Applied Mathematics and Statistics
Stony Brook University
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
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.
- 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.firstname.lastname@example.org
- phone (631) 632-8365 (office)
- fax (631) 632-8490
- office hoursWed 11am-1pm, Fri 11am-12 noon
- Editor-in-chief, Applied Mathematics Letters, http://ees.elsevier.com/aml
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.
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.
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
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,
for a Math Assoc. of America Centennial volume to be published in 2015. It
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.
Tucker Family-- Alan, Edward, Ann, James (left to right)-- summer, 2010.
Applied Math & Statistics --
SUNY Stony Brook
Last update: January, 2015