Math 3345 - Foundations of Higher Mathematics 

(Spring 2019)
 

Course syllabus

List of useful tautologies

In-class exercises for 1/11/2019 and 1/14/2019

Homework #1 (due Wednesday, January 16 Friday, January 18)

p. 7 #2, 3 (first sentence only)

p. 8 #5

p. 16 #17 (see the hint on p. 17)

p. 19 #22

p. 23 #31, 32

For problem 17, you are not required to write the proof in the formal style of Example 2.24 and explicitly discharge assumptions, but your argument should be as efficient as possible and avoid cases (i.e. don’t analyze different possible combinations of truth values for P,Q,R separately, which effectively would be a proof by truth table).



Revised office hours (for rest of semester): Mondays 4:45-6:45pm

Homework #2 (due Wednesday, January 30)

p. 28 #1, parts (g) through (k)

p. 31 #7

p. 35 #10

p. 36 #13

p. 37 #14, parts (g) and (h)



Homework #3 (due Wednesday, February 6)

p. 41 #3

p. 43 #8 (b) and (c) [You may use part (a) without proving it.]

p. 44 #10 (b) and (d)

p. 45 #12 [You may assume that pi is irrational.]

p. 46 #13 (a) and (b)

p. 47 #16



Homework #4 (due Wednesday, February 13)

Revised due date: Friday, February 15

(click on link for PDF file)



Homework #5 (due Wednesday, February 27)

p. 60 #2

p. 61 #5

p. 62 #6, 7, 8



Midterm 1 on Wednesday, February 27 (in class)

In addition to the “review problems” below, you should study the homework problems from the first four assignments and the examples discussed in class. (To answer two common questions: there is no need to memorize the list of tautologies, and induction won’t be on this exam.)

Review problems for Midterm 1

(click on link for PDF file)



Homework #6 (due Wednesday, March 20)

1. Prove by induction that n! > 2n for all integers n > 3.

2. p. 66, #12

3. Use the binomial series to estimate (4/3)3/4 to two decimal places. (Show how this can be done without a calculator.)

4. p. 71, #18

5. p. 71, #22 (Caution: On the left-hand side of the identity, fg is differentiated n times; you are not raising fg to the nth power. The notation on the right-hand side should be interpreted similarly. Your proof should be similar to the one for the binomial theorem.)

6. p. 74, #1 (You may use the formula in Ex. 1, p.60 without reproving it.)



Midterm 1

High: 96

Median: 80

Average: 76.3

Distribution of scores

90+ : 3

80-89: 14

70-79: 6

60-69: 6

<60 : 2



Homework #7 (due Wednesday, March 27)

(click on link for PDF file)



Midterm 2 on Wednesday, April 3 (in class)

In addition to the “review problems” below, you should study the homework problems from HW#5-7 and the examples discussed in class.

Review problems for Midterm 2

(click on link for PDF file)



Homework #8 (due Friday, April 5) [handout includes in-class exercises for 3/27 and 3/29]

(click on link for PDF file)



Homework #9 (due Friday, April 12)

p. 118 #33, parts (a) through (d)

p. 122 #3

p. 124 #9

p. 125 #10

p. 133 #2

p. 137 #12



Homework #10 (due Friday, April 19)

Reading: “Hilbert’s hotel” on page 159

p. 127 #15

p. 160 #1

p. 162 #5, 6, 7

p. 175 #11 (you don’t need to use the material in section 16)



Midterm 2 (updated)

High: 101

Median: 88

Average: 86.0

Distribution of scores

100+: 1

90-99 : 11

80-89: 12

70-79: 5

60-69: 2

<60 : 0



Final Exam on Friday, April 26, 4:00-5:45pm (in usual classroom)

Review sheet for Final Exam

(click on link for PDF file)