Skip to content

Quantum Algorithms Via Linear Algebra

December 6, 2014


Announcing publication of our textbook with MIT Press

OLYMPUS DIGITAL CAMERA
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.
Read more…

Susan Horwitz 1955–2014

December 2, 2014


Susan and a paradigm shift in software engineering

horwitz

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.
Read more…

Cornell CS at 50

November 26, 2014


Plus a long-promised discussion on diagonalization

kozen_1227028300
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.
Read more…

Two Versus Three

November 19, 2014


The role of 2 and 3 in mathematics

Farrar
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.
Read more…

Alexander Grothendieck 1928–2014

November 16, 2014


Creating vast beautiful mansions from the becoming of nothing

Grothendieck1975
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.
Read more…

Three In The Room

November 12, 2014


A puzzle and a conference

manna2

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.
Read more…

A Conjecture Of Ulam

November 8, 2014


A pointed question about the plane

7205311_1046261214

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…

Follow

Get every new post delivered to your Inbox.

Join 2,364 other followers