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Due
Date |
Homework
from Monday/ Wednesday lectures |
Preparation
for Certification Exam |
Class
Projects |
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1/18 |
p.
203: 19(a-c) p.
214: 16, 18 p.
243: 2, 3, 6, 9, 10, 19(a), 20, 31 |
For this and all future reviews, you can choose which 5 exercises to do. Please submit a total of 5 exercises only; the grader will be instructed to only grade the first 5 solutions that are submitted. At the top of your write-up, you must also write a statement attesting that you have at least thought about all assigned problems. Points will be deducted if you do not write this statement. (This does not mean that you solved all of the problems --- just that you gave some thought about how to solve every problem.) |
Be
ready to present your responses to Questions 1-9. All presentations will be peer-graded. |
The
class project concerns various ideas that could
be used to engage students with topics in the secondary mathematics
curriculum. Topics
will be assigned on a first-come, first-served basis. You are welcome to sign
up by e-mail, but please suggest about 5-10 different topics (in priority
order) in case your first choice is no longer available. Be
sure to title your file in the form John_Doe_15.docx, as indicated in the
instructions. See some exemplary
projects of the past for more about how your work should be submitted. |
|
1/25 |
p. 244: 22, 24, 32, 33, 37, 43, 48 Hints: #32: Try x = 10p, where p is a prime greater than or equal to
7. #33: It’s false. Find a
counterexample. #48: Argue by contradiction.
Suppose that p is a prime that
divides bd. Show that p can’t divide ad+bc. FYI: This theorem is a follow-up
to p. 203 19(a-c) from last week. |
For
this week and the rest of the semester, be ready to answer any of the next
few questions. |
Part
1 (Pre-Algebra and Probability/Statistics) is due. If you are available, I encourage you to attend the talk
“Mathematics and Voting” by Dr. Bridget
Tenner from DePaul University. This will be held on Tuesday, January 29 from
5-6 in GAB 105. |
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|
2/1 |
p. 244: 25, 30, 31, 36(a), 51 p. 251: 3, 4, 5, 6, 10, 15, 16 Note: I have resassigned p. 244, #31, as I realized that I should not
have assigned that problem in the first homework assignment. Naturally, you
can rewrite your work if you think you got this correct the first time. |
|
For
the next part of the class project, you may select any topic from Part 2 or
any unselected topic from the Probability/Statistics section (topics 38-59 of
Part 1). |
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2/8 |
p.
253: 2, 4, 6, 9 p.
254: Let’s Go 4 p.
263: 10, 31 Hint for
p. 253 #9: Remember that to show a proposition is false, you only
need one counterexample. Problem 4.1: Here's a popular magic
trick for children: (a) Take any 3-digit number in
which the first and last digits differ by 2 or more. (b) Reverse the number, and
subtract the smaller of the two numbers from the larger (e.g. 782-287=495). (c) Then reverse the result and
add (thus 495+594=1089). Prove
that you always end up with 1089. Problem 4.2: (a) Here's a second magic trick. Cut out the six numbered cards, read the
instructions, and perform this trick (either by yourself or for a friend).
Write a statement attesting that you actually did do this. (b) Use binary numbers to
explain why this magic trick works. Hint:
Find the binary representation of the first few numbers on each of the six
cards. Do you see a pattern? |
Note:
For Problem 4.1, the ray from the origin intersects the unit circle at the
point (0.8, 0.6). |
|
Part
2 (Algebra I and Algebra II) is due. |
|
2/15 |
None. EXAM #1 The
review questions should help prepare you for the
exam. There are also solutions
for the review questions; I encourage you to watch these videos only
after attempting the review questions for yourself. Also,
I don’t claim infallibility. If you think I made an inadvertent mistake
while recording these videos, please let me know so I can take a look at it. |
None because of exam. |
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2/22 |
p.
254: Let's Go 3 p.
263: 18, 19, 20(a-d), 23, 24, 33(a) |
|
You are
invited to the talk Teaching with GeoGebra, which will be given Friday, February 22 from 12-1 in GAB 201.
I hope that you will find this helpful for your future lesson-planning. |
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|
3/1 |
p.
229: 2, 3(cd), 5, 8 p.
265: 21, 22, 26, 27, 28 |
Break from presentations.
All students will meet in GAB 317 on Friday, March 1. |
Part 3 (Geometry)
is due. If
you haven't selected a question from all five areas yet, I encourage you to
select questions from the remaining area(s) for this week's submission. |
|
|
3/8 |
p.
230: 6, 7 p.
347: 2, 5, 9(a) p.
353: 4, 5, 10 Notes: For p. 230 #6 and #7, the expressions were given in class
and in the class notes. You need to prove that these expressions are true.
