What you need to know for The Final Exam
Math 108 SSII 2015
This is a writing course. You are expected to get better at writing as the course goes on. On
the final, you can lose points any ways you could lose points on the midterms. Additionally, you will
HW20
Math 108 SSII 2016
Exercises
Due 9/7, 1pm at the class box.
6.4 # 6a,20b
6.5 # 10b,15a
I Proofs (also Due 9/7)
Present two famous proofs. Decide which of is your favorite and give a substantial rationale for your
choice. (It is my favorite because it
HW5
Math 108 SSII 2016
Reading
2.1, 2.2, and 2.3
You will want to go back to 1.7 occasionally to see more examples, but dont think that you need to
read all of it in one go.
Exercises
Due 8/9, 1pm at the class box.
1.5
1.6
2.1
2.2
2.3
#2b,3c
# 1g,7f,9f (7
Name:
SID:
Gateway Opportunity III
MATH 108, SSII 2016,
Prof. Cherney
1
1. Define universal quantifier. Define inductive set.
n
P
Prove by induction that (n N) i = n(n+1)
.
2
i=1
Instructors Response
Definition: A subset of the natural numbers S is induct
HW8
Math 108 SSII 2016
Reading
Midterm solutions
3.1 and 3.2
Exercises
Due 8/15, 1pm at the class box.
1.6 #4d
2.4 # 4h,
3.1 #2,6bd,8b,
3.2#1bcd, 4a,5a,9ac
Instructors Solutions
1.6
4d Claim: For integers a, b, c, if a divides bc, then either a divides b
HW17
Math 108 SSII 2016
Reading
6.3
Exercises
Due 8/31, 1pm at the class box.
4.6 # 5l
6.3 # 2b,4ac,17b
Announcements
1. Monday is a holiday (Labor Day)
2. Extra Credit opportunity #1: Midterm Mistake Celebration!
Submit an itemized list of mistakes you m
HW14
Math 108 SSII 2016
Reading
4.6
Exercises
Due 8/24, 1pm at the class box.
3.3
3.5
4.2
4.3
4.4
4.5
4.6
#7e
# 2d
# 5b
#9b
# 5b
# 12b,14c
# 4a,5dj,13a
NOTE: With this assignment we will have a zero tolerance policy regarding the following rule:
Re-establ
HW12
Math 108 SSII 2016
Read 4.2 and 4.3
Exercises
Due 8/22, 1pm at the class box.
1.6
2.4
3.3
3.5
4.1
4.2
4.3
#1i
# 4k
#4c
# 2c
# 1e
# 2bj,4b,9b,10,16b
#3bd,4bd,14a
Instructors Solutions
1.6
1i Claim: For all odd integers m and n, if mn = 4k 1 for some i
HW16
Math 108 SSII 2016
Read 6.2
Exercises
Due 8/30, 1pm at the class box.
2.4 # 5c
4.5 # 4a
4.6 # 5g
6.1# 1g,3,16c
6.2 #1a,3,13,18a
and by request.
Common MTII mistakes
1. .
e.g. of the mistake)
If a relation R does not contain the identity relation IA
HW7
Math 108 SSII 2016
Reading
2.6
MT1 study guide (mt1s.pdf)
Exercises
Due 8/11, 1pm at the class box.
1.2#7e
1.3 #1p
1.5 #3d
1.6 #1h
2.2 # 6b
2.3 #1m
2.4 # 4de,8d
2.5# 7c
2.6 #2acd,12a,12b,25b
Extra credit
Only if you complete the exercise set above, th
HW6
Math 108 SSII 2016
Read 2.4, and 2.5
Exercises
Due 8/10, 1pm at the class box.
1.2#12c
1.3 #10eg
1.5 #2e
1.6 #4c
2.1 # 6d
2.2 # 13c
2.3 #1j
2.4 # 3ab, 8ab,4bc,6b,12e
2.5# 3,7ab,14a
There are three distinct ways that letters (meaning symbols other than
HW1
Math 108, SSII 2016
Due Tuesday, 8/2,1pm in the class box, 1st floor of MSB.
A video walk to the class box (where homework is to be handed in) can be found in the smartsite
announcements.
Follow the rules presented in lecture.
Note:
These problems are
HW15
Math 108 SSII 2016
Reading
6.1
Exercises
Due 8/29, 1pm at the class box.
