TMATH 403 Spring 2026

Contact Information:

Instructor: Ruth Vanderpool

email: rvanderp@uw.edu

Social Hours: can be zoom if requested through my zoom link

Tuesdays 2:30-3:30 & Thursdays 12:30-1:30pm 

in the Teaching & Learning Quantitative space (SNO 2nd floor)

website

Office: MDS 303C (do not expect me there!!)

Class Time:  Tuesdays & Thursdays 10:10am to 12:10pm 

For class structure or content questions I have created the "Technical or Course Related Discussion Board" which I would encourage you to use instead of emailing me. Generally I'll check and post answers there more quickly than through email and would encourage others in the class to answer questions posted there as well.

Course Description:

This course continues abstract algebra by studying the theory of rings and fields, including ideals; homomorphisms; quotient rings; integral domains and fields of fractions; polynomial rings; vector spaces; field extensions; geometric constructions via straight-dege and compass; the classification of finite fields; unique factorization domains; and Euclidean domains. Prerequisite: minimum grade of 2.0 in TMath 402.

Course Objectives:

By the end of the course students should be able to:

derive and prove elementary results about rings and fields

construct ring homomorphisms and identify quotient rings

construct field extensions and explain the connection to straight-edge and compass constructions

construct examples that satisfy or do not satisfy certain algebraic criteria,

build complex mathematical arguments and proofs, and

clearly communicate technical and complex mathematical concepts in writing.

The course supports the following Mathematics Program Student Learning Objectives

comprehend, discover, and communicate common principles from algebra, geometry, and analysis

recognize, understand and also make his/her/their own mathematically rigorous arguments

interpret and present results to a technical audience both in writing and verbally, and

apply quantitative theory, modeling, or mathematical principals to other disciplines to solve problems. 

These objective relate to the UW Tacoma-wide objective: Student will acquire skills and familiarity with modes of inquiry and examination from diverse disciplinary perspectives, enabling them to access interpret, analyze, quantitatively reason, and synthesize information critically.

Rights of the Learner

As a student in this class, you have the right:

to be confused,

to make a mistake and to revise your thinking,

to speak, listen, and be heard, and

to enjoy doing mathematics.

Opportunities for Mastery: 

Daily Homework that provides feedback and support in a low stakes manner.

Up to three missing Daily Homework assignments excused from course percentages.

Existing token that allow for either a late Written Homework submission or regrade. 

Opportunities for additional presentations beyond those required so as to replace lowest presentation marks.

Required Items: 

Textbook (not yet published but shared by the author through Canvas):  Matthew Macauley, Visual Algebra Ch 8 (Previous chapters are available if needed: Ch 1, Ch 2, Ch 3, Ch 4, Ch 5, Ch 6)

Optional supplement material provided by author (freely available)

Optional supplement textbook (freely available & open-source): Ernst's IBL Abstract Algebra text

Optional supplement material (freely available & open-source): Thomas Judson, Abstract Algebra, Theory and Applications 

Calculators: Either scientific or graphing are welcome. Although no internet tools are allowed during exams, you are welcome to use Desmos Test Mode on a smart device if you have one. 

Grades:

The following weights are used to determine your total score in the course:

Content Weights for Course

Daily Homework Assignments | 20%
In Class Presentations | 20%
Formal Homework Assignments | 15%
Midterm | 20%
Final | 25%
Total | 100%

Your final percentage, LaTeX: x  will then be converted to the UW 4.0 scale by the piece-wise defined function

f(x)=4.0 if 90<x,

f(x)=.1x-5 if 57<=x<=90, or

f(x)=0 if x<57.

Typical Day:

10-15 min: Announcements & observations about materials collected and reviewed.

30 min: Presentation Prep-meet with your group members to go over problems responsible to present, compare work, hammer out understanding.  

15 to 65 min: Presentations & Class discussions. The class comes together and groups take turns facilitating presenting their work & answering questions on their assigned problems.  Each group will have two students called on, randomly by the instructor to present.  Make sure everyone is comfortable enough with the material to lead the class!

10 min: Determine which problem from Presentations will become part of WrittenHW.

Homework:

There are two kinds of homework:

Daily Homework:

The Daily Homework will have approximately 5 −8 new statements to parse, justify or contradict, and write up. This work will be collected from each student at the end of each class meeting and will be evaluated for evidence of productive struggle, NOT correctness.  Daily Homework will be graded using a ✓-system described below.

On the day that a Daily Homework is due, the majority of the class period will be devoted to students presenting some subset (maybe all) of the proofs/solutions that are due that day. At the end of each class session, students will submit their work for all of the proofs that were due that day.  Students are allowed (in fact, required!) to modify their written proofs in light of presentations made in class; however, you must do so in a different color. This will allow me to differentiate the work done in class versus the work you completed before class.  Note that in order to earn complete marks all problems must have been attempted before class, and either you participated in the class conversation or added edit marks on the Daily Homework.  

Rubric for Daily Homework

Grade | Criteria
✓+ (4 pts) | Exceeding. It need not be 100% complete but material brought to class is mostly complete & correct with good ideas consistent with class content for all problems. And important annotations have been added from today's discussions that fill in gaps.
✓ (3 pts)  | Meeting. Material brought to class have some problems complete & correct with good ideas consistent with the class present for other problems. All problems have some work but some have yet to be fully engaged with. 
✓- (2 pt)  | Emerging. Material brought to class has few problems complete & correct. Content inconsistent with the class appears. I acknowledge your work but there are some serious flaws. 
(1 pt) | Attending. Scarce materials brought to class before presentations.
0 |

You can miss up to 3 Daily Homework assignments without impacting your score but I would advise you minimize this as it adversely effects both your and your presentation group's learning! 

