· Chapter 1 covers regular expressions.
· How regular expression matching is implemented in utilities such as the grep command in unix.
· xkcd comic about regular expressions.
· Alan Turing’s original article from 1936 introducing his computing machine, which we cover in Chapter 3. Below are some implementations of Turing machines:
· The Imitation Game and Breaking the Code are movies about Alan Turing.
· An article from The New Yorker magazine about two Ukrainian brothers living in New York who built a supercomputer in their apartment from mail-order parts, and how they used it to calculate the first two billion digits of pi. The article also mentions Hilbert’s 10th problem, which we cover in Chapter 3.
· In Chapter 4, we prove that the set of all real numbers is uncountable using Cantor’s diagonalization argument. This shows that the cardinality of the set of all real numbers is strictly larger than the cardinality of the set of all natural numbers.
· Here is a short video about this.
· An article in Quanta Magazine describes a 2016 mathematics paper on a problem about two infinite cardinalities, denoted p and t. This is also related to Hilbert’s 1st problem.
· In Chapters 4 and 5, we prove that some problems are undecidable. Below are links to examples of other undecidable problems.
· Here is a proof that the problem of testing whether a program prints “hello, world” is undecidable, which is taken from the book Introduction to Automata Theory, Languages, and Computation, 3rd Edition, by Hopcroft, Motwani and Ullman.
· These lecture notes show the virus-detection problem is undecidable.
· Here is a paper that presents a wide range of examples of undecidable problems from CS and math.
· In Chapter 7 we cover the P vs. NP problem.
· This is one of the Millennium Problems of the Clay Math Institute, and solving it (or any of the other Millennium Problems) will get you a million-dollar prize. Another of the Millennium Problems is the Poincare Conjecture. The New Yorker magazine has an article about a Russian mathematician who solved the Poincare Conjecture, but refused to accept the prize.
· xkcd comic about the subset-sum problem, which we cover in Chapter 7 (slides 7-83 and 7-84).
· Games and puzzles such as Minesweeper, Sudoku, jigsaw puzzles, and Tetris are NP-complete.
· A movie about the P vs. NP problem and the travelling salesman problem, which we cover in Chapter 7.
· The New York Times and the Communications of the ACM have articles discussing the P vs. NP problem.
· The New Yorker magazine has a blog post on the P vs. NP problem.
· Richard Lipton (Georgia Tech) and Ken Regan (University of Buffalo) have a blog about the P vs. NP problem and the theory of computation.
· A webpage devoted to the P vs. NP problem, including a list of over 100 claimed proofs that P = NP or P != NP.
· Quanta magazine has an article about the history of the P vs NP problem, which quotes Michael Sipser, the author of the course textbook. A video accompanying the article provides a short summary.
· The New York Times (10/31/2006) published an article on the future of computing. It mentions Alan Turing and some of the concepts we cover in class. Several prominent computer scientists are quoted in the article.
· On May 14, 2007, Stephen Wolfram, the developer of the Mathematica software package, offered a $25,000 prize to anyone who could prove that a small Turing machine that Wolfram had previously developed is universal. It was previously known that any smaller Turing machine could not be universal. Five months later, Alex Smith, a 20-year-old undergraduate student in the UK, won the prize. Thus, Alex Smith has proven the existence of the smallest possible universal Turing machine.
· Letter to the Editor of The Vector (NJIT’s student newspaper) about cheating.
Last Modified: 4/16/2024 7:42:05 PM