L24 Math 430 (Modern Algebra) Syllabus
This is the class webpage and syllabus for Math 430 in Spring 2020. Any changes or updates to the syllabus will be posted here and will be announced in class. Changes due to the online restructuring of the class are marked in
red.
Course Information
- Instructor: Dr. Tyler Bongers, tyler.bongers@wustl.edu
- Office hours: conducted via Zoom; meeting IDs are posted on Canvas. Regularly scheduled office hours will be 1-2 PM on Monday, 1-2 PM on Tuesday, and 10-11 AM on Friday. I know that everyone's schedule is in flux right now, so please let me know if you would like to meet outside these times.
- Course location and times: conducted via Zoom; meeting IDs are posted on Canvas; MWF 12-12:50.
Course Description
An introduction to groups, rings, and fields. Includes permutation groups, group and ring homomorphisms, field extensions, connections with linear algebra. Prerequisite: Math 429 (Linear Algebra).
The textbook for the course is A First Course in Abstract Algebra (7th edition) by John B. Fraleigh. I strongly recommend that you have (and use!) a copy of the book; an older edition is fine.
This course serves as a rigorous introduction to the study of algebraic structures as their own objects. Structures such as groups, rings, and fields let us expand and rewrite our familiar algebraic rules, and these objects are some of the most fundamental ones to study in modern mathematics. The ability to form abstractions and generalizations is a critically important mathematical skill to cultivate, and this course will focus on that. See the course schedule (updated April 15) for a more detailed list of course content.
Homework and Presentation
A large part of this course is about developing your mathematical communication skills, and proof-writing is one of the best ways to do this. As such, we will have weekly written homeworks throughout the semester. Homeworks will involve writing up full and complete proofs for each problem, and will be submitted via Crowdmark. Assignments will typically be due on Tuesdays. You are very strongly encouraged to type your homework with TeX, which is the gold-standard typesetting system for mathematics - this class is a great opportunity to learn how to use TeX. If you have questions on how to get started, let me know.
On each of these, you are strongly encouraged to collaborate with each other and discuss the problems; however, your writeups must be done individually and without copying. You are welcome to use any resources to help you solve a problem, but each problem must also include a citation. If your proof is based on an idea that you got from a classmate, an internet resource, or some other place, then you must cite your sources; if you solved a problem completely on your own, then indicate that instead; on each problem, the citation will be worth 1 point.
The lowest homework will be dropped when computing grades. Additionally, you are allowed one 24-hour extension on any homework during the semester; you must request this before the deadline. Beyond this, no late homework submissions will be accepted for credit. Grading of homework problems will be based on both mathematical content and clarity of the presentation; see the assessment standards for more information.
An additional important skill is to be able to communicate your mathematics orally. As such, there will be 10 minute in-class presentations of homework problems throughout the semester. Presentations will be assessed based on the correctness of the mathematics, the write-up of the proof, and the oral presentation of it. Some homework problems will be eligible for presentation, and will be marked; you can claim a problem to present on Canvas.
If you have not presented before Spring Break, then in lieu of a presentation requirement there will be a small writing project, exploring more deeply some aspect of abstract algebra. Options will be posted on Canvas, but if there is something that you're interested in reading and writing up on your own, feel free to suggest extra topics.
Exams
There will be two midterm exams on February 19 and April 7, as well as the final exam. The course schedule has the final exam from 10:30 am to 12:30 pm on May 6; we will discuss the online format of both the second midterm and the final exam in class. Your lowest midterm exam grade will be replaced with your final exam grade if this improves your score. Attendance at each exam is expected, and there will be no make-up exams; absences at both midterms or at the final exam require an excuse with documentation, as well as meeting with me.
Grading
The points for the course will be distributed as follows:
| Presentation | 5% |
| Homework | 20% |
| Exam 1 | 20% |
| Exam 2 | 20% |
| Final Exam | 35% |
Your final grade will be assigned given the cutoffs in the table below; these may be adjusted downwards during the semester. Please note that scores will not be rounded - a 79.99% will still translate to a B, not a B+. If you are taking this as pass-fail, then the cutoff for a passing grade is C-. The grade of A+ will be given at the instructor's discretion.
| Grade | Points |
| A | ≥ 90% |
| A- | ≥ 85% |
| B+ | ≥ 80% |
| B | ≥ 75% |
| B- | ≥ 70% |
| C+ | ≥ 65% |
| C | ≥ 60% |
| C- | ≥ 55% |
| D | ