Math 63
Real Analysis
Last updated June 27, 2016 13:25:50 EDT

General Information Syllabus HW Assignments


Announcements:

Homework Assigments

Week of January 7 - 11, 2013
(Due on Monday, January 14th)
Assignments Made on:
Monday:
  • Study: Chapter I.1 to I.4
  • Do: Chapter I: 3ab, 5a, 7cf, 10ab
Wednesday:
  • Study: Chapter II.1 and II.2
  • Do:Chapter II: 2ab, 3, 6.
Friday:
  • Study: Chapter II.3 and II.4
  • Do: Chapter II: 10a, 11, 12, 13.


Week of January 14 - 18, 2013
(Due Tuesday, January 22)
Assignments Made on:
Monday:
  • Study: Read III.1
  • Do:Chapter III: 1a
Wednesday:
  • Study:Read III.2
  • Do:Chapter III: 3, 4, 5.
Friday:
  • Study: Read III.3
  • Do:Chapter III: 8, 10, 11, 18.
  • Reminder:No class Monday. Homework is due Tuesday in our x-hour.


Week of January 21 - 25, 2003
(Due Monday, January 28)
Assignments Made on:
Monday:
  • NO CLASS:
  • Think:"Rarely do we find men who willingly engage in hard, solid thinking. There is an almost universal quest for easy answers and half-baked solutions. Nothing pains some people more than having to think." -- Martin Luther King Jr.
Tuesday (X-HOUR):
  • Study:Read III.4
  • Do:Chapter III: 24
  • Comments: Here are some solutions to the first assignment: click here.
Wednesday:
  • Study: Read III.5
  • Do: Chapter III: 32
Friday:
  • Study: Read III.5
  • Do: No additional assignments this week. Study for exam on Tuesday.


Week of January 28 - February 1
(Due WEDNESDAY, February 6)
Assignments Made on:
Monday:
  • Study: Read section III.6 and start IV.1. Of course, you should also continue to prepare for the minor midterm on Tuesday.
  • Do: In Chapter III: 38
X-Hour:
  • IN CLASS EXAM: The in-class portion of the exam will be given during our x-hour.
  • TAKE HOME: The take-home portion of the exam will be passed out Tuesday and will be due at the start of class on FRIDAY. You may access your text and class notes, but NO OTHER SOURCES are allowed annimate or inannimate.
Wednesday:
  • Study:Read section IV.1 (and yes, I know you also have a take-home exam.)
  • Do:No written assignment because; because, yes, I know you also have a take home exam.
Friday:
  • Study:Read section IV.2
  • Do: In Chapter IV: 1d, 2, 4. By popular demand, this assignment is now due Wednesay. Note that Monday's assignment, once its posted, will also be due Wednesday.
  • Here is a link to some solutions for the first exam.
  • Here is a link to a hist-o-gram of the scores on the first exam. Please remember that the exam was out of a total of 75. While it is a bit early in the game to think seriously about grades, let's say that scores above 50 are "A-ish". Everything else is some flavor of "B".


Week of February 4 to 8, 2013
(Due Wednesday, February 13)
Assignments Made on:
Monday:
  • Study: Read section IV.3
  • Do: In Chapter IV: 9ab and 10bc. Please note that this is due Wednesday (the 6th) in class.
Tuesday (X-HOUR):
  • Study: Read section IV.4
  • Do: In Chapter IV: 14ab (see Example 2 in section IV.1). Please note that his assignment is due a week from Tomorrow: Wednesday, February 13th.
Wednesday:
  • Study: Read section IV.5.
  • Do: In Chapter IV: 29b. This assignment is due Wednesday, February 13th.
  • There is no class Friday.
Friday:
  • Study: No Class
  • Do: Enjoy Winter Carnival.


Week of February 11 - 15, 2013
(Due Wednesday, February 13 & 20)
Assignments Made on:
Monday:
  • Study:Section IV.6
  • Do: In Chapter IV: 33 and 37. These problems are due Wednesday the 13th.
Wednesday:
  • Study: Section IV.6
  • Do: In Chapter IV: 42 and 43. This assignment is due Wednesday, February 20th -- that day after the in class portion of our second midterm.
Friday:
  • Study: Study Chapter IV and think about exam on Tuesday.
  • Do:
    1. Show that if $f:E\to F$ is a continuous bijection between compact metric spaces, then the inverse $f^{-1}:F\to E$ is continuous. (Hint: why is it enough to show that $F(S)$ is closed if $S$ is closed in $E$?)
    2. Use the above to show that there is no continuous bijection from the unit interval $I=[0,1]$ to the unit square $I^2:=[0,1]\times [0,1]$. You are allowed to assume the validity of problem 29a in Chapter IV and that $I^2\setminus \{pt\}$ is arcwise connected.
  • In class demos: animation. And the web page.


Week of February 18 to 22, 2013
(Due Wednesday, February 27)
Assignments Made on:
Monday:
  • Study: Read sections V.1, V.2 and V.3
  • Do:Study for exam.
X-HOUR:
  • Midterm exam:In class portion.
  • Take Home: Is due on Friday
Wednesday:
  • Study: Section V.4
  • Do:In Chapter V: 1b, 12.
Friday:
  • Study: Section VI.1 and VI.2
  • Do:In Chapter VI: 11. (In problem 11, you can assume that $f$ is Riemann integrable.) This was originally written as problem 11 in Chapter IV, but of course, there is no $f$ in that problem.


Week of February 25 - March 1, 2013
(Due Wednesday, February 27 and Wednesday, March 6)
Assignments Made on:
Monday:
  • Study: Read section VI.3
  • Do: In Chapter VI: 5, 8 and 20. This assignment is now due Friday, March 1st.
  • Exams:The exams will be returned in class on Monday.
    • Although final grades are far from determined, you can approximate your grade on the first two exams as follows. (Note that this does not take homework into account.) If you total (out of 200) on the first two exams is 156 or above, then you are doing "A"-ish work. A score of 122 or above is most likely some sort of B.
    • You should read over these partial solutions.
    • You may also want to view this hist-o-gram of the scores on the second exam.
Wednesday:
  • Study: Read section VI.4 and IV.5
  • Do:In Chapter VI: 17. This assignment is due Wednesday, March 6th.
Friday:
  • Study: Read section VII.1
  • Do: In Chapter VII: 1 and 4.


Week of March 4 - 8, 2013
(Due Wednesday, March 6)
Assignments Made on:
Monday:
  • Study: Read VII.1.
  • Do:
    • In Chapter VI (Riemann Integration): problems 16 and 21.
    • Let $s_n:= 1 +\frac1{1!}+\frac1{2!}+\cdots +\frac1{n!}$. Use Taylor's Theorem to show that for $n\ge 1$ we have $\frac 1{(n+1)!} < e-s_n <\frac e{(n+1)!}$, where $e=\exp(1)$.
    • Use the above to show that $e$ is irrational. (Hint: suppose that $e=m/n$, and multiply the above inequalities by $n!$. Note that there is no integer $m$ such that $ 0< m <1 $.)
    • This assignment is due Wednesday. This is the last assignment that will be collected.
Wednesday:
  • Study: Read VII.2
  • Do: In Chapter VII: 8 and 9.
  • Although homework is no longer collected, this material is fair game for the final. However, you can ask about any assigned homework even after the take home final has been passed out.
Friday:
  • Study: TBA
  • Do: TBA


Dana P. Williams
Last updated June 27, 2016 13:25:50 EDT