MATH 300-SPRING 2012-COURSE LOG

1/11   W    Course policies/ logical connectives

1/13   F      Quantifiers

HW 1 (due F 1/20): Handout 1: 3, 4(ii)
Velleman 2.1: 3, 9 (in 3, "analyze the logical form" means: write using quantifiers.)
Velleman 2.2.2(c)(d), 2.2.3

1/16   M       Martin Luther King, Jr. Holiday (no class)

1/18   W   Quantifiers (examples), sets (start)

1/20  F   continuity (9 in handout 2); proofs involving inclusion/equality of sets

HW 2 (due F 1/27) Handout 3: 2, 3(ii), 4(ii), 5, 8(i)(iv)
(others may be prepared for presentation in class next week)

1/23 M   discussion of HW1 (negation of bounded quantifiers)/ cartesian products

1/25  W cartesian products--examples [ref: Velleman, section 4.1]

1/27  F  relations  [ref: Velleman, sections 4.2, 4.3]
HW 3 problems (due Friday, Feb 3):  4.2: 2(b), 5; 4.3: 4(b)(c)(d), 10 (for i_R), 14
For discussion: 4.2: 9, 4.3: 4 (a), 6 ,8, 10 (for i_D), 13

1/30  M relations: discussion of problems

2/1  W  discussion of HW problems
Functions [ref: Velleman, chapter 5]-basic definitions
Problems: (5.1) 4b, 6, 15, 16

2/3   F Functions: discussion of problems
Problems: (5.2) 5, 6, 7, 8

2/6   M  Functions: discussion of problems
Problems: (5.3) 4, 5, 6
Problems: (5.4) 1, 2, 3, 4

HW 4 due Friday, 2/10:
the problems in boldface listed above for sections 5.1 to 5.4 (six problems)

2/8  W Functions: discussion of problems

2/10  F  Equivalence relations: partitions, quotient set, examples

2/13  M Discussion of HW3/ functions and equivalence relations

2/15  W equivalence relations and functions (handout 4)

2/17  F  Problems 3, 4, 5, 6, 7 discussed
HW 5: Problems 1, 2, 3, 8, 9  (due Monday 2/20)

2/20 M  Discussion of HW problem 9/From the natural numbers to the rationals (start)

2/22  W Problem 10 due.

2/24 Friday: Exam 1 (material up to lecture of Monday, 2/20)
Includes corresponding sections in the text.
Exam 1

2/27 M  From the natural numbers to the integers (cont'd)/discussion of exam 1

2/29 W  Ordering relations (Velleman 4.4)--Lecture by Dr. Lind

3/2   F   Ordering relations--Lecture by Dr. Lind

3/5  M  Ordering relations--examples

HW6 (due Friday 3/9) (from Velleman, 4.4): 6,9,11,16, 20(b)

3/7 W  Ordering relations--examples

3/9 F  From the integers to the rationals

3/12 M  Fields, ordered rings, well-ordering

3/14 W Ordered fields, Archimedean property/ discussion of HW6

3/16 F  Discussion of HW6/ density of Q in R, absolute value

3/19-3/23 SPRING BREAK

3/26 M Supremum property of R

3/28 W Supremum property/discussion of problems

3/30 F Test 2. Included: sec. 4.4 and 4.6 of Velleman
Test 2

4/2  M handout 7, cont/discussion of test

4/4  W handout 7: convergence of sequences, approximation property

4/6  F SPRING RECESS (no lecture)

4/9  M monotone convergence property
Homework (due Friday 4/13)  3,5B,5C,8,9

4/11 W  Cauchy sequences (section 5)

4/13  F Decimal expansions of real numbers (section 6)

4/16  M  Countable vs. uncountable

4/18  W Uncountable

4/20  F Uncountable

4/23  M Uncountable/review

4/25 W THIRD TEST (material up to 4/20)
Test 3

4/27 F uncountable/review (last day)

FINAL EXAM: Monday, May 7, 10:15-12:15 (comprehensive)
Final

Grades: B-=2, C-,C,C+=7, D,D+=2, F=3 (14 students took the final, of 19 initially enrolled)