3.3 #4d
4.2 # 1b
4.4 # 7b
4.5 # 5a
4.6 # 5f,6c
6.1# 1bc,10b,11a,16a
Instructors Solutions
3.3
4d The equivalence relation R defined by
(x, y R)xRy x2 = y 2
induces the partition
Name:
SID:
Midterm II
MATH 108, SSII 2016,
Prof. Cherney
Anything you write and do not cross out will be read and graded.
Write in pencil. You will want to edit your writing by erasing.
Write your name and student ID at the top of this page.
Each prob
Name:
SID:
Practice Midterm I
MATH 108, SSII 2016,
Prof. Cherney
Write in pencil. You will want to edit your writing by erasing.
Write your name and student ID at the top of this page.
Each problems is worth 20 points. There are six problems.
Your exam
HW13
Math 108 SSII 2016
Reading
4.4 and 4.5
Exercises
Due 8/23, 1pm at the class box.
2.4
4.2
4.3
4.4
4.5
# 5a
# 1f
#4c
# 2ab,3d,7c,10a
# 1b,3f,5b,10b,17b
Be sure you are using set builder notation for the functions you write about; in this class function
Name:
SID:
Midterm I
MATH 108, SSII 2016,
Prof. Cherney
Write in pencil. You will want to edit your writing by erasing.
Write your name and student ID at the top of this page.
Each problems is worth 20 points. There are six problems.
Your exam score wi
Name:
SID:
Gateway Opportunity
MATH 108, SSII 2016,
Prof. Cherney
1
1. Define universal quantifier. Define inductive set.
n
Q
1
1
Prove by induction that (n N)
1 i+1
= n+1
.
i=1
Instructors Response
Definition: A subset of the natural numbers S is inducti
Name:
SID:
Gateway Opportunity II
MATH 108, SSII 2016,
Prof. Cherney
1
1. Define universal quantifier. Define inductive set.
n
P
Prove by induction that (n N) 2i = 2n+1 2.
i=1
Instructors Response
Definition: A subset of the natural numbers S is inductive
Name:
FINAL EXAM
MATH 108, SSII 2016,
Prof. Cherney
Anything you write and do not cross out will be read and graded.
Write in pencil. You will want to edit your writing by erasing.
Write your name at the top of this page.
Each problems is worth 20 poi
HW19
Math 108 SSII 2016
Read 6.5
Exercises
Due Tuesday 9/6, 1pm at the class box.
(Monday, 9/5 is a holiday)
2.4
3.5
4.6
6.2
6.3
6.4
6.5
#
#
#
#
#
#
#
5d
2e
5n
4
11c
5b
2,5,10a
Make a list of the two most important theorems from each chapter (not section
HW2
Math 108, SSII 2016
Due Wednesday, 8/3, 1pm in the class box, 1st floor of MSB.
Note: Rule 3 for homework is now a soft rule;
Reading
1.2 and 1.3 of the text.
I recommend working in the following order
Do the exercises for 1.1
read the exercises for
HW4
Math 108 SSII 2016
Reading
Read 1.5 and 1.6.
Most students want to read 1.7 to see more examples.
Exercises
Due 8/8, 1pm at the class box.
1.2
1.3
1.4
1.5
1.6
#4a
# 1ef,6bd
#5c,9b
# 1bdf, 2d, 3bg, 6ac, 7ab,12ab
#1b by construction, 1d by contradiction
HW9
Math 108 SSII 2016
Reading
Read 3.3 and 3.4
Exercises
Due 8/16, 1pm at the class box.
2.4 # 4i,
3.3 # 2abc,4a,7a,15a
3.4 #1ehi, 6a as a proof, 9b
Instructors Solutions
2.4
4i Claim: (n N)
n
P
k=1
1
(2k1)(2k+1)
Proof: Let S = cfw_n N |
n
P
k=1
The numb
HW18
Math 108 SSII 2015
Reading
6.4
Exercises
Due 9/1, 1pm at the class box.
NOTE: With this assignment we will have a zero tolerance policy regarding the following rule:
Re-establish the context (so our reader knows what you are saying without needing to
HW3
Math 108 SSII 2016
Reading
Read 1.4
Read the solutions to HW1 and HW2 posted on smartsite; if you ever asked can you go over #6,
the answer is yes, Im doing the homework too, and you can see them a few hours after the HW is
due. You didnt have to ask!