9/25/24: From now on, everything will only continue
on Canvas.
9/25/24: From now on, everything will only continue
on Canvas.
9/25/24: We have got a NEW DATE and TIME for our Final Exam:
1:30-3:30 p.m., Monday, December 16, regular classroom (VinH 207).
9/20/24: Homework 2, due September 26, is posted. See
the main
course web page.
9/19/24: Today's 12:05-12:55 pm office hours will be on Zoom only. If
I need to write something while on Zoom, I will be able to write on
the screen of my iPad with a stylus and share the iPad screen with
you. If you have a tablet, you should be able to do the same. This
should make online office-hours experience close to in-person ones. I
will make sure to be available online from 11:55 am. If you cannot
make it to this short hour, you are always welcome to make an
appointment for a different time or send me an email or Discord
message.
9/18/24: At the end of the class today, while proving the statement
that given an ε > 0, there exists a rational x > 0 such that
x2 < 2 < (x+ ε)2, I made a claim
nε < 1 for each positive natural n, which would be impossible
to prove by induction, in which we want to use the assumption that for
any x > 0, the inequality x22 < 2 implies (x+
ε)22 < 2. The correct claim should be
(nε)22 < 2 for each positive natural n. And this
implies nε < 2 for all natural n, which contradicts the
existence of a natural N such that N > 2/ε, guaranteed by
Prop. 4.4.1. See the textbook (the proof of Prop. 4.4.5) for
details. My apologies!
Also, the text proves a slightly weaker statement: there is a rational x ≥ 0 such that x2 < 2 < (x+ ε)2. This allows to start the induction with n=0, while to prove the existence of x > 0, we would have to base the induction at n=1, like we did in class. This is a minor point, and either wording of the proposition is good enough for the rest of this course.
9/6/24: Homework 1, due September 12, is posted. See
the main
course web page.
9/4/24: You will be getting your homework from Canvas. When you are
done with it, you will need to upload it to Gradescope (accessible
through Canvas). Then it will be graded on Gradescope.
9/4/24: Suggestion on doing homework: I believe working in study
groups is beneficial to learning things. It is not cheating, if it is
done right. The most productive thing is to give the problem a thought
before discussing it with your friends. If you are stuck, ask your
friend for a hint. This is perhaps also the best way to use
ChatGPT: instead of asking ChatGPT to give you a complete
solution, ask it for a hint. Otherwise, you might end up excelling at
homework and doing poorly on tests.
9/4/24: I recommend the following way to study for this class. Attend
each class, take notes, participate in class actively. After each
class review your notes and study the corresponding part of the
text. You can find out which part of the text on
the Class Outlines page in the beginning of
the semester and on the Canvas course page later on. Then do the
assigned homework problems pertinent to that material. I also
encourage you to work on homework in study groups.
9/4/24: If you need to register for this course, please, send a
message to ugrad@math.umn.edu and ask for a permission number. If
permission is granted, go to OneStop and register.
Last modified: (2024-09-25 01:21:05 CDT)