21-127 Concepts of Mathematics, Spring 2014
Homework 1
Due: Thursday, January 23rd
The following problems from the course textbook are assigned but will not
be collected:
Pages 48-49
Pages 83-86
:
:
1
Practice List Solutions
March 20, 2014
1. [Divisibility by 3] Prove that a number, x, is divisible by 3 i the sum of its digits
is divisible by 3. Start by assuming that x is a number with r + 1 digit
Practice List Solutions
March 20, 2014
1. [Divisibility by 3] Prove that a number, x, is divisible by 3 i the sum of its digits
is divisible by 3. Start by assuming that x is a number with r + 1 digit
21-127 Concepts of Mathematics
Spring 2014
Test 3 Solutions
Andrew ID:
Name:
Please circle your section:
Professors Picollelli and Harchol-Balters Sections:
Section A
12:30
Clive Newstead
Section B
1:
21-127 Concepts of Mathematics
Spring 2014
Test 1 Solutions
Andrew ID:
Name: Solutions
Please circle your section:
Professors Picollelli and Harchol-Balters Sections:
Section A
12:30
Clive Newstead
Se
21-127 Concepts of Mathematics, Spring 2014, MIDTERM II
SOLUTIONS
Name:
Andrew ID:
Please circle your section:
Professors Picollelli and Harchol-Balters Sections:
Section A
12:30
Clive Newstead
Sectio
21-127 Concepts of Mathematics, Spring 2014, MIDTERM II
SOLUTIONS
Name:
Andrew ID:
Please circle your section:
Professors Picollelli and Harchol-Balters Sections:
Section A
12:30
Clive Newstead
Sectio
21-127 Concepts of Mathematics, Spring 2014
Homework 10 Solutions
1. Proof: We prove this by strong induction on n. Well allow for two base cases: n = 1
and n = 2.
BC: If n = 1, the assertion is that
21-127 Concepts of Mathematics, Spring 2014
Homework 7
Due: Thursday, March 20th
The six problems given below will be collected:
DIRECTIONS: For each problem be very careful to show all your work and
21-127 Concepts of Mathematics, Spring 2014
Homework 6
Due: Thursday, March 6th
The six problems given below will be collected:
DIRECTIONS: For each problem be very careful to show all your work and i
21-127 Concepts of Mathematics, Spring 2014
Homework 5 Solutions
1. Suppose xn Z for every n N, and that xn = 2xn1 + 3xn2 for all n 3.
a. Prove that if x1 and x2 are both odd, then xn is odd for all n
21-127 Concepts of Mathematics, Spring 2014
Homework 5
Due: Thursday, February 27th
The following problems are assigned but will not be collected:
1. (i) Page 136 : 2.7.15: 4. and 5.
2. (ii) Pages 358
21-127 Concepts of Mathematics, Spring 2014
Homework 4
Due: Thursday, February 13th
The following problems from the course textbook are assigned but will not
be collected:
Pages 134-137
Pages 357-359
21-127 Concepts of Mathematics, Spring 2014
Homework 3 Solutions
Solutions to the Collected Problems:
1. a. Negation: x Z . P (x) Q(x).
The original statement is False, since if x = 1, then x Z, P (1)
21-127 Concepts of Mathematics, Spring 2014
Homework 3
Due: Thursday, February 6th
The following problems from the course textbook are assigned but will not
be collected:
Pages 303-307
:
4.11.2, 4.11.