DD2442 Seminars on Theoretical Computer Science Autumn 2014: Algebraic Gems in TCS
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This webpage provides all documentation and information about the course, so there is no separate course memo ("kurs-PM") PDF file.
In the last few decades, algebraic methods have played an important role in theoretical computer science. Many recent important results in different areas have been obtained by strikingly elegant proofs using very simple properties of polynomials and linear algebra. This progress has also underlined the importance of improving our understanding of such algebraic properties.
The purpose of this course is to survey a selection of interesting (and often surprising) applications of linear algebra and polynomials to problems in combinatorics, complexity theory, and algorithm design. The algebraic tools needed are developed along the way.
A list of questions that we wanted to study (but which, as expected, turned out to be somewhat optimistic) is as follows:
This course was given in periods 1-2 in the autumn of 2014. It We had a total of 21 lectures, with 2 lectures per week on average. In accordance with the academic quarter tradition at KTH, 10 am in the schedule below actually means 10:15 am et cetera. See the list of rooms at KTH to locate the different lecture rooms.
The main lecturer on the course is Jakob Nordström, who is responsible for all aspects of the course.
Michael Forbes from the Simons Institute for the Theory of Computing at UC Berkeley gave two guest lectures on the course.
We are using Piazza for teacher-student interaction on the course. Thus, questions should not be e-mailed to the lecturer, but instead posted on Piazza (where you can send private notes to the instructor if needed, and also ask questions anonymously).
All course participants should be signed up at Piazza to receive all announcements related to the course (but note that this does not replace the official course registration at KTH).
The course is open to anyone, but the main target audience are
advanced Master's students and PhD students
in computer science and mathematics.
There is no need to register beforehand—you can just show up at
the first lecture (or send an e-mail to the
instructor if you have questions).
You will need to formally register for the course in order for the
instructor to be able to report your results, however.
As of the autumn term 2013,
students at KTH CSC should register via the
"personal menu" ("personliga menyn" in Swedish), which was previously
known as "my pages" ("mina sidor").
This replaces the registration previously done via the
The formal requirements as stated on the Study Handbook webpage are that you should have taken DD1352 Algorithms, Data Structures, and Complexity or DD2352 Algorithms and Complexity or corresponding courses at other universities, but actually most of what we do will be independent of this material. You will need to know some probability theory and basic linear algebra, and some knowledge of abstract algebra (groups, rings, and fields) will also be helpful, although we will review briefly all concepts that we will need.
The lectures will be given in English.
Although the formal prerequisites are very limited, you will need mathematical maturity and a willingness to learn new stuff. It should be noted that this will be a somewhat demanding course. (But hopefully even more fun!)
After having completed the course, the student should be able to:
To pass the course, students will be required to solve and hand in solutions to three problem sets. The scores on the problem sets are what will mainly determine the final grades on the course (except as explained below).
For each each problem set, each student will also have to evaluate the solutions of a fellow student (but not assign grades), who will be randomly chosen by the instructor. This part of the examination will only be pass/fail as discussed in the description of the grading process below.
If you are a PhD student, you can take this course as a research-level doctoral course with a different course code. The requirements are slightly tougher and the grading is only pass/fail, but the course counts fully towards the course credit requirements in the PhD program.
The grades for Master's students taking DD2442 are determined according to the following principles:
For PhD students taking the research-level course, in addition to fulfilling the above requirements the average grade on the problem sets should be at least C and the oral presentation of a research article is mandatory. PhD students also have the option to take the Master's level course.
Note that solutions to the problem sets should be handed in strictly by the deadlines. Being able to work towards a deadline and deliver the best possible result within a given time frame (rather than a 100% polished product that arrives too late) is an important skill, and is something that you will have the opportunity to practise during the course. Having said that, exceptional circumstances, such as severe illness, can be accepted as an excuse for late problem set solutions. It should be emphasized, however, that lack of time due to work outside the university or due to many parallel courses is not considered as a legitimate reason for handing in problem set solutions late.
The KTH CSC code of honour applies to all aspects of this course including the problem sets. There are also some additional rules specific to (the problem sets of) this course. These rules are available below on this webpage and are stated on each problem set
Note that the information below about course material will be updated as we go along.
The course has no official textbook. Below follows some information about books and articles that might be useful for participants on the course. Note also that there are links to handwritten notes for the lectures in the schedule.
Some of the material that we will cover can be found in:
Especially during the second half of the course, some lectures will be based on research articles. Below follows a list of links to these articles. The intention is that the lectures will cover the material in the papers that we need, so students are not expected or required to read these papers (especially since some problems on the problem sets involves working out details in the papers that we did not have time to cover in class). The references below are provided only for completeness and for students interested in further reading.