Formal Homework:

Due most every Friday by 8 pm will be 1-3 formally written proofs. Typically, these problems will come directly from the Daily Homework assigned the previous week. 

You are encouraged to type your submission (I recommend using (Overleaf) LaTeX; MSWord is OK) but it is not required. 

Each problem on the Writing Homework assignments is subject to the following rubric:

Rubric for Formal HW

Grade | Criteria
4 | Exceeding. All problems assigned are 100% complete, correct, typed, and easy for another undergraduate math major to read with all variables defined. Logic is clear, easy to follow, and aligned with the class. 
3 | Meeting. This is a good piece of work, yet there are some mathematical errors or writing improvements that need addressing.  All problems are written mostly completely, correctly and aligned with class content. If not typed, this is the highest attainable score.
2 | Emerging. There is some good intuition here, but there is at least one serious flaw or misaligned content.
1 | Work has been done on all problems assigned. I don't understand this, but I see that you have worked on it; come see me!
0 | I believe that you have not worked on this problem enough or you didn't submit any work.

COLLABORATION & AI POLICY:

Give credit to who or what you work with!! Consider adding a "worked with: ***" line in your homework write up. 

You are allowed and encouraged to work together on homework and seek out resources beyond materials on Canvas. Ultimately, all students are expected to exhibit mastery of the class content. Note that most content has in-class assessments with limited to outside resources (only a calculator!), so it is critical that each student takes ownership over the material. 

Peers are a powerful resource in this class. Consider using the Canvas DHW or WHW Questions Discussion Board to connect with your peers and get some help.  Feel free to share your work with others and provide editing help or general feedback to improve your peer's work. Although collaboration is encouraged, each student is expected to turn in their own work composed and written by themselves (although edited by others).

If you choose to use AI or an LLM, be aware that these tools can fabricate materials and use inappropriate methods.  Minimally, if you choose to use AI run through the following checklist:

Are all facts, data, and citations correct?

Is it aligned with the learning objectives or task requirements?

Is it free from bias, stereotypes, or inappropriate content?

Does the reading level and tone fit the assignment?

Token:

You start the quarter with 1 token.

You may exchange one token for the opportunity to rework and resubmit a written homework. The new work will replace the original score only if the new score is higher.

You may exchange one token to submit a late written homework without penalty. 

Late written homework without tokens will be penalized 50%, if marked at all. 

In Class Presentations:

Though the atmosphere in this class should be informal and friendly, what we do in the class is serious business. In particular, the presentations made by students are to be taken seriously since they spearhead the work of the class.

Each class day your group will present 1 to 2 problems (from the Daily Homework) with two presenters randomly selected by the instructor. Four presentations are required during the quarter with one occurring in the first four days of student presentations.  The second presentation must occur in the following four days of student presentations.  This continues until the fourth presentation which must occur in the last four days of student presentations in the quarter.  If you have the opportunity to present more than once in one period, only the top score will be recorded for that assignment.

Here are some of my expectations:

The purpose of class presentations is to make the ideas in the solution/proof clear to the other students.  It is not to prove to me that the presenters have done the problem. 

Presenters should explain their reasoning as they go along and call out any struggles, not simply write everything down and then turn to explain.

Fellow students are allowed to ask questions at any point and it is the responsibility of the people making the presentation to answer those questions to the best of their ability.

Since the presentation is directed at the students, the presenters should frequently pause to connect with the students in class and provide time for questions to arise.

Both presenters are evaluated with the rubric below so both need to speak! 

Presentations will be graded using the rubric below.

Rubric for Presentation

Grade | Criteria
4 | Exceeding. Well paced class discussion wherein the proof/solution is explained and annotated with reasons behind the steps that were taken, well paced, and aligned with class content. Approach to problem is explained with illuminating examples. 
3 | Meeting. Solution/proof has minor technical flaws, some unclear language, or lacking some details that is corrected when pointed out. Essentially correct and aligned with the class content.
2 | Emerging. A partial explanation or solution is provided but either misaligned with class content or still contains a significant gap even with the support of the class.
1 | Attending. Minimal progress has been made that includes relevant information & could lead to a solution/proof.
0 | You were completely unprepared.

However, you should not let the rubric deter you from presenting if you have an idea about a solution/proof that you’d like to present, but you are worried that your solution/proof is incomplete or you are not confident your solution/proof is correct. You will be rewarded for being courageous and sharing your creative ideas! Yet, you should not come to the board to present unless you have spent time thinking about the problem and have something meaningful to contribute.

Exams

Thursday, Apr. 30th: Midterm exam.

Thursday, June 11th: Final comprehensive exam.

The exams are to be done individually within the assigned two hour class time while proctored.  Both exams may have a take-home portion that will be distributed the class day before and collected at the beginning of the exam times. One one-sided page of 8.5 by 11 inch paper of notes is allowed for each exam with what ever you would like written/typed/photo copied/etc on it.

Make-up tests will only be given for absences deemed justifiable by the instructor (e.g., illness, family emergency), and may be considerably more difficult than the original test. If you must be absent for an exam, I will only give a make-up exam if notified in advance.

Getting Help:

Many resources exist, are available, and are intended to help you with math, technology, and personal issues and questions. Math, tech & some UWT supports.

General Policies:

Campus-wide and class policies regarding inclement weather and emergency procedures are postedUWT emergency resources andUWT e-syllabus policies.