MATH 300- FALL 2011- Course log

8/18 Th    Importance of writing proofs/ Three contrasts: (i) understanding vs. repetition; (ii) inductive vs. deductive reasoning; (iii) common language vs. object language/ Components of mathematical theories
(example: Euclid's postulates, 300 B.C.E.)

Statement calculus (formalizing deductive reasoning): sentences, composite sentences, the logical connectives not, and, or, implies, if and only if/ definition via truth tables

Problems in text (for discussion on Tuesday): 1.1 3, 7/ 1.2 3, 6/1.5 2

8/23 Tu  statement calculus,  quantifiers.  Sections: 1.2, 2.1
for discussion: 1.5: 4 2.1 5,6,7 for HW: 1.5 5,9

8/25 Th  quantifiers, sets Sections: 2.2, 1.3, 1.4
for discussion: 2.2 3,6   1.4 5,9 for HW: 2.2 2, 12

8/30 Tu  quantifiers, sets: problems from  1.4 and 2.2

9/1  Th  solution of first and second HW sets; example 1 from sect 2.3 (families of sets)

9/6  Tu families of sets: union, intersection (2.3)

9/8  Th  structure of proofs (3.1); Russell's paradox

9/13 Tu  proofs involving negation and conditionals (3.2) discussion: 3.1:7,11,12,13 HW: 3.1: 8,9
Examples: 3.2: 2,3,7,8

9/15 Th proofs involving quantifiers (3.3) examples 3,7,9,13 discussion 10,12,15,16 hw 6,8

9/20 Tu proofs involving conjunction, biconditionals (3.4) examples 10, 12, 16, 18 discussion 6, 11, 17, 29 hw 8, 13

9/22 Th proofs involving disjunctions (3.5) examples 1,2,9,11,15,19

9/27: Exam1

10/4 discussion of survey/discussion of test/Cartesian products (4.1) HW: 4.1, no. 8 (due 10/6)
Oct 4 Lecture
(4.1) 8 (hw) 5, 9 (discussion)

10/6 relations: representation, domain, range, inverse, composition/ reflexive, symmetric and transitive relations (4.2, 4.3)
Oct 6 Lecture
(4.2) 1 (ex.), 5 (hw)
(4.3) 4(hw) 13, 14 (discussion)

10/11 Order relations: examples, minimal and smallest elements (4.4)
Oct 11 Lecture

10/13 Th Order relations: discussion of problems 1, 3, 8, 9 (4.4)
Oct 13 Lecture

10/18 Tu Order relations: discussion of problems 6,9,11,17 (4.4)/ Equivalence relations (def)
(4.4) 1,6, 9 (hw) 3,8,11,17 (discussion)

10/20 Th Equivalence relations: examples, equivalence classes, quotient set, partitions (4.6)
Oct 20 Lecture
(4.6) 2, 4(hw) 11, 12 (discussion)

10/25 Tu Problems on equivalence relations/functions (Ch. 5)
Oct 25 Lecture
(5.2) 5,6,8,14 (hw), 16 (discussion)
(5.1) 6 (ex.) 17a, 18 (discussion)

10/27 Th Problems on equivalence relations and functions. (Ch.5)
Oct 27 Lecture
(5.3) 6 (hw) 13 a,b (discussion)

11/1 Tu  Equivalence relations, functions; image and preimage of a set under a function (Ch.5)
Nov 1 Lecture

handout: 6 (hw) 1,2,5,7 (discussion)

11/3 Th Problems on equivalence relations and functions
(5.4) 1 (hw), 2,3,4 (discussion)

11/8 Tu  Review based on student questions--problems discussed: (4.4) 1a, (4.6) 11, (5.3) 13 a)b),  (5.1) 18 a)b)
Discussed also: handout, pages 3,4 (NEW); suggested for practice: (5.1) 19 a)

11/10 Th EXAM 2: Included--ch.4 and ch.5  material
Exam 2

11/15 Tu Proofs by mathematical induction
(6.1) hw 5,11/discussion 6,8,12,17

11/17 Th countable vs. uncountable sets (7.1, 7.2 up to Thm 7.2.2)
(7.1) 1b, 2a, 3, 11b, 27 (7.2) 1
Nov17 Lecture

11/22 Tu countable and uncountable sets: some proofs/ supremum property of the real numbers

11/24 Th THANKSGIVING (no classes)

11/29 Tu (last day) Problems: countable and uncountable sets/ supremum property of the real numbers

FINAL EXAM: Thursday 12/8, 8AM to 10AM
FINAL EXAM

Comprehensive: problems on the final may refer to any topic introduced in the course. For the material
already included in exams 1 and 2, the problems on the final will test the same concepts (this does not mean similar questions
necessarily. There will also be problems dealing with material presented in the last four lectures.

Final grades (16 students took the final, of 24 initially enrolled)
A, A-  4
B+,B,B-  4
C, C-  8