian mathematics by Eleanor Robson at Oxford.

      Images of pages from some of the rare books in the Vatican collection of Greek mathematics.

      There are a number of sites devoted to Euclid's Elements, easily the most influential work in all of mathematics:

o   Ralph Abraham maintains the Visual Elements of Euclid site.

o   David Joyce maintains another site focued on the Elements of Euclid.

      A page devoted to Archimedes by Chris Rorres at Drexel University.

      The Maya calendar site (maintained at the Maya World Studies Center in Mrida, Yucatn, Mxico) has a good article on Mayan mathematics.

      Japanese sangaku (temple geometry problems) are exhibited at this page by Hiroshi Kotera. There is a related page showing how sangi are used to solve polynomial equations.

      The Biblioteca Nazionale Centrale and the Istituto e Museo di Storia della Scienza, both of Florence, Italy, and the Max Planck Institute for the History of Science in Berlin have prepared an electronic publication of the Ms. Gal. 72, a manuscript by Galileo Galilei.

      Biographies of Women Mathematicians are being prepared by students at Agnes Scott College.

      My colleague here at Xavier, Sheila Doran, has designed a course called (MATH 125 Mathematical Perspectives:Women in Mathematics).

Number Theory

      The Number Theory Web provides links to more than 1400 number theorists worldwide. Of special interest is their constantly updated New Listings page where one can learn about the latest news in the field.

      Check out the Prime Pages, the prime source of information on prime numbers!  It is maintained by Chris Caldwell at the University of Tennessee at Martin.

      There is also an interesting page, designed by Chen Shuwen (at Jiang Xing Electronic Ltd., in Jiangmen City, Peoples' Republic of China) and mirrored at a server in France, on equal sums of like powers of integers.

General Mathematics


o   The Mathematical Association of America

  HOM SIGMAA (the History of Mathematics Special Interest Group of the MAA): I am currently Past Chair of HOM SIGMAA.

  MAA Ohio Section (I am President of the Section for the 2015-2016 academic year, and am also the Section Archivist.) The Section is preparing for its Centennial celebration in 2015-2016.

   I helped to run a (very successful) MAA Ohio Section Summer Short Course during the summer of 2008 here at Xavier University along with Prof. David Pengelley (New Mexico State University). The course was entitled Study the Masters: Using Primary Historical Sources in Teaching and Research. Participants started work on individual projects creating classroom modules based on primary historical documents for teaching a nice variety of mathematical topics. David & I and the 11 participants had a great time!

   The Ohio Section has put together a nice local resource called Ohio Masters of Mathematics, a collection of short biographies of noted personalities in the history of mathematics in Ohio.

o   The American Mathematical Society

Miscellaneous links

o   The Math Forum

o   Wolfram MathWorld is sponsored by Wolfram Research.

o   The Online Encyclopedia of Integer Sequences, created by Neil Sloane, is one of the most incredible sites on the web.  Look up any important sequence of integers and find out what it is and who has written about it.  Also a neat way to determine the next term of the sequence!

o   Plouffe's Inverter: a database of mathematical constants

o   The Jordan Curve Theorem: another short article

o   Math on the Web

o   Project MATHEMATICS!


o   Interactive Mathematics Miscellany & Puzzles (Cut the Knot)

o   The Bohlen-Pierce Musical Scale

o   Zentralblatt Database

o   The Riemann Hypothesis from MathWorld

o   The Riemann Hypothesis from the Prime Pages

o   Fibonacci Numbers, the Golden section and the Golden String

o   AMS Mathematics Subject Classifications

o   The Somos Sequence Site

o   The Three Ages of Pi

o   Mudd Math Fun Facts

o   Dynamical systems java applets

with MAPLE

o   Waterloo Maple (current release is Maple7) has an Applications Center and a Student Center as a resource for using the software.

with TI calculators

o   TIMath is a resource site for users of TI calculators.


      Xavier University Library has its digital catalog.

      American University is home to two rare books collections in mathematics, the Artemas Martin Collection and the Karen Dee Michalowicz Collection.

      A collection of mathematics books kept at Georgia Tech University

      Here are some of the more fascinating objects in the collections at Columbia University. (My favorite is Plimpton 322.)

The Teaching of Mathematics

      The MAA hosts a blog called Launchings, written by past MAA President (and former professor of mine) David Bressoud.

       From 1991 to 2008, I was the site coordinator for the OCTM Mathematics Tournament (sponsored by the Ohio Council of Teachers of Mathematics) for high school students, held on the last Saturday of February at dozens of sites around Ohio.