You’re right, I left out many parts of TCS for several reasons. They don’t have much overlap with applied math (more on that later), I wrote about the parts of both fields I am most familiar with, and Boaz original post was in response to Candes’ talk on an area where, I think, there is quite a bit of overlap.

I think that there are parts of applied math that do make use of some of those other TCS topics you mentioned (e.g., pseudo-random number generators, data structures, perhaps graph algorithms) but those areas are not necessarily elevated to the level of independent, mathematical study. Monte carlo simulations certainly need random number generators! Highly efficient, large scale scientific simulations must leverage good data structure design, computational geometry solutions, nearest neighbor data structures, etc. for efficiency. Again, I don’t know those areas of math all that well but my impression is that the algorithmic contributions are mainly a means to an end.

There is one area that really does seem to have a good meeting of the minds: numerical linear algebra. It’s not an area I know well but only as an observer. After I wrote my post, it occurred to me that it was a good example of fruitful interactions. I hope that the innovative algorithms have an impact on scientific computing too!

Yes, applied math has lived within a cocoon as well for a while. I am just now starting to see students (and faculty) interested in broader areas such as machine learning, bio-informatics (or more discrete parts of mathematical biology), computer vision, image processing of all sorts, and “data stuff.” TCS is far ahead of math in respect to being outward-looking.

I also didn’t mean to give the impression that TCS folks aren’t interested at all in implementations while applied mathematicians are. I’d like to be able to convince the applied math and engineering students I teach that they’d really benefit from an algorithms course, that that sort of course would help them think about their computation more rigorously and thoroughly. I really like all of the innovations in TCS teaching and I am thinking about how to change/update our own numerical analysis classes. Sounds like a combined intro to numerical analysis + algorithms course!

]]>Places < 10 minutes and good for a quick lunch:

Luke's Lobster (Lobster Rolls)

HipCityVedge (vegetarian, not necessarily healthy, tasty)

Rotisseur (roast chicken, chicken/tofu Bahn Mi's)

Philadelphia Chutney Company (Dosas)

Dizengoff (Humus)

Federal Donuts (Donuts, fried chicken)

HoneyGrow (Design your own salads and stir frys)

Pure Fare

Metropolitan Cafe (The sandwich arm of a good bakery)

Nom Nom Ramen

Shake Shack (fast food hamburgers)

500 degrees (slightly fancier fast food hamburgers)

Village Whiskey (Very fancy hamburgers)

Vic Sushi Bar (Good, cheap sushi. Only about 6 seats though)

In any case, here is the raw data (there is not much in the way of description, but all of them were recommended by Nadia and Aaron – the places not tagged “lunch” may still have lunch, but the places tagged “lunch” are those that Nadia and Aaron said are good for lunch and within < 10 minute walk from the hotel.

Vernick (lunch,dinner) website new american 2031 Walnut St, Philadelphia, PA 19103

a.kitchen (lunch,dinner) website 135 S 18th St, Philadelphia, PA 19103

Matyson (lunch,dinner) website new american 37 S 19th St, Philadelphia, PA 19103

Monk’s Café (lunch,dinner) website great beer 264 S 16th St, Philadelphia, PA 19102

Audrey Claire (lunch,dinner) website 276 S 20th St, Philadelphia, PA 19103

Zama (lunch,dinner) website sushi 128 S 19th St, Philadelphia, PA 19103

Alma de Cuba (lunch,dinner) website modern latin cuisine 1623 Walnut St, Philadelphia, PA 19103

Tinto (lunch,dinner) Tinto 114 S 20th St, Philadelphia, PA 19103

Village Whiskey (lunch,dinner) website fancy hamburgers and Whiskey 118 S 20th St, Philadelphia, PA 19103

Tria (lunch,dinner) website wine cheese beer 123 S 18th St, Philadelphia, PA 19103

Vedge (lunch,dinner) website one of the best vegan restaurants in the country. Good for carnivores too 1221 Locust St, Philadelphia, PA 19107

Luke’s Lobster (lunch) website 130 S 17th St, Philadelphia, PA 19102

HipCityVeg (lunch) website 127 S 18th St, Philadelphia, PA 19103

Rotisseur (lunch) website 102 S 21st St, Philadelphia, PA 19103

Philadelphia Chutney Company (lunch) website 1628 Sansom St, Philadelphia, PA 19103

Dizengoff (lunch) website 1625 Sansom St, Philadelphia, PA 19103

HoneyGrow (lunch) website 110 S 16th St, Philadelphia, PA 19103

Nom Nom Ramen (lunch) website 20 S 18th St, Philadelphia, PA 19103

Sansom Oyster House (lunch) website 1516 Sansom St, Philadelphia, PA 19102

Capogiro Gelato (dessert) website 117 S 20th St, Philadelphia, PA 19103

La Colombe (coffee) website 130 S 19th St, Philadelphia, PA 19103

All of these are achieved by the parity coloring: the color of is . It is easy to see this has discrepancy 0 for any subcube of dimension greater than 0 (i.e. any subcube which is not a vertex).

]]>Some thoughts:

(a) I think you are refering to a small fraction of TCS (and even a small fraction of algorithms research) whose concerns overlap with that of Applied math. Streaming, compressed sensing and related algorithms are the main examples, as you mention.

What about crypto, complexity theory (e.g. you mention approximation; how about showing that certain approximations are not possible?), information/coding, distributed computing, learning theory, graph algorithms, data structures, etc., all of which are parts of TCS? There are no analogous topics in applied math as far as I know.

(b) I think all fields are circumscribed/cocooned to some extent, which prevents them from failing to see the full picture. Usually the founders introduced a bunch of problems and a worldview. 30-40 years later, the problems may change but the worldview remains. And the worldview may be inherently incapable of considering other ways of formalizing and approaching new situations. TCS is no exception, though the broad variety of topics studied in it give it a somewhat larger cocoon.

(c) Implementability of algorithms is indeed something that TCS should re-embrace. To some extent it is liberating to be able to design inefficient algorithms at first and then worry later about making them practical. Not everybody takes the second step nor should they feel forced to (though there are famous practical algorithms that came out of STOC/FOCS work). But more people should do it.

Programming assignments disappeared from TCS courses long ago but are beginning to be reintroduced. I find simple programming assignments quite instructive in my grad algorithms course (geared towards all CS grads, not TCS grads): http://www.cs.princeton.edu/courses/archive/fall13/cos521/

I know of others who are also trying this (eg Tim Roughgarden and Ashish Goel at Stanford). Tools like matlab and scipy make implementations and experimentation much easier.

Are the following known? Any references or pointers would be welcome.

1. Fix $n$. Let $A_k$ be the $C_k^n \times 2^n$ matrix encoding subcube queries with $k$ of $n$ input variables fixed. What is the (plain, nonhereditary) discrepancy of $A$? In the 2 norm? In the infinity norm?

2. What about including all $k$ from 1 to $n$? Hence what is the discrepancy of all subcube queries?

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