General Information
Course Syllabus: Syllabus for Math 110B
Class times: Mon + Wed + Fri from 09:00–09:50 AM [Alpine 232]
Instructor: Dr. Joshua Wiscons (he/him/his)
Email: joshua.wiscons@csus.edu
Office: Brighton Hall (BRH) Room 144
Student office hours:
- In person: Monday from 3:00–4:00 PM + Wednesday from 12:30–1:30 PM [Brighton 144]
- Virtual: Thursday 1–2 PM [only via Zoom]
- Also by appointment. Just send me an email.
Daily Homework
Writing Assignments
Course Log
Week 5
[10.02.26] - Friday
| What we covered: One quick problem about units in matrix rings and then moved on to polynomial rings. |
| Due next class meeting: Please look over and try some of the initial problems in HW14, but you will not turn it in. Instead, I will discuss the problems over the next two class meetings. Try to use the extra time to start preparing for the exam. |
[09.30.26] - Wednesday
| What we covered: The main focus was on units and zero divisors in various rings. Among other things, we looked at \(\mathbb{Z}_{20}\) as well as matrix rings. |
| Due next class meeting: HW13 |
[09.28.26] - Monday
| What we covered: Started on rings today, mostly collecting examples of rings with/without various properties like commutativity, being a division ring, and having zero divisors. |
| Due next class meeting: HW12 |
Week 4
[09.25.26] - Friday
| What we covered: Wrapped up Chapter 4 today! The definitions of ‘radical extensions’ and polynomials being ‘solvable by radicals’ are quite technical, but it seems like folks are getting pretty good with them. We have now seen various examples of polynomials that are solvable by radicals like $x^4+2x^2+5$, $x^3-2$, $x^n-1$, and $x^6-3x^3-1$, and now—for the rest of the course—our goal will be to find one that is not. To do this, we need to explore polynomials in more depth, and this leads us into the topic of rings. |
| Due next class meeting: HW11 |
[09.23.26] - Wednesday
| What we covered: Looked at radical extensions today and finally made it to our formal definition of a polynomial being solvable by radicals. |
| Due next class meeting: HW10 |
[09.21.26] - Monday
| What we covered: More on generating subfields today along with practice arranging various subfields into pictures and lattices. |
| Due next class meeting: HW09 |
Week 3
[09.18.26] - Friday
| What we covered: Spent most of the time getting caught up on problems from last time, and then chatted a bit about generating subfields. We ended by showing that \(\mathbb{Q}(i) = \{a+bi \mid a,b \in \mathbb{Q}\}\). |
| Due next class meeting: HW08 |
[09.16.26] - Wednesday
| What we covered: Saw even more examples and nonexamples of fields, mostly in the context of searching for subfields of \(\mathbb{C}\). Got lots of work on the board but had to save most of the presentations for next time. Sorry about that! |
| Due next class meeting: HW07 |
[09.14.26] - Monday
| What we covered: Looked at more examples of fields (including the finite fields \(\mathbb{F}_4\) and \(\mathbb{Z}_5\)) as well as some nonexamples (such as \(\mathbb{Z}\), \(\mathbb{H}\), and \(\mathbb{Z}_6\)). We also started proving some basic properties of fields. |
| Due next class meeting: HW06 |
Week 2
[09.11.26] - Friday
| What we covered: Explored some structures that were similar to the complex numbers. We first looked at the quaternions, noticing that we could add, subtract, multiply, and even divide with all the familiar properties except that multiplication was not commutative. Second, we looked at the subset \(S = \{a+b\sqrt{5}\mid a,b\in \mathbb{Q}\}\) of \(\mathbb{R}\), noticing again that we could add, subtract, multiply, and divide, this time with truly all the familiar properties. |
| Due next class meeting: HW05 |
[09.09.26] - Wednesday
| What we covered: Took a close look at roots of unity, proving properties about them and counting the number of nth roots of unity. We then used our results to write out all complex roots of polynomials of the form \(x^n -a\). |
| Due next class meeting: HW04 |
Week 1
[09.04.26] - Friday
| What we covered: Spent a little more time exploring the idea of a polynomial being ‘solvable by radicals’ and then got started on complex numbers. We (re)learned some of the basics of complex numbers and then got started on roots of unity. Thanks for a great first week you all! Enjoy the long weekend! |
| Due next class meeting: HW03 |
[09.02.26] - Wednesday
| What we covered: Got started on Chapter 2 today looking at roots of polynomials and how we express them—this is the background motivation for all of our work this semester. Thanks to everyone for a fun first real day of class, especially to all those who presented work on the board! |
| Due next class meeting: Please work on: HW02. You will not be graded on this assignment, but we will talk about it in class. |
[08.31.26] - Monday
| What we covered: First day! Mostly just introductions and the syllabus today, but so great to see everyone again! |
| Due next class meeting (09/02): Please work on: HW01. You will not be graded on this first assignment, but we will talk about it in class. |