Homework: Fall 2008, Math 505  (Finotti)


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****  Don't forget to write up your homework according to the guidelines in the syllabus! ****

General Guidelines 
** Remember - confusion is the first step to wisdom! It's not only normal to not immediately understand something, it's often necessary for learning and very necessary for curiosity.

**The purpose of the homework sets are for you to work through the understanding of the material and see what it is you do and do not understand so that you can fine tune your understanding from there -- please keep this viewpoint in mind when working through problems. 

**Educational research shows that studying and learning in peer groups often leads to better comprehension of the material.  Get to know your classmates and form study groups. 

**The other side of the coin is that just as beneficial to your learning is time spent grappling with the material alone.  Always do your final homework writeups on your own, and feel free to reach for help when you need it.  Doing it first on your own helps you to know what it is that you really do or don't understand

**If you are suspected of plagerism (think solution manual), you will get a zero for the homework set, and will be reported to University authorities.

*Please look at the following interesting graph of material retention vs. time lapse from first exposure until review (retention curve) and the subsequent tips for textbook reading

Keep this in mind when writing up your homework solutions -- it IS as important for learning math to practice explaining your solutions well as it is finding them!  Mathematics is a language.

Homework Set #

 Due Date

Homework/Boardwork Assigments




 1
8/27

Homework:    Write up proofs for problems 1, 3, and 5 on page 8 of   505_LogicHandout.pdf
Boardwork:  Prepare problems 2, 4, 6, and 7 from the same page of the same handout

 2

9/3

Homework:  Pg 188 - 1,4,6
Boardwork: Pg 188 - 3,7


3
9/10
Homework: Pg 193 - 1,3; Pg 198 - 1,3,5
Boardwork: Pg 193 - 2,6;  Pg 198 - 2, 4, 6
4
 9/17

 Homework: Pg 198 - 7b;  pg 202 - 1,3
Boardwork:  Pg 202 - 2,4,6

5
9/24

 Homework:  Pg 206 - 1,4,6
Boardwork:  Pg 206 - 2,3,5







6






10/1
 Homework:  Pg  - 1,3,6

For numbers 1 and 3, just approximate the integral by a Riemann sum  with n >= 3.

Also:
1.  Try to prove that the integral of (df/dx) from a to b is equal to f(b)-f(a), using the definition of Riemann integration and the definition of the derivative.

2.  Prove that the integral of  f(x) = (x^2)*sin(1/x) on the interval [-pi,pi] is between -2(pi^3)/3 and 2(pi^3)/3.


No Boardwork this week - we'll have a Q&A for the test instead..

7
10/15
 Homework:  pg 218 -  1, 4, 5, 6
Boardwork:  pg 218  -  2, 3, 7
8
 10/22
 Homework:  pg 223 - 2, 6, and: 
1. Prove that if s_n converges as n-> infinity, then |s_n| must also converge.  Is the converse true?
2. Prove that if x_n  -> a and y_n -> b are both convergent sequences,then x_n + y_n  -> a+b.

Boardwork: 1, 4, and:
Prove that if x_n ->a and y_n -> b, then x_n*y_n -> a*b.
9
 10/29
 Homework:  pg 228 -  1,2,3,7
Boardwork:  pg 228 - 4,5,6
10
 11/5
  Homework:  pg 232 - 1,3 and:
1.  If a set E has a supremum, prove that it has only one supremum.
2.  Prove that if M is an upper bound of a set E and M is in E, then M is the supremum of E.
3.  Write up the proof that "If E is nonempty subset of the real numbers and is bounded below, then E has an infimum."
11
 11/26
 Homework:  pg 242 - 2,3,5,6 (part c and e only)