Sergei Yakovenko's blog: on Math and Teaching

Friday, July 6, 2018

Calculus on manifolds 2017/8 – Exam

Filed under: Calculus on manifolds course,problems & exercises — Sergei Yakovenko @ 5:12

Finally the summer is here, and with it the exams.

The revised lecture notes are available here. The problems for the exam are at the end of the notes.

The rules of the game are extremely simple.

    1. The grading is by the pass/fail scheme.
    2. There is no predefined minimum of problems/items to get “pass”. Everything is decided in a purely subjective matter. Please avoid writing nonsense just for the sake of writing something: if accumulated beyond certain critical mass, it may result in the unlikely “fail”.
    3. All textbooks are at your disposition: actually, you are encouraged to consult as many of them as you feel like it. Solutions of the form “this is theorem 123 from [XXX]” are accepted, provided that they indeed are coherent (e.g., not based on a different set of definitions).
    4. You are welcome to talk to each other during preparation, but please spare me from checking identical submissions. The art of writing math texts is in itself important and you can learn it only by trial and error/corrections.
    5. The deadline for submission is August 3, 2018 as set by the Feinberg Graduate school. I can cover you for some extra time in case you have unexpected circumstances, but please don’t try to stretch the deadline beyond reasonable limits.
    6. If you find an error, invalidating one of the exam problems (errare humanum est), please post a comment to this post, and I will try to correct the formulation (or cancel the problem outright if it is beyond repair, – things happened…)
    7. All questions concerning the exam/notes can be posted here in the comments or (if you prefer) in an email to  (that’s me, in case you didn’t notice). I am essentially around here until the deadline, so if you prefer a personal communication, you are welcome to lay an ambush when I am in my office (Zyskind 150, usually every day between 15:30 and 18:00). But in any case, I’d prefer to be notified about request for a meeting in advance.
    8. The choice of the language for submission is yours. My preference is the pidgin English typeset in LaTeX, but this is by no means mandatory. On the other hand, if you plan to write in Mandarin or Basque, I’ll have to disappoint you. Please double check if your the language of your choice is covered.
    9. Problems marked with asterisks are considerably more difficult then the rest. If you love challenges, this is for you to try, but don’t get frustrated if you fail. If not, just register them as subtle math results which are so close to a general math course.

Good luck, and … and good luck!



Saturday, February 11, 2017


Filed under: Calculus on manifolds course,lecture,problems & exercises — Sergei Yakovenko @ 5:22

Problems for the take-home exam

Here is the file with the problems for the exam.

The rules are simple:

  1. The submission is due on the last day of the exam period (including the vacations) as per the FGS rules, that is, March 26, 2017.
  2. English is preferred over Hebrew, typeset solutions to the handwritten ones, although no punishment for the deviant behavior will ensue. Hardcopy solutions should be put into my mail box in the Zyskind building,  otherwise feel free.
  3. Nobody is perfect: if you believe you find an error and the problem as it is stated is wrong, don’t hesitate to write a talkback to this post. All bona fide errors will be corrected or the problem cancelled outright.
  4. I tried to make the exam as instructive as the course was. Most of the problems are things that I planned to include, but didn’t have time to. To simplify your life, they were split into what I believe are simple steps. Don’t hesitate to consult textbooks, but let me see that you indeed read and digested them. The presumptively harder items are marked by the asterisk.
  5. To get the perfect grade 100, you don’t have to submit solutions to all problems. The grade will be based on my purely subjective assessment of your exam and in any case will not be additive neither multiplicative.  Please be aware that writing patently stupid things may be more detrimental to the outcome than just skipping an item that you cannot cope with.
  6. I hope to post on this site the aggregated and slightly polished lecture notes in hope they might help you.
  7. I hope to be able to answer any questions you might have concerning the problems, better posted here than emailed to me. Moreover, I encourage open discussions here as long as they don’t result in posting complete solutions. Sometimes one stumbles over the most stupid things and needs to talk to other to overcome that. That’s fairly normal. To enter math formulas, you type the dollar sign $ immediately followed by the word “latex”, and after the blank space type in your formula. Don’t forget to close with another $.
  8. If you cannot meet the deadline for serious reasons, write me. Everything is negotiable.

Good luck and merry ט”ו בשבט!

Monday, October 28, 2013

First homework assignment

Here is the first take-home assignment that Inna prepared for the course. This homework should be submitted in three weeks, i.e., on November 14, 2013.

If you have questions, leave them here or address directly to Inna (inna.entova שטרודל

Good luck and בהצלחה! See you tomorrow.

Monday, February 13, 2012

החזרת תרגיל בית מס’ 4

שלום לכולם,

התרגילים הבדוקים נמצאים בתוך מעטפה חומה שבתיבת דואר שלי בבניין זיסקינד.


Monday, February 6, 2012

מבחן בית – גרסא עברית



בהצלחה לכולם!

Sunday, February 5, 2012

Take-home exam

The last effort

Here you can find the problems for the take-home exam. The rules of the game are outlined in the preamble, I copy them here for your convenience.

The following problems are suggested for the home exam, to be submitted no later than by March 8, 2012. Almost each problem consists of several subproblems, arranged in a specific order. This order is not accidental and should be considered as an implicit hint: solutions of subsequent problems are based on the preceding ones. Please take care to avoid the words “obvious”, “clearly” etc., use as few “plain” words as possible and instead write the intermediate assertions in a closed and precise form using the quantifiers and standard set theoretic notations.

The problems have different complexity: some are easier, some require additional ideas, but none of them is “computational”: if your solutions involves too many identical transformations and/or other computations, have a second look, whether you indeed answer the question that was asked, or something different.

To get the full score 100, it is not necessary to solve all problems and answer all questions: the grade will be awarded based on your demonstrated understanding of mathematics and not on your familiarity with some theorems.

Don’t forget to consult the lecture notes: sometimes you may find useful hints or examples there.

For your convenience Dima will soon post the Hebrew translation of these problems.

Don’t hesitate to ask questions in the comment field: we’ll try to answer them to the extent permissible for an independent home assignment 😉

Good luck!

UPD (Feb 06, 2012, 8:30 am) A small correction of Problem 9 made (sign corrected + more accurate wording).

Sunday, January 22, 2012

תרגיל בית מס’ 4


מצורף קישור לתרגיל בית רביעי ואחרון.

תאריך הגשה: 31 בינואר. הפעם לא יתקבלו איחורים.



Tuesday, January 17, 2012

פתרון של תרגיל בית מס’ 2

בלינק זה תמצאו את הפתרון של תרגיל בית מס’ 2



Wednesday, December 28, 2011

תרגיל בית מס’ 3

אין זמן למנוחה, ועל כן מוגש בפניכם תרגיל בית מס’ 3.

שימו לב כי יש לכם את כל הכלים לפתור את התרגיל, למרות שהוא עלול להיראות קשה ממבט ראשון.

תאריך אחרון להגשה: 10 בינואר.


Tuesday, December 27, 2011

סיכום תירגולים בנושא סדרות והתכנסות

שלום לכולם,

מצורף קישור לקובץ בו תמצאו סיכום של הנושאים שלמדנו בשבועות האחרונים.  כל הערה/תיקון יתקבלו בברכה רבה.


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