Loren C. Larson

The William Lowell Putnam mathematical competition

The following results of the thirty-first William Lowell Putnam Mathematical Competition held on December 5, 1970, have been determined in accordance with the regulations governing the Competition. This competition is supported by the William Lowell Putnam Intercollegiate Memorial Fund left by Mrs. Putnam in memory of her husband and is held under the auspices of the Mathematical Association of America. The first prize, five hundred dollars, is awarded to the Department of Mathematics of the University of Chicago, Chicago, Illinois. The members of the team were Robert Israel, Robert A. Oliver, and Robert Tax; to each of these a prize of one hundred dollars is awarded. The second prize, four hundred dollars, is awarded to the Department of Mathematics of Massachusetts Institute of Technology, Cambridge, Massachusetts. The members of the team were David M. Christie, Don Coppersmith, and Steven Winker; to each of these a prize of seventy-five dollars is awarded. The third prize, three hundred dollars, is awarded to the Department of Mathematics of the University of Toronto, Toronto, Ontario, Canada. The members of the team were Daniel Gautreau, Daryl Geller, and Joseph S. Repka; to each of these a prize of fifty dollars is awarded. The fourth prize, two hundred dollars, is awarded to the Department of Mathematics of the Illinois Institute of Technology, Chicago, Illinois. The members of the team were George F. Cornelius, Zbigniew Friedorowicz, and Wayne F. Mroz; to each of these a prize of fifty dollars is awarded. The fifth prize, one hundred dollars, is awarded to the Department of Mathematics of the California Institute of Technology, Pasadena, California. The members of the team were Leonidas Guibas, Andrew M. Odlyzko, and David J. Smith; to each of these a prize of fifty dollars is awarded. The six persons ranking highest in the examination, named in alphabetical order, are Jockum Aniansson, Yale University; Don Coppersmith, Massachusetts Institute of Technology; Jeffrey Lagarias, Massachusetts Institute of Technology; Robert A. Oliver, University of Chicago; Arthur Rubin, Purdue University; and Steven K. Winker, Massachusetts Institute of Technology. Each of these has been designated as a Putnam fellow by the Mathematical Association of America and is awarded a prize of two hundred and fifty dollars. The five persons ranking second highest in the examination, named in alphabetical order, are Daryl Geller, University of Toronto; Zbigniew Friedorowicz, Illinois Institute of Technology; Dale H. Peterson, Yale University; Joseph S. Repka, University of Toronto; and Jonathan Rosenberg, Harvard University. To each of these a prize of one hundred dollars is awarded. The following teams, named in alphabetical order, won honorable mention: University of California at Davis, the members of the team were Dean Hickerson,

The William Lowell Putnam mathematical competition: problems and solutions: 1965-1984

1. Dedication 2. Preface 3. Recollections of the first Putnam examination by Herbert Robbins 4. List of problems 5. Solutions to the list of problems in the various competitions Twenty-sixth Twenty-seventh Twenty-eight Twenty-ninth Thirtieth Thirty-first Thirty-second Thirty-third Thirty-fourth Thirty-fifth Thirty-sixth Thirty-seventh Thirty-eighth Thirty-ninth Fortieth Forty-first Forty-second Forty-third Forty-fourth Forty-fifth 6. Appendices Winning teams Winning individuals 7. Index of problems.

Monomial patterns in the sequence Akb

Abstract We consider the pattern of zero and nonzero elements in the sequence A k b , where A is an n × n nonnegative matrix and b is an n × 1 nonnegative column vector. We establish a tight bound of k n for the first occurrence of a given monomial pattern, and we give a graph theoretic characterization of triples ( A, b, i ) such that there exists a k , k ⩾ n , for which A k b is an i -monomial. The appearance of monomial patterns with a single nonzero entry is linked to controllability of discrete n -dimensional linear dynamic systems with positivity constraints on the state and control.

The Sixty-Third William Lowell Putnam Mathematical Competition

The following results of the fifty-third William Lowell Putnam Mathematical Competition, held on December 5, 1992, have been determined in accordance with the governing regulations. This annual contest is supported by the William Lowell Putnam Prize Fund for the Promotion of Scholarship, left by Mrs. Putnam in memory of her husband, and is held under the auspices of the Mathematical Association of America.

The Sixty-second William Lowell Putnam Mathematical Competition

The results of the Seventy-Second William Lowell Putnam Mathematical Competition, held December 3, 2011, follow. They have been determined in accordance with the regulations governing the Competition. The contest is supported by the William Lowell Putnam Prize Fund for the Promotion of Scholarship, an endowment established by Mrs. Putnam in memory of her husband. The annual Competition is held under the auspices of the Mathematical Association of America. The first price,

The Sixty-Fourth William Lowell Putnam Mathematical Competition

25,000, was awarded to the Department of Mathematics of Harvard University. The members of the winning team were Eric K. Larson, Evan M. O’Dorney, and Alex (Lin) Zhai; each was awarded a prize of

The Sixtieth William Lowell Putnam Mathematical Competition

1,000. The second prize,

The Fifty-Seventh William Lowell Putnam Mathematical Competition

20,000, was awarded to the Department of Mathematics of Carnegie-Mellon University. The members of the winning team were Michael T. Druggan, Albert Gu, and Archit U. Kulkarni; each was awarded a prize of

The Sixty-Sixth William Lowell Putnam Mathematical Competition

800. The third prize,

The fifty-first William Lowell Putnam Mathematical Competition

15,000, was awarded to the Department of Mathematics of the California Institute of Technology. The members of the winning team were Zarathustra E. Brady, Samuel S. Elder, and Brian R. Lawrence; each was awarded a prize of