## Quantum Algorithms Via Linear Algebra

* Announcing publication of our textbook with MIT Press *

By permission of Nataly Meerson, artist : source |

Richard Feynman had a knack for new ways of seeing. His Feynman diagrams not only enabled visualizing subatomic processes, they also rigorously encapsulated an alternative formalism that cross-validated the equations and procedures of quantum field theory. His 1948 *path-integral* formulation sprang out of work by Paul Dirac that re-interpreted a continuous Lagrangian operator as a *matrix multiplication*. Fast forward to his 1985 article “Quantum Mechanical Computers” (a followup to his 1981/82 keynote speech “Simulating Physics With Computers”) and there are only matrices and circuit diagrams to be seen.

Today, December 5 as Dick and I write, is the US publication day of our textbook with MIT Press, titled *Quantum Algorithms Via Linear Algebra: A Primer*. It is also available from Amazon. Both places offer it for less than two adult IMAX tickets to see “Interstellar.” Publication abroad is on 1/1/15.

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## Susan Horwitz 1955–2014

* Susan and a paradigm shift in software engineering *

Susan Horwitz was—it is hard to type “was”—a computer scientist who did important work in the area of software engineering. She passed away this summer on June 11th.

Today Ken and I wish to talk about Susan’s work.

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## Cornell CS at 50

* Plus a long-promised discussion on diagonalization *

TRUST security source |

Dexter Kozen has been on the faculty of computer science at Cornell for almost 30 of the department’s 50 years. He first came to Cornell 40 years ago as a graduate student and finished a PhD under Juris Hartmanis in just over 2 years. He was named to the Joseph Newton Pew, Jr., professorship 20 years ago, and celebrated his 60th birthday in 2012. Besides many research achievements he co-authored an award-winning book on Dynamic Logic.

Today we salute the 50th anniversary of Cornell’s department and keep a promise we made 5 years ago to talk about a diagonalization theorem by Dexter. It yields what may be an interesting finite puzzle.

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## Two Versus Three

* The role of 2 and 3 in mathematics *

Electrika source |

Margaret Farrar was the first crossword puzzle editor for The New York Times. Ken fondly recalls seeing her name while watching his father do the daily and weekly NYT puzzles—they were under Farrar’s byline as editor until 1969 when she retired from the Times. More than a maker of countless puzzles, she also created many of the meta-rules for crossword puzzles, which are still used today in modern puzzle design.

Today Ken and I wish to discuss a light topic: how 2 and 3 are different in many parts of theory and mathematics.

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## Alexander Grothendieck 1928–2014

* Creating vast beautiful mansions from the becoming of nothing *

L’espace d’un homme film source |

Alexander Grothendieck, who signed his works in French “Alexandre” but otherwise kept the spelling of his German-Jewish heritage, passed away Thursday in southwestern France.

Today we mourn his passing, and try to describe some of his vision.

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## Three In The Room

* A puzzle and a conference *

Zohar Manna is an expert on the mathematical concepts behind all types of programming. For example, his 1974 book the *Mathematical Theory of Computation* was one of the first on the foundations of computer programming. He wrote textbooks with the late Amir Pnueli on temporal logic for software systems. As remarked by Heiko Krumm in some brief notes on temporal logic, there is a contrast between analyzing the internal logic of pre- and post-conditions as each statement in a program is executed, and analyzing sequences of events as a system interacts with its environment.

Today I want to talk about an encounter with Zohar years ago, and how it relates to a puzzle that I love.

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## A Conjecture Of Ulam

* A pointed question about the plane *

Stanisław Ulam was one of the great mathematicians of the last century. We talked about him in a recent post on his prime spiral and other strange mathematical facts. He is associated with several famous problems, including the 3n+1 problem and the Graph Reconstruction conjecture.

Today we want to talk about one of his oldest conjectures.

The conjecture was first stated in 1945. It is simple to state, seems plausible that it is true, but so far has resisted all attempts at resolution. René Descartes could have stated in the 1600s—well almost. Read more…