Math 235 - Foundations of Mathematical Proof
Fall 2024 Daily Assignments and Tasks
- My teaching style is very adaptive, so I only post class assignments and tasks as we become ready to cover that material.
- These are labeled Preliminary before class.
- AFTER class, I adjust the list to accommodate for any flexing we did DURING class that day, and mark the listing Confirmed.
-
Listings go in order of most RECENT date on top.
***** WEEK FIVE IS BELOW. *****
- CONFIRMED For Monday, Sept. 23, 2024 - Direct Proof of "For all"
- Study your notes.
- Read/:
- "Universal Conditional" excerpt from Epp (distributed in class, aslo in D2L Content)
- Section 1.6 pp.51 through end of top paragraph on p.53
- Exam #1 is in class Friday, Sept. 27.
- The link opens the PDF Topics List/Objectives List.
- There is no HW due until after the exam.
***** WEEK FOUR IS BELOW. *****
- CONFIRMED From Friday, Sept. 20, 2024 - Proof Analysis and Launches
- Study your notes, Discussion/Participation #4, and Activity: Proof Launches.
- Solutions to DP #4 will be uploaded to D2L Content over the weekend.
- We will discuss the Activity on Monday, and solutions will then be uploaded to D2L as well.
- There is no new reading.
- HW #4 is due by 4pm today.
- HW #5 will not be due until the week after Exam #1. (I will distribute it at the exam.)
- Exam #1 is next Friday, Sept. 27. (Link opens Topics List)
- CONFIRMED From Wednesday, Sept. 18, 2024 - Biconditionals: Chain-style Proof
- Study your notes.
- Read Section 1.5 bottom of p.46 (immediately under the end of the Proof) and top Example and Proof on p.47.
- HW #4 is due FRIDAY, Sept. 20, by 4pm.
- CONFIRMED For Monday, Sept. 16, 2024 - Biconditionals: Two-Part Proof
- Study your notes and the in-class Activity: Group Biconditional Proofs.
- Read:
- Section 1.5: Beginning with "Proofs of biconditional sentences often..." near bottom p.45 through end of Proof on p.46
- The Proof's (i) is the => direction, while (ii) is the <= direction.
- Label your own proofs with the arrow notation.
- Section 1.7: "P if and only if Q" on p.70
- HW #4 is due FRIDAY, Sept. 20, by 4pm. (Refresh the page to see the full handout, not just Part A.)
***** WEEK THREE IS BELOW. *****
- CONFIRMED From Friday, Sept. 13, 2024 - Proof by CONTRADICTION (XX)
- Study your notes.
- Read/reread:
- Section 1.5: p.43
- Section 1.5: p.45 ONLY the Example and Proof in the top half of the page
- Section 1.5: BOTTOM Example on p.47 through the Proof by Contradiction at the top of p.48
- Section 1.7: "Any statement - Try a proof by contradiction" bottom p.69 and top 3 lines on p.70
- HW #3 is due TODAY by 4pm.
- HW #4 is due FRIDAY, Sept. 20, by 4pm.
- CONFIRMED From Wednesday, Sept. 11, 2024 - Proof by Contrapositive
- Study your notes.
- Read:
- Section 1.5: p.42 through top 4 lines on p.43
- Section 1.5: p.47 BOTTOM Example, Direct Proof, Proof by Ctp
- Section 1.7: "If P, then Q - Try a proof by contraposition" from bottom p.68 through end of example and proof atop p.69
- Notice the CORRECT distinction between function variable x and proof variable t here!
- They do use some "previous results" in the sentence "Because t^2+t is even..." - Beware! I would require the DEFINITION of even for us!
- HW #3 is due FRIDAY, Sept. 13, by 4pm.
- CONFIRMED From Monday, Sept. 9, 2024 - Proof by Cases, Proof by "Or Conclusion" style
- Study your notes.
- Read/reread:
- Supporting reading from Friday, Aug. 30-Friday, Sept 6
- About "without loss of generality":
- Section 1.4: p.38, starting with "Finally, there are proofs by exhaustion..."
- Section 1.7: p.69
"'If P, then Q' - Try a proof by cases" paragraph, example, and proof
- About "or conclusion style":
- Section 1.4: p.36 paragraph near bottom that begins "To prove a conditional sentence whose consequent is a disjunction..."
