Martin Flashman's Courses- Math 381


MATH 381 (1 unit)   TUTORIAL IN WRITING
Tentative Assignments In Solow, How to read and Do Proofs, 4th Edition [old 3rd Edition]      M. Flashman
Fall, 2007 [In revision!]
  1. First week: Read Solow: To the Student, ch 1-3. and Chapter 13 Summary.
    Read and outline 3 editorials from NYTimes.
  2. First and Second week :
  3. Do: 1.1-1.8; 2.3,2.4,2.7, 2.9(a,b)
  4. Due   : Read Handouts.
    Bring 2 definitions (one you like, and one you don't like) for a 1:1 function and an onto function.
  5. Consider what makes a definition effective for you.
    Review Ch 3 in Solow.
    Do: Solow: 2.19;  3.1,3.2, 3.3
  6. Due  : Review Ch. 4. Read Solow Ch. 5
  7. Do: Solow 3.9-3.11,3.15;
    Look at-Do: 4.1,4.2,4.4,4.5, 4.7, 4.8
    Use the definition of 1:1 to prove a) f(x) = 3x+5 is 1:1 and b) f(x)= 3x2 + 5 is not 1:1.
Use the definition of onto to prove a) f(x) = 3x+5 is onto and b) f(x)= 3x2 + 5 is not onto.
We will continue a disucussion of definitions , especially with regard to 1:1 and onto functions
  1. Due . Read 5  [If you have time:Read Solow Ch 8 and 9.]
    We will discuss problems from ch 4 and 5, 1:1 and onto with regard to the choose method of ch 5.

  2. Due  : Read Solow Ch 5, 7, 8, [8]Do: Solow 5.1,5.2, 5.5 ,5.6, 5.7, 5.9, 5.11
    Rewrite proofs of 1:1 and onto.
  1. Due  : Read 7,8,9
    We will begin indirect proofs. [Contradiction and Contrapositive methods.]
    Read / Do: Solow:  7.3,7.7 ,8.1, 8.3, 8.7, 8.8, 8.11; 9.1,9.3
    Nested quantifiers....(Problems Not done)
  2. Due  : Continue with indirect proofs and the Knot of nots. Read 8,9 and 10.
  3. Do: Solow: 9.7, 9.8, 9.11,10.1,10.2,10.5, 10.7-10.10;
  4. Due : read ch 11, pp 133-141, ch 7, Specialization, Uniqueness, [and Alternatives.
    Do: 10.2, 10.3, 10.5, 10.7, 10.8, 11.1, 11.3; 11.4, 11.5,12.1-12.4, 12.9
    Specialization, Uniqueness, and Alternatives.
  5. Due  ch.6. Induction.
    Do: 11.4,11.5,12.1-12.4, 12.9; 7.3, 7.5, 7.6