Papers by Richard Milgram
Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180)
Asian Journal of Mathematics, 1997
Lecture Notes in Mathematics, 1979
We discuss the role of long division in the K - 12 mathematics curriculum. We begin by reviewing ... more We discuss the role of long division in the K - 12 mathematics curriculum. We begin by reviewing the reasons that most math educators today depreciate the topic and other topics in the curriculum that derive from it, such as polynomial long division or polynomial factorization. Later we show that this view is simply wrong mathematically. The role of long division is not just to divide one rational number by another, but the algorithm itself contains the initial exposure of topics which become crucial in the core applications of mathematics in our society today. Following the introduction, we discuss methods for teaching long division in such a way that the underlying concepts can be understood by students. We then provide more details about the ways in which these concepts develop in later mathematics course, and why they are so important.
In this paper we show that the mod 2 cohomology ring of any finite simple group of rank 3 or less... more In this paper we show that the mod 2 cohomology ring of any finite simple group of rank 3 or less (at the prime 2) must be Cohen-Macaulay.
Handbook of Algebraic Topology, 1995
Contemporary Mathematics, 2001
Selected Titles in This Series 279 Alejandro Adem, Gunnar Carlsson, and Ralph Cohen, Editors, Top... more Selected Titles in This Series 279 Alejandro Adem, Gunnar Carlsson, and Ralph Cohen, Editors, Topology, geometry, and algebra: Interactions and new directions, 2001 278 Eric Todd Quinto, Leon Ehrenpreis, Adel Faridani, Fulton Gonzalez, and Eric Grinberg, Editors, ...
Grundlehren der mathematischen Wissenschaften, 1994
Transactions of the American Mathematical Society, 1986
Transactions of the American Mathematical Society, 1989
Transactions of the American Mathematical Society, 1970
Proceedings of the Edinburgh Mathematical Society, 1982
In studying the cohomology of the symmetric groups and its applications in topology one is led to... more In studying the cohomology of the symmetric groups and its applications in topology one is led to certain questions concerning the representation rings of special subgroups of . In this note we calculate the Chern classes of the regular representation of (Z/p)n where p is a fixed odd prime in terms of certain modular invariants first described by L. E. Dickson in 1911. In a later paper [9] we apply these results to study the odd primary torsion in the PL cobordism ring. Some indications of this application are given in Sections 10–12 where we apply the result above to obtain information about the cohomology of . After circulation of this note in preprint form we learned that H. Mui [10], has also proved Theorem 6.2.
Proceedings of the American Mathematical Society, 1981
Mathematische Annalen, 1990
Journal of Pure and Applied Algebra, 1987
Journal of Pure and Applied Algebra, 2001
Journal of Pure and Applied Algebra, 1980
Journal of Computational Chemistry, 2007
Loop closure in proteins requires computing the values of the inverse kinematics (IK) map for a b... more Loop closure in proteins requires computing the values of the inverse kinematics (IK) map for a backbone fragment with 2n ≥ 6 torsional degrees of freedom (dofs). It occurs in a variety of contexts, e.g., structure determination from electron‐density maps, loop insertion in homology‐based structure prediction, backbone tweaking for protein energy minimization, and the study of protein mobility in folded states. The first part of this paper analyzes the global structure of the IK map for a fragment of protein backbone with 6 torsional dofs for a slightly idealized kinematic model, called the canonical model. This model, which assumes that every two consecutive torsional bonds CαC and NCα are exactly parallel, makes it possible to separately compute the inverse orientation map and the inverse position map. The singularities of both maps and their images, the critical sets, respectively, decompose SO(3) × ℝ3 into open regions where the number of IK solutions is constant. This decompo...
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Papers by Richard Milgram