note to yourself of due date |
SG HW § |
ER HW Variant of |
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Homework from Ch. 1 and Ch. 2. |
Wed 2/22
| 3.1 | |
Study Guide Homework for this section.
This section will be helpful for Exam 1.
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Mon 3/13
| 3.2 | |
Study Guide Homework for this section.
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| 5.0 |
Read the handout
§5.0: Set Theory Transition, which contains ideas needed for the upcoming ER's
variants of 5.1.8, 5.5.2, 5.5.3. Note the handout applies ideas covered thus far in class
to tranform your high school basic set theory knowledge to a more advanced level.
There really is no new ideas but rather just a different viewpoint; thus, it will not be covered in class. Please come see the professor is you have questions.
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Wed 3/15
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Class lectures over the problems due Wed. 3/15 were completed before Exam 1.
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Handout needed for the below Ch5 problems:
§5.0: Set Theory Transition.
| | 5.1.8 |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 5.5.2 |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 5.5.3 |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.1.3C |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.1.3H |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
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Mon 3/20
| 3.3 | |
Study Guide Homework for this section.
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| 3.1.6B |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.1.6C |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.1.14 |
Will not be graded. Do the Redo, which is due 3/27.
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
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Wed 3/22
| | 3.1.19D |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
|
| 3.2.19A |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
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Mon 3/27
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Review the Intermediate value theorem (from calculus).
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| 3.1.9B |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
|
| 3.1.21A |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.1.14 Redo |
Most students struggled with this problem so a hint is added. Let's (everyone) do a try again.
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| 3.2.1CD |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| 3.4 | |
Study Guide Homework for this section.
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Wed 3/29
| | 3.2.19B |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
|
| 3.2.7 |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| 3.5 | |
Study Guide Homework for this section.
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Mon 4/3
| | 3.2.13 |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
|
| 3.2.14B |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.2.14C |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.2.16 |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.3.0 |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.3.6A |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.3.6B |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.3.6C |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
|
Wed 4/5
| | 3.3.20B |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
|
| 3.3.8A |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.3.20A |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.3.20C |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.4.5A |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.4.8 |
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
|
Mon 4/10
| 3.6 | |
Study Guide Homework for this section
Review of Proof Methods, which will be an excellent review
for the exam. Think of it as getting points for studying for the exam.
|
3.7 | |
Take advantage of this Chapter Summary. Nothing to hand in.
| | 3.4.13A |
Be ready to discuss this ER, having the evalation of proof (e.g. T1) done. Nothing to hand in.
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.5.22A |
Be ready to discuss this ER, having the evalation of proof (e.g. T1) done. Nothing to hand in.
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
| | 3.5.22B |
Be ready to discuss this ER, having the evalation of proof (e.g. T1) done. Nothing to hand in.
For the variant/hints, see the
PDF file. To LaTex the ER, load this
LaTex file to Overleaf.
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Exam 2 is Wednesday April 12.
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Exam 2 cover material (from class and lectures) from §3.1-3.5.
Sections 3.6 and 3.7 are helpful review sections.
So basically Exam 2 covers Ch. 3.
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See
Study Suggestions and Details for Exam 2, which included
- dates,
- material covered,
- sample formatting of proof problems,
- highly recommended Practice Proof Problems (along with hints/solutions).
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Exam2 Practice Problems
the sooner the better
not to turn in |
| §3.6
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Section 3.6 is called appropriately Review of Proof Methods.
In each section of Ch. 3, you learned some methods of proofs.
Now the book throws a whole bunch of exercises at are you and
asks you to proof them (but does not indicate which Proof Method
to use). So you have to choice which method to use and then execute the
method properly. Sometimes several methods work but a certain method
is much easier than the other methods. Sometimes only one method is
do-able given what you know thus far in you math career.
§3.6 is a excellent source of exam problems.
You should be able to do the following problems when
you walk into Exam 2 (and also be able to write each one symbolically
but you do not have to hand them in as of now):
3.6.1 ; 3.6.3 ; 3.6.4 ; 3.6.5 ; 3.6.7 ; 3.6.12 .
The class is encouraged to discuss these problems on Pizza
(under the exam folder).
Please post your thoughts/questions on problems to the entire class
(rather than just to the instructor).
Since these problems are not to hand in, feel free to post your solutions
(to the entire class) on Piazza
(can just post a cell phone picture or scanned pdf file - just use "insert" as a "file",
if needed see the "piazza folder" on how to do this).
Last minute craming for exams is discouraged.
Prof. Girardi will happily answer questions/comments/posts which are posted on Piazza
before 24 hours before the exam. However, the class can continue using Piazza until the start of the exam if they so want.
Hints:
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3.6.1. Symbolically looks like
(∀ x∈ ℝ) (∀ y∈ ℝ)
[ P(x,y) ⇒ Q(x,y) ] where P(x,y) and Q(x,y)
are open sentences (they will be inequalities here) in variables x and y.
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3.6.3. Each one is true.
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3.6.5. You may use Thm 3.20 (pg. 124) which say is irrational.
Try cases. Consider the number
square root of 2 raised to the power of the square root of 2, i.e,
,
which is
either rational or irrational (who knows, but who cares since ...)
Case 1: The 22 is rational.
Case 2: The 22 is irrational.
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3.6.7. Try proof by contrapositive. So assume there exists
n∈ ℕ that is a solution to the cubic.
Then use with book`s hint to help you factor
n3 + 13.
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3.6.12. Parts a,b,d are true. Part c is false.
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