21-127 Spring 2013

Instructor: Professor Michael E. Picollelli, Wean Hall 8124, ext. 8-2086, mpicolle@gmail.com

Textbook: D’Angelo and West, Mathematical Thinking: Problem Solving and Proofs, Second Edition.

Website: 21-127 Concepts of Mathematics, Spring 2013.

Teaching Assistant for Section C & D: Zilin Jiang (Roy), Wean Hall 7213, zilinj@andrew.cmu.edu

Office Hours for Roy (Teaching Assistant) in WEH 7213: M 6:30PM – 7:30PM, W 5:30PM – 6:30PM.


  • I will hold additional office hours on May 6 (Monday) and May 8 (Wednesday) from 4PM to 5PM. (May 4, 2013)
  • As I promised before, the office hours on Mondays are resumed to the time they were used to be from 5:30 to 6:30 pm. This is effective from today. (April 29, 2013)
  • I have to move my office hours on Mondays to 6:30PM-7:30PM due to the conflict with the maths seminars. This is effective from today. And I will resume the usual office hour as soon as the seminars are over. (April 1, 2013)
  • To help students prepare for the next test, I will hold office hour this Sunday from 3:30PM – 4:30PM. And the office hour on next Wednesday is canceled. (March 21, 2013)
  • I have to move my office hour today 30 minutes earlier. So I will be in WEH 7213 from 5:00PM to 6:00PM. Sorry for the late notice. (March 20, 2013)
  • My apologies for being absent for my office hours yesterday due to some personal issues. And I would like to compensate with extra office hours today from 4:30pm to 5:30pm at Wean 7213. (February 28, 2013)
  • As the test is on Wednesday, I will hold office hour tomorrow from 4:30PM – 5:30PM. Therefore, the office hour on Wednesday is canceled. (February 11, 2013)
  • Usual office hours on Mondays and Wednesdays have been reduced from 5:30PM – 7:30 to 5:30 – 6:30. (February 1, 2013)


Homework Feedback for Section C & D:

  • Assignment 1: Due on Thursday, January 24, 2013.
  • Assignment 2: Due on Thursday, January 31, 2013.
  • Assignment 3: Due on Thursday, February 7 , 2013.
  • Assignment 4: Due on Thursday, February 21, 2013.
  • Assignment 5: Due on Thursday, February 28, 2013.
  • Assignment 6: Due on Thursday, March 7, 2013.
  • Assignment 7: Due on Thursday, March 21, 2013.
  • Assignment 8: Due on Tuesday, April 2, 2013.
  • Assignment 9: Due on Tuesday, April 9, 2013.
  • Assignment 10: Due on Tuesday, April 16, 2013.
  • Assignment 11: Due on Thursday, May 2, 2013.



  1. Hi, I have a couple of questions regarding the homework. Firstly, can we prove 1.40 with Venn Diagrams. Secondly, For question 1.51, can we explain using schematic representations? Thanks!

    1. Aditya, I think using Venn Diagrams is acceptable for 1.40. But it’s better to know different approaches other than that. For 1.51, schematic representation would help you understand the problem. But to write up a rigorous proof, drawing graphs is not enough. In general, drawing pictures is just an auxiliary method to supplement a mathematical proof, though graphic thinking is a good way to understand a proof.

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