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