- Section 1.7: p.70 "If P, then Q1 v Q2" paragraph, example, and proof
- BEWARE: the authors use x,y as both proof variables AND function variables here.
- That's NOT a good idea at our level of study!
- HW #3 is due FRIDAY, Sept. 13, by 4pm.
***** WEEK TWO IS BELOW. *****
- CONFIRMED For Friday, Sept. 6, 2024 - Proof by Cases
- Study your notes.
- Read/reread:
- Section 1.4: mid p.36 ("When either P or Q...") through end of section
- CAUTION: DO NOT USE "if" intros for cases, as the proof on p.37 does.
- INSTEAD, use "suppose" language like the 1st proof on p. 38.
- Section 1.8: p.76 only, and contrast it to ...
- Xeroxed supplement from Fraleigh (posted in D2L Content)
- HW #3 is due FRIDAY, Sept. 13, by 4pm.
- For MONDAY: Prepare to briefly discuss Problem #11, p.41, in class.
- CONFIRMED For Wednesday, Sept. 4, 2024 - Direct Proof
- Study your notes.
- Read/reread supporting reading from Friday, Aug. 30.
- Text: Section 1.4: pp.34- end of SECOND proof on p.36
- HW #2, Part A - DUE Friday, Sept. 6, by 4pm; OMIT Problem #1(e).
- Remember always to leave lots of room for my written feedback .
- You may put your physical copy in my Department mailbox, or bring it to my office.
- In unusual circumstances, I can accept a PDF-format as ONE file sent via email, but I prefer the physical original.
- You are also welcome to give me your physical HW at class-time.
- Monday, Sept. 2, 2024 - Labor Day
- There are no SRU classes today due to the Federal holiday.
***** WEEK ONE IS BELOW. *****
- Confirmed From Friday, Aug. 30, 2024 - What is proof?, Direct Proof
- Study your notes.
- Read:
- Text: Preface to the Student: pp.xii-xiv
- Text: Section 1.4: pp.28-33
- Omit the 2nd example on p.31.
- Beware typo: In the 1st example on p.31, we should see x->2, NOT x->0.
- Text: pp.64-66
- Text: Section 1.7: p.67 through top paragraph on p.68
- Xeroxed excerpt from Epp (scanned as PDF in D2L reading Content)
- Xeroxed handout "Some Mathematical Conventions" (also posted in D2L reading Content)
- HW #2, Part A - DUE DATE TO BE DECIDED NEXT CLASS - for now, do attempt #1-2
- Remember always to leave lots of room for my written feedback .
- You may put your physical copy in my Department mailbox, or bring it to my office.
- In unusual circumstances, I can accept a PDF-format as ONE file sent via email, but I prefer the physical original.
- You are also welcome to give me your physical HW at class-time.
- Confirmed For Wednesday, Aug. 28, 2024 - Review of Logic
(continued)
- Study your notes.
- Review as needed from:
- Your relevant notes and text from Discrete Math
- I've put some excerpts from last semester's text in D2L Content.
- Sections 1.1-1.3 in our text (pp.1-27)
- ESPECIALLY the middle of p.14 in our text
- HW #1 is due FRIDAY, Aug. 30, by 4pm.
- Remember always to leave lots of room for my written feedback .
- You may put your physical copy in my Department mailbox, or bring it to my office.
- In unusual circumstances, I can accept a PDF-format as ONE file sent via email, but I prefer the physical original.
- You are also welcome to give me your physical HW at class-time.
- Confirmed For Monday, Aug. 26, 2024 - Course Intro, Review of Logic
- Study your notes.
- Read the syllabus.
- Review as needed from:
- Your relevant notes and text from Discrete Math
- I've put some excerpts from last semester's text in D2L Content.
- Sections 1.1-1.3 in our text (pp.1-27)
- ESPECIALLY the middle of p.14 in our text
- HW #1 is due FRIDAY, Aug. 30, by 4pm.
- Remember always to leave lots of room for my written feedback .
- You may put your physical copy in my Department mailbox, or bring it to my office.
- In unusual circumstances, I can accept a PDF-format as ONE file sent via email, but I prefer the physical original.
- You are also welcome to give me your physical HW at class-time.
Dr. J. Lyn Miller, Mathematics and Statistics, Slippery Rock University