"Mathematics is, in its way, the poetry of logical ideas" - Albert Einstein
Class times: Mon + Wed + Fri from 12:00–12:50 PM [Brighton 214]
Book: Introduction to Proof via Inquiry-Based Learning, Spring 2025 version, by Dana C. Ernst. The book is free: pdf version or HTML version.
Syllabus: Syllabus for Math 108
Email: joshua.wiscons@csus.edu
Office: Brighton Hall (BRH) Room 144
Office hours:
Email: erbreck@csus.edu
Office hours: Thursday from 1–3 PM [Shasta 170]
| What we covered: 3.18, 3.19, 3.21(a), 3.23, 3.28. We started with several more problems on subsets, including a couple proofs. One thing that got highlighted was the benefit of translating statements about sets into precise logical sentences to better understand or manipulate them. The second proof also provided a great example of proving set equality by separately proving each set is contained in the other. We wrapped up with our first problem on power sets. More next time! |
| Due next class meeting: HW14 |
| What we covered: 2.91, 3.16, 3.17. Started with outlining 2.91, and then left it for folks to fill in for the next Writing Assignment. We then continued with set theory, looking at the basic operations of intersection, union, complementation, and set difference, but had to save 3.18 and 3.19 for next time. |
| Due next class meeting: HW13 |
| What we covered: 3.2, 3.3, 3.5, 3.7, 3.10. Got started on set theory today looking at set-builder notation and the concept of subsets. We didn’t have time for 2.91, which is an existence and uniqueness proof, but we’ll pick up there next time. |
| Due next class meeting: HW12 |
| What we covered: 2.78(a,c,f,g), 2.86(c,f), 2.87, 2.88. We started with a problem about negating more complex sentences. After that, we looked at proving/disproving sentences where we compared and contrasted the approach for universally quantified and existentially quantified statements. The next problem had us critically read a “proof” to spot an error, which was quite subtle, and the final problem was a proof by cases. And that mostly wraps up Chapter 2—on to set theory. |
| Due next class meeting: HW11 |
| What we covered: 2.70, 2.71, 2.72(a,b,c,d), 2.73, 2.77(a,b,j). We spent some more time translating back and forth between math with quantifiers and english, and then we worked on negating statements with quantifiers. Thanks to CL, AS$_2$, and ASC for presenting and to everyone else for helping out as we worked problems together! |
| Due next class meeting: HW10 |
| What we covered: 2.64, 2.66, 2.67, 2.68. Started working on translating back and forth between math with quantifiers and english. It’s going to take some time to get comfortable, but we had a good start today. More Wednesday! Thanks presenters: BL + MY + AS$_1$ + AM!! And sorry we didn’t make it to all the problems: 2.70, 2.71, 2.72(a,b) were delayed to next time. |
| Due next class meeting: HW09 |
| What we covered: 2.56, 2.57, 2.59, 2.61, 2.63. Two main topics today: more with proofs and getting started with quantifiers. The first proof problem was treated by contradiction, which gave us our first exposure to that technique. The second proof was a biconditional; one of the implications was done directly but the other gave us a second example of proof by contradiction. Proof by contradiction will likely take us a little while to get comfortable with, but today was a great start! The problems about qualifiers got us thinking about the effects of the order of the quatifiers when there are more than one and also about the similarities and differences in proving/disproving for all and there exists statements. Thanks presenters: AP, MH + SG, IY, KA, JT! And thanks all! |
| Due next class meeting: HW08 |
| What we covered: 2.46, 2.47, 2.50, 2.51, 2.52. After a couple of general problems on logic, we got to the main topic of the day: proof by contraposition. Next time we’ll pick up with proof by contradiction, proofs of biconditionals, and also get started on quantifiers. Todays presenters were: JL, VC, CL, JG, and AC. Thanks all!! |
| Due next class meeting: HW07 |
| What we covered: 2.32, 2.37, 2.38, 2.39, 2.40, 2.41. More about implications today, with a key result being that implications are logically equivalent to their contrapositive. Many thanks to the presenters: AS$_2$, AOH, BL, AM, EB, KA! Also, in addition to raising great questions, the audience is showing up strong with comments of support and appreciation (especially AP). It’s so great—keep them coming! |
| Due next class meeting: HW06 |
| What we covered: 2.23, 2.24, 2.26, 2.27, 2.28, 2.30. Started by discussing implications, and then transitioned to logical equivalence. We saw proofs of De Morgan’s laws and worked an example where we used them to negate some mathematics. We wrapped up with a proof of a logical equivalence about the relationship between implications and conjunctions/disjunctions. Thanks presenters: WL, BL, NB, JG, JT! |
| Due next class meeting: HW05 |
| What we covered: 2.15, 2.17, 2.19, 2.22. After wrapping a harder number theory proof, we got to work on propositional logic, looking at the definition of propositions as well as logical connectives and truth tables. More next time! Thanks to everyone, especially our presenters: KA, IY, AP, and MH! |
| Due next class meeting: HW04 |
| What we covered: 2.7, 2.11, 2.12, 2.13. Another fun day working through some number theory proofs (but have one to wrap up next time). Excellent presentations (thanks MY, SG, AC, SS!) and great comments from the audience. |
| Due next class meeting: HW03 |
| What we covered: 2.2, 2.3, 2.4. Great first real day of class! Had some time in groups, got the problems on the board, and had really good conversations about them. Many, many thanks to EB, CL, AS$_1$, SS, and BS sharing their work on Day 1—you all did awesome! And thanks to everyone for the great questions and supportive environment! |
| Due next class meeting: HW02 |
| What we covered: First day of class! Started with some brief introductions and then had a discussion about the role of a university education and what folks are hoping to get out of our class. Thanks for all of the participation you all! We ended by looking over the syllabus and talking about what the work will look like this year. Looking forward to Friday! |
| Due next class meeting (01/24): Please work on HW01. You will not be graded on this first assignment, but we will talk about it in class. |
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