Class times: Mon + Wed + Fri from 09:00–09:50 AM [Alpine 212]
Book: An Inquiry-Based Approach to Abstract Algebra by D.C. Ernst (the book is free and open source)
Syllabus: Syllabus for Math 110A
Instructor: Dr. Joshua Wiscons (he/him)
Email: joshua.wiscons@csus.edu
Office: Brighton Hall (BRH) Room 144
Student office hours:
- In person: Monday 2–3 PM and Wednesday 2–3 PM [Brighton 144]
- Virtual: Thursday 1–2 PM [only via Zoom]
- Also by appointment. Just send me an email.
Teaching Assistant: Emma Breck (she/her)
Email: erbreck@csus.edu
Office hours: Tuesday from 3:00–4:30 PM [Brighton 118]
Daily Homework
Writing Assignments
Course Log
[02.16.26] - Monday
| What we covered: Lot’s more group tables today: \(D_4\), \(S_3\), \(S_2\), \(V_4\). As we talked through them, we also started to take note of the key relations in some of these groups. For example, in \(R_4\) the main relation is just that \(r^4 = e\); whereas in \(D_4\), we have \(r^4 = e\) and \(s^2 = e\) together with \(srs = r^{-1}\) describing the interaction of the two generators. In \(S_3\), we have \(s_1^2 = e\), \(s_2^2 = e\) and \(s_1s_2s_1 = s_2s_1s_2\). We also worked through a proof that each element of a group appears exactly once in each row and each column in any group table for the group. Great day! |
| Due next class meeting: HW10. |
Week 3
[02.13.26] - Friday
| What we covered: Continued with generating sets today, and saw \(D_3 = \langle s, s' \rangle\), \(S_3 = \langle s_1, s_2 \rangle\), and \(\mathbb{Z} = \langle 1 \rangle = \langle -1 \rangle\) (the last of which generated—pun intended—a good discussion on the subtleties of how we generate groups). We finished by constructing the group table of \(R_4\). Didn’t get to everything today, so we’ll start with the tables for \(D_4\) and \(S_3\) on Monday. Happy weekend |
| Due next class meeting: HW09. |
[02.11.26] - Wednesday
| What we covered: Covered a lot of ground today. We start with several more theorems: inverses of inverses, inverses of products, and when \((ab)^2 = a^2b^2\). We also got working on generating sets, and saw—among other things—that \(R_4 = \langle r \rangle\) (so \(R_4\) is cyclic) and \(D_3 = \langle r,s \rangle\). Great day! |
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| Due next class meeting: HW08. |
[02.09.26] - Monday
| What we covered: Wrapped up our work (for now) on building examples and nonexamples of groups, and also saw a couple more theorems: cancellation and uniqueness of inverses. We’re still catching up with all of the past problems, but we should get there next time. Thanks all! |
| Due next class meeting: HW07. |
Week 2
[02.06.26] - Friday
| What we covered: Continued looking at examples and nonexamples of groups. Adding to the list of examples, we have \((D_3,\circ)\) and \((\mathbb{Z},+)\); nonexamples include \((\mathbb{N},+)\) and \((\mathbb{Z},\cdot)\). We also talked through our first proof, showing that there is a unique identity element. Thanks for a fun day, and happy Friday!! |
| Due next class meeting: HW06. |
[02.04.26] - Wednesday
| What we covered: Looked at another problem about commutativity and associativity of binary operations, this time presented as a table. We then saw our first problem proving that something was a group: $R_4$ together with the operation of function composition. We talked through identifying the identity element as well as the inverse of each element. We didn’t get to the rest of the problems today, but we’ll pick up there next time. Another great day–thanks! |
| Due next class meeting: HW05. |
[02.02.26] - Monday
| What we covered: Discussed more about binary operations today, and met two more collections of symmetries: $D_4$, and $S_3$. We also explored the properties of commutativity and associativity. Thanks for another fun day, and many thanks to all of the presenters! |
| Due next class meeting: HW04. |
Week 1
[01.30.26] - Friday
| What we covered: We finished Section 2.1 by confirming that we could solve all Spinpossible boards using a sequence of compositions of spins, and we also briefly explored the idea of generating sets. Then got started on Section 2.2 by looking at the rotational symmetries of a square and all symmetries (rotations and reflections) of an equilateral triangle. Thanks all…with extra thanks to all the presenters today! |
| Due next class meeting: HW03. Try to build community to collaborate on these problems, but also please avoid using outside resources to solve them. (More info in the syllabus.) |
[01.28.26] - Wednesday
| What we covered: We played a little Spinpossible together and then worked through the beginning of Section 2.1. We computed the number of Spinpossible boards (thanks PV!), found various relations among the net actions (like $s_{12}s_{23}s_{12}=s_{23}s_{12}s_{23}$), and asked many questions. Thanks for a great day! |
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| Due next class meeting: Please work on HW02. You will not be graded on this assignment either, but we will talk about it in class again. |
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[01.26.26] - Monday
| What we covered: First Day! We started with a quick check in and talked a bit what we want out of a university education and this class. We also talked through the syllabus and the plan for the semester ahead. Looking forward to Wednesday! |
| Due next class meeting: Please work on HW01. You will not be graded on this first assignment, but we will talk about it in class. Also, if you couldn’t make it to class on Monday, please read over the syllabus. |