Note that if you are not at KTH, or if you are connected to the KTH
network via wireless, then you might not be able to access the PDF
files with the articles linked to above.
One way around this problem is to search for the titles of the papers
in your favourite search engine—this should hopefully help you find
free versions of the same papers on the webpages of the
authors or similar.
Another, often better, solution to this problem
is to invoke the KTH library proxy server directly in the address field of
the browser. You do this by adding
Solutions to the
problems sets should be submitted as PDF files by e-mail to
When you are working on the problem sets, discussions of ideas in groups of two are allowed, but you should always write down your own solution individually and understand all aspects of it fully. You should also acknowledge any collaboration. For each problem set, state at the beginning if you have been collaborating and with whom.
You can (and should) ask the instructor if anything about the problem sets is unclear. Make sure to post private messages to the instructor on Piazza in that case, so that your questions do not accidentally give away unintended information about the problems to the other students. If there is some issue needing clarification regarding some problem, the instructor will make a public post on Piazza.
Some of the problems are "classic" and hence it might be easy to find solutions on the Internet, in textbooks or in research papers. It is not allowed to use such material in any way unless explicitly stated otherwise. You can, however, use in your solutions anything said during the lectures on in the lecture notes, unless you are specifically asked to show something that we claimed without proof in class. It is hard to pin down 100% formal rules on what all this means—when in doubt, ask the lecturer.
We will try out a new approach for the seminar course this year which will involved some peer evaluation (and hopefully tons of interaction among the students). All final grading will be done by the instructor, however. Here is how it is intended to work.
Step 1: Work on the Problem Set
Students solve the problem set, on their own or collaborating in pairs, and write down their own solutions and submit as a PDF file by e-mail before the deadline. During this phase no discussion of problem set solutions is allowed other than with the collaborating partner (but sending a private message on Piazza to the instructor asking for clarifications is of course OK).
Step 2: Discussion of Solutions
After the deadline, the instructor distributes the problem set solutions randomly to the students as PDF files by e-mail. All students will have a day or two to go over the received problem set solutions, compare with their own solutions, and try to figure out what might be good or bad approaches to solving the various problems on the problem set.
When a day or two has passed, the instructor gives the start signal for discussions of solutions to the problems on Piazza. During this phase all students on the course should work together to find solutions (possibly many different ones) to all problems on the problem set.
During the discussions a maximum of collaboration is allowed and encouraged. There is no incentive not to collaborate here since nothing that happens after this point can lower the grade of any student. Instead, there will be bonus points for writing down correct solutions on Piazza, as well as for helping to improve on not fully correct or complete solutions. Note that a student need not have solved the problem him- or herself in order to contribute a solution on Piazza. It is sufficient to have understood and be able to present a solution. (However, just quoting from the received set of solutions verbatim is not encouraged—the bonus points are meant to award understanding, not copying skills.)
The instructor will not take part too actively in the exchange of comments, but will try to nudge the discussions in the right direction if need be.
Step 3: Peer Evaluation
Simultaneously, and using material learned during the discussion phase, each student should evaluate all the solutions in the set of received problem set solutions and write down comments on a print-out.
Here is how the solutions should be evaluated:
The solutions together with the evaluation comments should be should be put in the lecturer's mailbox on the 4th floor at Osquars backe 2 or handed to the lecturer before beginning of class on the day of the peer evaluation deadline.
Step 4: Final Grading
Finally, the lecturer will grade all problem set solutions and assign scores, and will at the same time evaluate the evaluations. Each student will receive both the instructor grading comments and the peer evaluation copy.
The problem set will be regarded as a pass if it reaches the threshold for E as specified in the problem set.
The problem set evaluation will be regarded as a pass if at least 50% of the solutions marked as "correct" or "incorrect" are properly identified as such (with relevant explanations), and if no solution is marked "unknown" unless there is a convincing explanation as to why this solution was not possible to understand. In particular, the lecturer might look at the discussions at Piazza to check if the student has made a good faith effort to get help to figure out what is going on in the solution.
Motivation for this Set-up
There are a number of reasons why this approach will be used. It is intended to:
This new approach will be thoroughly evaluated during (and certainly after) the course, and might be modified based on the conclusions from such evaluations. One of the reasons we are doing this is that a similar approach was used for the course DD2446 Complexity Theory and received overall very positive reviews. If you have any views or comments already now, feel free to contact the instructor on Piazza or by e-mail.
Below follow links to some other courses that have influenced the contents of this course to a greater or lesser degree: