Institute of Mathematics and Statistics
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  • 2023/24 fall
  • Finite fields I (MTMM.00.355)

Finite fields I 2023/24 fall

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Tutorials

During the tutorials students will present and discuss their solutions to homework problems.

In addition to regular problems, there will be more challenging ones marked with an asterisk *. The solutions to the latter must be presented in writing. A challenging problem gives 4 points if there is only one person who has solved it, 2 points if there are several solutions. A regular problem upgrades to a challenging one if only 20% or less of the total student number manages to solve it. Fractional students are rounded up.

Tutorial schedule

  1. Group theory, ring theory, extension fields. (2.10 25.09)
  2. Finite field arithmetic. Trace and norm. (30.10 23.10)
  3. Roots and cyclotomic polynomials (20.11 13.11)
  4. Bases and elliptic curves (18.12)

Tutorial organisation

Participation in a tutorial can be replaced by solutions written in some manner of TeX and submitted before the start of the tutorial: by e-mail (lauri.tart@ut.ee), on paper (must be pre-approved, during/before/after a lecture or tutorial, to the lecturer's postal box on the fourth floor of N18, to room N18-4069), if you want to use a method not listed here, ask the lecturer first.

TeX 'source code' (generally the .tex file and extras like style files, images, computer code, etc) is both necessary and sufficient. The lecturer will appreciate people pre-compiling their code and sending the final result as well (PDF, DVI, PS, etc). Solutions submitted after the beginning of the tutorial will not be graded. Every set of solutions formatted in TeX where the number of correct solutions is at least 50% of the number of homework points awarded to the student for that tutorial (again, excepting the points due to the more challenging problems) will give the student an additional minute of note-use during the exam. So there's some incentive to both attend a tutorial and to present written solutions for the same problems.

Wrong solutions, i.e. problems that are marked down as solved but these solutions turn out to be incomplete during the tutorial, will mean that you need to present all the solutions to all the problems you're claiming credit for, except the ones that already turned out to be incomplete. This must be done in writing, within 2 weeks of the respective tutorial. In this specific case, TeX is not required not provides any bonuses, but it's still encouraged. You can present your solutions multiple times, but not after the two-week deadline. If not enough correct solutions are presented, you will get zero points for the whole tutorial. If there are, you retain the points, except for the problem(s) failed during class.

Challenging problems must be presented in writing before the beginning of the corresponding tutorial. The solutions must be complete modulo the lectures, i.e. everything not covered there (including results from later chapters of L&N) must be either proved as well, or you must get the lecturer's specific permission to omit these proofs. A solution can be in any sort of visual form, submission channels are the same as for the regular TeX submissions. Cloned solutions will have their points distributed among the authors, even if some of the authors is not among the students of the course, cannot be identified, is a LLM, has been dead for two centuries, etc. Every such solution that receives at least 1 point as a grade and is also formatted in TeX, gives another extra minute of note-use during the exam.

  • Institute of Mathematics and Statistics
  • Faculty of Science and Technology
  • University of Tartu
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Contact the course organizers with the organizational and course content questions.