Don't just state them without proof. Regarding p. 347 #2 and #5: We will not cover Section 12.1
in class. So I just expect you to (1) experiment with a graphing calculator
until you find cubic polynomials that meet the given criteria, and then (2)
once you have your polynomial, then you should explain why it meets the given
criteria. You may need to use factoring and/or calculus to produce an
adequate explanation. (It is possible to construct such polynomials more
systematically, and you are welcome to try to find out how to do these
problems without blindly guessing.) Hint for p. 353 #5: Start with f(x) = x2 – p, and argue by contradiction. For p. 353 #10, find the both the possible number of
positive roots and the possible number of negative roots. |
Break from presentations. All students will meet in GAB 317 on
Friday, March 8. |
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3/15 |
SPRING BREAK |
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|
3/22 |
None. EXAM #2 The
review questions should help prepare you for the
exam. There are also solutions
for the review questions; I encourage you to watch these videos only
after attempting the review questions for yourself. |
None
because of exam. |
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|
|
3/29 |
DUE DATE CHANGED TO MONDAY,
APRIL 1 p.
347: 6, 8(ab), 10 p.
353: 1, 2 p.
365: 2, 3(a), 7(bcde) Notes: · For p. 347
#8, the local extrema and point of inflection are
found by solving f '(x) = 0 and f ''(x) = 0, respectively. Then verify that the x-coordinate of the point of inflection is the average of the x-coordinates of the two local extrema. · For p. 347
#10, be sure to give a short proof as well as the answer. · For p. 365
#2(c), it may also be helpful to also graph the polynomial (with a
calculator) on the interval [-2,3]. · Hint for p.
366 #7(e): (1-a)(1+a+a2)
= 1-a3. |
DUE DATE CHANGED TO MONDAY,
APRIL 1 |
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4/5 |
p.
266: Your Turn 34 p.
269: 1, 3(bc), 4 p.
278: 2, 3, 11, 12 p.
280: 1(a-d) Notes: For p. 269 #4, let the following guide your thinking: You
can easily check that x = 2 is a
root of f(x) = x3 + 4x2 – 2x – 20
and that x = -2 is a root of g(x)
= -x3 + 4x2 + 2x – 20. So, if you know that f(a) = 0, is there a way to modify f and create a new polynomial g so that g(-a) = 0? Once you see
how to do this, then you’ll need to prove that your idea actually
works. |
Due
to a conflict, the presentations will happen on Wednesday, April 3 in GAB
317. We will start with Question
#48. Nobody
should go to Bio A111. On
Friday, April 5, we will have a regular lecture in GAB 317. |
Part 4 (Precalculus) is due. Remember that you can schedule a make-up Q&A session if you earned a 0 (or a low grade) on a prior Friday presentation. You will need to prepare answers for Questions 79-90 and will be asked to answer several of these questions. These sessions are made by appointment. |
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4/12 |
p.
284: 3, 13 p.
288: 1, 3, 12(ab) p.
291: 6, 16 p.
307: 1, 2, 5(ac) For p. 307 #5(c), ignore the
instruction that says "If a product is required within an exponentiation
problem, compute it via logarithms." |
All
students not in PBI will meet in GAB 317 on Friday, April 12. |
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|
4/19 |
None. EXAM #3 The review questions should help prepare you for the exam.
There are also solutions
for the review questions; I encourage you to watch these videos only
after attempting the review questions for yourself. |
None
because of exam. |
. |
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|
4/26 |
p. 129: 6, 8 p. 231: 15, 23(abde) p. 317: 6 p. 319: 5, 7(abd) p. 328: 4, 6,
8, 9 Notes: For
p. 231 #23(de), only answer the parts involving 1-i. For
p. 317 #6(b), you just need a value of h,
not the largest value of h that
meets the condition. ·For
p. 328 #6, be sure to consult Section 9.3.1 (pp. 281-283) before answering. |
All students will meet in GAB 317 on Friday, April 26. There will be no more Friday presentations. All students who have not presented 5 times should make an appointment with me for completing the presentations. Also, you can schedule a make-up Q&A session if needed (see note on 4/5). |
The SETE should now be available by logging into http://my.unt.edu You are
invited to my talk Verifying
Einstein’s Theory of General Relativity using First-Semester
Differential Equations, which will be given Friday, April 26 from 12-1 in
GAB 461. |
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|
Wednesday, 5/1 |
The
review questions should help prepare you for the
final. There are also solutions
for the review questions; I encourage you to watch these videos only
after attempting the review questions for yourself. Due
on 5/1: p.
334: 1, 2, 3, 4(b), 6(bc), 8 p.
337: 1 Please
remember to complete the SETE. |
Certification Review #15 due on 5/1 |
None
because of Reading Day. |
If
you missed class on Monday, April 29, be sure to
pick up a course survey from me. Completing the survey counts as a free 100
for both the book homework as well as the certification reviews. |