Math 235 - Foundations of Mathematical Proof
Spring 2025 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 FOUR IS BELOW. *****
- Preliminary For Wednesday, Feb. 12, 2025 - Biconditionals: Two-Part Proof
- Study your notes and Discussion/Participation #4.
- 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, Feb. 14, by 4pm.
- Exam #1 is NEXT Friday, Feb. 21.
- Nothing else will be due NEXT week because of the exam.
- Confirmed For Monday, Feb. 10, 2025 - Proof by CONTRADICTION (XX) continued
- Study your notes and Discussion/Participation #3.
- 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 #4 is due FRIDAY, Feb. 14, by 4pm.
- Exam #1 is NEXT Friday, Feb. 21.
- The Topics List will be released later this week.
***** WEEK THREE IS BELOW. *****
- Confirmed For Friday, Feb. 7, 2025 - 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, Feb. 14, by 4pm.
- Confirmed For Wednesday, Feb. 5, 2025 - Proof by Contrapositive (ctp)
- Study your notes and Discussion/Participation #2
- 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, Feb. 7, by 4pm.
- Confirmed For Monday, Feb. 3, 2025 - Proof by "Or Conclusion" style
- Study your notes.
- Read/reread:
- Review "without loss of generality" (you need it on HW #3):
- 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, Feb. 7, by 4pm.
***** WEEK TWO IS BELOW. *****
- Confirmed For Friday, Jan. 31, 2025 - Proof by Cases (Wrap-Up)
- Study your notes.
- Read/reread supporting info from Wednesday.
- DP 1 score is for work/questions during work time today.
- HW #2 is due by 4pm TODAY.
- HW #3 is due by 4pm next Friday, Feb. 7.
- Confirmed For Wednesay, Jan. 29, 2025 - More Proof by Cases
- Study your notes.
- Read/reread:
- Section 1.4: "When either P or Q is a compound proposition..." in mid-p.36 through the end of the section
- Remember: 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
- HW #2 is due by 4pm this FRIDAY, Jan. 31, also in my office or box. (You can do all but #4 now.)
- For class FRIDAY: Prepare for Discussion/Participation Score #1:
- DP scores are worth 3/3 if you contribute, right or wrong.
- We'll use some of Friday's class time to complete HW #2.
- I will decide by then whether Problem #4 is also something we work on, or if it will be pushed OFF of HW #2.
- Confirmed For Monday, Jan. 27, 2025 - Proof by Cases
- Study your notes.
- Try to finish our 2nd proof on your own, to go over on Wednesday.
- If you've not already done so, read the Syllabus completely and keep the printed copy someplace handy.
- Read:
- Appendix II. Number Systems: p.381 up TO "Complex Numbers" on p.383
- Our new definition, "divides," is here. Master it and all its variations.
- There's some useful Discrete Math review here, to0.
- Section 1.4: Bottom two lines on p.33 ("You'll find that...") through end of FIRST proof on p.38
- 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.
- The page 37 proof is an example of "hidden" cases: the word "OR" didn't appear in the Proposition itself.
- HW #1 is due by 4pm TODAY in my office or VSC 200 mailbox.
- HW #2 is due by 4pm this FRIDAY, Jan. 31, also in my office or box.
- You are now equipped to tackle everything except #3(c) and #4.
- Reminder: My Student Hours are MTWF 10:30-11:30am (not Thurs.) and F 2-4pm, and also by capture.
***** WEEK ONE IS BELOW. *****
- Confirmed From Friday, Jan. 24, 2025 - 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 (also posted as PDF in D2L reading Content)
- Xeroxed handout "Some Mathematical Conventions" (also posted in D2L reading Content)
- HW #1 is still due Monday.
- HW #2 is due Friday, Jan. 31, by 4pm in my office or office mailbox.
- HW is regularly due on Friday afternoons for this course.
- Remember always to leave lots of room for my written feedback.
- I prefer that you submit a physical copy, but in unusual circumstances, we can arrange an alternative submission.
- You are also welcome to give me your physical HW at class-time.
- Confirmed From Wednesday, Jan. 22, 2025 - Course Intro, Review of Logic
- Study your notes and read the Syllabus.
- Review as needed from:
- Your relevant notes and text from Discrete Math
- There are excerpts from the Fall 2024 Discrete Math text in D2L Content.
- Sections 1.1-1.3 in THIS SEMESTER's text (pp.1-28)
- ESPECIALLY the middle of p.14 in our text, covering "only if," trailing "if," etc.
- HW #1 is due MONDAY, Jan. 28, by 4pm.
- Always leave lots of room for my written feedback on HWs for this course.
- 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, Jan. 20, 2025 - MLK Day
Dr. J. Lyn Miller, Mathematics and Statistics, Slippery Rock University