Math 3325: Transitions to Advanced Mathematics, Fall
2015
Assignments
Optional:
Homework #11, Due Wednesday, December 2
Sec. 5.4 #5(a),(b),(c),(d), #7, #12, #14; Sec. 5.5 #3, 5, 8
(Also: Look at and try to do Sec. 5.4 #16, but do not turn in.)
Proof Problem #5, Due Wednesday, December 2
Here is Proof Problem #5.
In addition to the homework you turn in, watch the following three videos:
Finally, I want you to look at the proofs you did on your last homework, and then compare
them to homework proofs you did on some of the first homework assignments in the class, and
observe how much you've learned in this course and how much better at writing proofs
you've become.
No Class and No Office Hours on Wednesday, November 18
Proof Problem #4, Due Monday, November 16
Here is Proof Problem #4.
Homework #10, Due Monday, November 16
Sec. 5.3 #9(a), (b), (c), (d), (e), (f), #10 (a), (b), (c), (d), (e) #11,
#14 (a), (b), (c), (d); Sec. 5.4 #8 (a),(b),(c), #10
Reading Assignment #10, to be done prior to class on Monday, November 16
Read Sec. 5.3, 5.4, and 5.5.
Proof Problem #3, Due Wednesday, November 4
Here is Proof Problem #3.
Homework #9, Due Wednesday, November 4
Sec. 4.4 #1(a)(b), #2(b)(c), #3(d); Sec. 4.5 #4(a)(d), #8(b)(d), #10(e)
Reading Assignment #9, to be done prior to class on Wednesday, November 4
Read Sec. 4.5, 5.1, 5.2
Exam 2 on Wednesday, October 28
The second exam is this Wednesday in class. Remember that Office Hours are MW 3-4PM.
Homework #8, Due Wednesday, October 28
Please complete and turn in these problems.
Reading Assignment #8, to be done prior to class on Wednesday, October 21
Read Sec. 4.1-4.4
Homework #7, Due Wednesday, October 21
Please complete and turn in these problems.
Some things to Consider
We said in class that "A picture is not a proof." This is because the way we draw a picture
can sometimes be misleading or inaccurate. A proof needs to provide a convincing argument
using logic, which covers all possibilities. Here are some examples of how pictures can be misleading:
Reading Assignment #7, to be done prior to class on Wednesday, October 14
Read Sec. 3.1-3.4
Homework #6, Due Wednesday, October 14
Sec. 2.6 #1(a)(d), #6, #7(c), #9(a)(b), #19(a)(b)(c), #23(c)
Reading Assignment #6, to be done prior to class on Wednesday, October 7
Read Sec. 2.6-3.1
Homework #5, Due Wednesday, October 7
Please complete and turn in these problems.
Proof Problem #2, Due Wednesday, October 7
Here is Proof Problem #2.
Reading Assignment #5, to be done prior to class on Wednesday, September 30
Read Sec. 2.3-2.5
Announcement:
You will get your graded Exam 1 back on Monday, September 28. There is no
homework due on Wednesday, Sept. 30. Instead, use this week to go over the exam and
review material and concepts covered on problems that you missed. In preparation for the next exam, the following
contains questions to help you think about how you study. If your score
on Exam 1 is significantly lower
than what you expected or are happy with, you may want
to consider withdrawing from the course.
Exam 1 on Wednesday, September 23
The first exam is this Wednesday in class. Remember that Office Hours are MW 3-4PM.
Homework #4, Due Wednesday, September 23
Sec. 2.1 #5(b),(d),(f),(h),(j),(l), #14 (b)(d), #15(b)(c); Sec. 2.2
#9(a),(d), #10(d), #11(b),(d);
Handouts from Class on Wednesday, September 16
Here are two handouts that you may find useful. The first gives some suggestions
on what to do when you're trying to prove a statement and you get stuck. The second is
a list of the ZF+C axioms (i.e., the Zermelo-Frankel axioms plus the Axiom of Choice).
ZF+C is the system of standard axioms of set theory, and hence they constitute the standard
axioms of most of mainstream mathematics. Although you don't
need to memorize the ZF+C axioms or even use them in any direct way in this course, I'm giving
them to you just so you can see them.
Reading Assignment #4, to be done prior to class on Wednesday, September 23
Read Sec. 2.1-2.2
Proof Problem #1, Due Monday, September 21
Here is Proof Problem #1.
Homework #3, Due Wednesday, September 16
Sec. 1.5, #3(f), #5(a), #7(c), #10; Sec. 1.6 #4(g), #6(f); Sec. 1.7 #2(a),(b),(c), #4(c)
Reading Assignment #3, to be done prior to class on Wednesday, September 9
Read Sec. 1.5-1.7
Homework #2, Due Wednesday, September 9
Please do these problems.
Reading Assignment #2, to be done prior to class on Wednesday, September 9
Read Sec. 1.3-1.4
Homework #1, Due Wednesday, September 2
Sec. 1.1, #2(b)(d), #3(b)(c), #6(e)(g) #9(a)(b)(c), 11(f)(g)(i)(j)(k)
Reading Assignment #1, to be done prior to class on Wednesday, August 26
Read Sec. 1.1-1.2
Homework #0: Nothing to Turn In.
Learning to write proofs is difficult, and you will be challenged
in many ways throughout this course. Research has shown that the students that are the
most successful are the ones who have two qualities: Growth Mindset and
Grit. View, read, and watch the following resources on Growth Mindset
and Grit. Throughout the course, do your best to keep these ideas in mind as you encounter
difficult portions of the material.
- Growth Mindset is the belief that your ability to learn is not fixed, that
you become better at any subject with effort and practice, and that failure is not
permanent.
- Grit is the ability to stick with and pursue a goal over a long period of
time. This includes the ability to stay determined and motivated
despite experiences with failure or adversity.
Dates of Exams
Exam 1: Wednesday, September 23 in class.
Exam 2: Wednesday, October 28 in class.
Final: Monday, December 14, 5--8PM in our usual classroom.