Instructions and Guidelines	Exercise (ER) HW Instructions	Study Guide (SG) HW Instructions	How to turn in a collection of Progress Checks
	Evaluation of Proofs	Symbolically Write	Math Induction (PMI)
Latex Help:	Overleaf	Overleaf's help	Detexify
Resources:	PDF of Book	Study Guides has Focus Questions	WG1-WG14 with details List of WG1-WG14

note to yourself of due date	SG HW §	ER HW Variant of
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.
Mon 3/13	3.2		Study Guide Homework for this section.
		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.
Wed 3/15			Class lectures over the problems due Wed. 3/15 were completed before Exam 1.
			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.
Mon 3/20	3.3		Study Guide Homework for this section.
		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.
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.
Mon 3/27			Review the Intermediate value theorem (from calculus).
		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.
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.
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.
Exam 2 is Wednesday April 12.
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.
			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).
Exam2 Practice Problems       the sooner the better not to turn in		§3.6	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: 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. 3.6.3. Each one is true. 3.6.5. You may use Thm 3.20 (pg. 124) which say $\sqrt{2}$ is irrational. Try cases. Consider the number square root of 2 raised to the power of the square root of 2, i.e, $\sqrt{2}$ \sqrt{2}$ $$$, which is either rational or irrational (who knows, but who cares since ...) Case 1: The $\sqrt{2}$ \sqrt{2}$ $$$ is rational. Case 2: The $\sqrt{2}$ \sqrt{2}$ $$$ is irrational. 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. 3.6.12. Parts a,b,d are true. Part c is false.