Freshman Seminar SP1201M

Mathematical Foundations of Computer Science

This seminar is part of a group of seminars with the code SP1201M organized by the Faculty of Science which gives an overview on these seminars on their webpage. They are for students in the first year of studies and give the opportunity to get some experience in presenting scientific talks to an audience. Each student has to prepare and present a talk and to provide a write-up on the talk. The URL of this webpage is 
      http://www.comp.nus.edu.sg/~fstephan/seminar-sp1201.html
and please check this url for updates on the seminar.

Lecturer

The lecturer is Frank Stephan from the Departments of Mathematics and Computer Science of the National University of Singapore. 
Frank Stephan's addresses are:

  (1) Department of Mathematics, National University of Singapore
      2 Science Drive 2, Singapore 117543
      Primary Office: S14#04-13, Telephone +65-6516-2759

  (2) School of Computing, National University of Singpore
      Law Link, Computing 1 (COM1), Singapore 117590
      Shared Secondary Office: COM1#02-16, Telephone +65-6516-4246

The telefax in the main office of the Department of Mathematics
is +65-67795452

Office Hours: Mondays 14:00-15:00 hrs in S14#04-13 and
Thursday 17:00-18:00 hrs in COM1#02-16.

The email address is
fstephan@comp.nus.edu.sg;
other email addresses are read less frequently, thus please use this one.

Time and Venue

The time is each Tuesday 16.00-18.00 hrs, the venue is S16#04-37 (Science Building S16, Level 4, Room 37).

Content

The history of Computing is quite linked to mathematics. Mathematicians like Blaise Pascal and Charles Babbage constructed calculators on a mechanical basis, George Boole's work on algebras became laid the foundations of the binary logic used in computers and Alan Turing contributed to the field in many ways. Alan Turing developed together with people like Kurt Goedel and Alonzo Church the theoretical foundations of computer science; but he contributed also to the more applied part by playing a key role in supporting his country's work on cryptography. The topics of this seminar will be the mathematical foundations of computer science, for example number systems (like binary, octal, decimal and hexadecimal), Boolean algebra, formal models of computing and the famous P-NP question. For students with less mathematical background will historical topics be available as well, for example the following: Charles Babbage and his Analytical Engine; the American census of 1890, tabulating machines and the founders of the company IBM; calculating tools before the age of electronics. In the case that a student wants to propose an own topic, this is possible as well.

Schedule

The seminar consists of two phases. In the weeks before the midterm break, talks will be prepared and practice talks will be given. After the midterm break, each student will do either 1 presentation about approximately 30 minutes or 2 short presentations about approximately 15 minutes plus some discussion.

Seminar Topics

The above talks were selected from the following list, topics can be added on the request of students.
  1. Number systems: historic outline
  2. The mathematics behind number systems: the base, representation of numbers, transforming numbers from one system into another, numbersystems important for computers (binary, octal, hexadecimal)
  3. Early computing devices: the Abacus, mechanical calculators, the slide-rule
  4. Algorithms: the basic ideas and formalizations; the first algorithm of Euclid
  5. Programming languages: variables, data-types, conditional statements and loops
  6. An application: algorithms to find the roots of polynomials: exact roots for polynomials of degree 2,3; impossibility to express roots of polynomials of degree 5; approximations in the general case
  7. The limits of computation - the halting problem (formalization of programming and its limitations)
  8. Computers and proofs: The four colour theorem
  9. Formalizing the theory of natural numbers and Goedel's incompleteness theorem; life and work of Kurt Goedel
  10. The history of pi: the art to compute many digits of a difficult number
  11. Computers and chess: from the beginnings until the time Big Blue defeated Chess Champion Kasparov
  12. Cryptography: The art of keeping secrets secret and the art of breaking other people's codes
  13. Blaise Pascal: a mathematician and inventor of calculating equipment
  14. Charles Babbage: the inventor of a computer which never became ready
  15. Ada Lovelace: Charle Babbage's programmer
  16. Hermann Hollerith: computing equipment for large statistical evaluations
  17. The computer revolution from the 1940ies to the 1960ies
  18. Modern trends in computing: personal computers, internet, mobile computing, ...
  19. Bill Gates: success with making software instead of hardware
  20. Linus Torvalds: Linux, an open source alternative to the operating system Windows
  21. History and overview of Google
  22. George Boole: laying out the theoretical foundations of binary logic
  23. Konrad Zuse: one of the pioneers in building the first working computers
  24. Ramanujam Iyer

Written Part of Seminar

Students have to attend all talks. Furthermore, they have to write either one long or two short essays. The essays should have together at least 3000 words. The essays should be sufficiently detailed in order to show that the student understands the subject presented in the talk. Try to be precise in the write-up.

Avoid Plagiarism and Respect Copyright

The essay should be written in your own words and you should make graphics explaining the talk by yourself.

Note that pictures on the internet have often a copyright and that it might therefore not be legal to reproduce them, in doubt omit them.

Although essays have to rely on sources, they should not be produced by copying and pasting from any other source. Cited text has to be marked with the source given and does not count for the 3000 word minimum length. Every place where text is cited has to be marked as a citation.

The NUS considers plagiarism - that is, copying text and claim that this text is own work - as a serious offence. Therefore it is better to write a non-perfect essay than to copy and paste text from the internet. Even getting the word minimum length full is not as important as to avoid plagiarism. See also the webpage on academic culture (http://emodule.nus.edu.sg/ac/launch.htm) and the section there about plagiarism.

Useful Links

  1. Alphabetic list of biographies of mathematicians: http://www-groups.dcs.st-and.ac.uk/~history/BiogIndex.html; this webpage has a large list of biographies of people working in mathematics and computer science.
  2. Google: http://www.google.com.sg; this is a general purpose search machine which displays links to desired webpages according to the keywords entered in the search.
  3. Altavista: http://www.altavista.com; this is a general purpose search machine which displays links to desired webpages according to the keywords entered in the search.
  4. Wikipedia: http://en.wikipedia.org; this webpage exists also in other languages and the search is slow, Wikipedia pages are fastest found by entering the search words plus the word "Wikipedia" into Google; Wikipedia often has external links to other webpages; Wikipedia is very comprehensive, but can be edited by everyone which results occasionally in one-sided information.
  5. Encyclopedia Britannica: http://www.britannica.com; An online encyclopedia, some parts are not as comprehensive as Wikipedia, but it is written by professional editors with the goal to give precise and reliable information; F. Stephan is subscriber of the online version of the Encyclopedia Britannica.
  6. Amazon: http://www.amazon.com; This online book shop displays a lot of information on books which can be bought; in the case that you want to order books, please note that this company sits in (several) foreign countries and hence postal charges are higher than displayed on the webpage, prices are given in foreign currencies and subcontractors do mostly not deliver to Singapore.