Topic outline

  • Materials

    Material


    Lecture notes

    Lecture notes will be written (note that the file is on GitHub, but instead of the GitHub pdf-viewer you should download the file to see the full file). The lecture notes are a work in progress, and will be frequently updated during the course (updates are announced on the course Zulip chat, and the link here always points to the most up-to-date version). Please inform Kalle Kytölä about mistakes you find in the notes!

    Lecture videos

    Recordings of lectures from the course of 2021 are available in this Panopto folder.


    Textbooks in English


    As English textbooks we recommend either of the following:

    • N. L. Carothers: Real analysis, Cambridge University Press 2000. (The contents of the course correspond roughly to part 1, "Metric spaces", of this textbook.)
    • W. Rudin: Principles of mathematical analysis,  McGraw-Hill 1976.

    You may find the following Finnish-Swedish-English dictionary on metric space related terminology helpful:


    Textbooks in Finnish and Swedish

    An excellent textbook in Finnish (translated also to Swedish) is:

    • J. Väisälä: Topologia I. Limes ry 1999.

    Past exams
    Here are two past exams of the course, with solutions and grading notes:
    Note that references in these solutions are to an old version of the lecture notes, the theorem numbers etc. do not correspond to the current version of the lecture notes. (Obviously you are not expected to memorize the theorem numbers anyway, but you are expected to be able to refer to correct statements proven in this course.)


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Exercises