Department of

Applied Mathematics and Statistics

Stony Brook University



Alan TUCKER

and son Teddy



Index: My Courses -- Corrections to my textbooks -- History of Undergraduate Program in Mathematics in America -- Park City Workshops -- Articles on Standards-Based Tests -- My Vita -- Vignettes from my father

How to Reach Me

Department of Applied Mathematics and Statistics
Physics A-137 (across bridge on first floor and to the left)
State University of New York at Stony Brook
Stony Brook, NY 11794-3600, USA
e-mail: alan.tucker@stonybrook.edu
phone (631) 632-8365 (office)
fax (631) 632-8490

Information on my fall 2014 course, AMS 301

AMS 301, Finite Mathematical Structures, covers introductory topics in graph theory and combinatorial enumeration. Click on the link to AMS 301 for more information about the course, including course syllabus, weekly assignments, and past tests.

Information on my spring 2013 class, AMS 303

AMS 303, Graph Theory, is a sequel course to AMS 301 (see above). It goes into the graph theory topics of connectedness, planarity and coloring in greater detail than AMS 301 along with Polya's Enumeration Theorem, network flows, progressively finite games, and elements of cryptanalysis.

Information on my spring 2013 class, AMS 311

AMS 311, Probability Theory, builds on AMS 301 and 310 to present an in-depth introduction to probability theory, a subject of immense importance in many areas of applied mathematics, particularly statistics and operations research.

Information on my fall 2013 class, AMS 341

AMS 341, Operations Research I, Deterministic Models, develops the theory and applications oflinear programming, including the simplex method and its variations, primal-dual program, along with an introduction to integer and dynamic programming.

Corrections to my text Applied Combinatorics, 6th and 5th ed., John Wiley and Sons

Link to Applied Combinatorics corrections.

Corrections to my text, Unified Introduction to Linear Algebra

Link to Unified Linear Algebra Corrections.

History of the Undergraduate Program in Mathematics in America,

written for an Math Assoc. of America Centennial volume to be published in 2015. It also appeared in the October 2013 issue of the American Mathematical Monthly. MAA History article

Park City Mathematics Standards Study Group

Each summer from 2004 to 2008, a group of research mathematicians met at the Park City Mathematics Institute to discuss issues about school mathematics. Three working papers were written by this author in collaboration with other mathematicians. The first workshop in 2004 produced a working paper entitled What is Important in School Mathematics . This topic was suggested by state mathematics coordinators (who met the week before our workshop) who felt that the long lists of state mathematics standards had lost track of the core goals of the school mathematics curriculum. The 2005 workshop refined the previous year's work to produce Some Organizing Principles for K-4 Mathematics. This document was the result of extended discussions with NCTM representatives. These discussions also played a significant role in the formulation of the 2006 NCTM Curriculum Focal Points report. This page is available in Czech language (translated by autip.com).
The 2006 PCMI workshop focused on fractions, with primary attention on the preparation for fractions in elementary grades as opposed to the middle grades teaching of fractions. The working paper from this workshop is Preparation for Fractions.
Two more workshops were held to refine the topic of fractions.
The most important aspect of these workshops was that they set the stage for mathematicians to play a major role in creating new school mathematics standards. Workshop participants have played a major role in designing all recent school mathematics recommendations, such as the 2010 Common Core State Standards.

Problems with Standards-based Mathematics Tests

Prof. Tucker has investigated problems in the psychometric methodology underlying the New York Regents Math A graduation test, and more generally in all standards-based mathematics tests. Prof. Tucker was a member of the special 2003 Regents Math A panel that investigated the failure of the June 2003 New York State mathematics graduation test. This panel was given unprecedented access to confidential test data which revealed the serious practical problems that arise in trying to use Item Response Theory to design a demanding standards-based mathematics graduation test. For a copy of the panel's report, go to www.regents.nysed.gov/2003Meetings/October2003/1003brd3.htm. All the recommendations in this report were adopt by the NY Board of Regents. This report documents the problems in the Math A test without explaining the source for these problems. Subsequent analyses after the panel's report was submitted found systemic flaws in the theory of standards-based tests.

Click here for a short version of Tucker's findings about problems with the theory of performance standards, as it was applied to the Math A test.
Click here for for a complete analysis of problems with the Math A test. This article appeared in the May, 2011 issue of the American Mathematical Monthly.

VITA of Alan Tucker

An earlier academic world-- stories that my father A W Tucker told me.


Tucker Family-- Alan, Edward, Ann, James (left to right)-- summer, 2010.



atucker@notes.stonybrook.edu -- Applied Math & Statistics -- SUNY Stony Brook
Last update: October, 2012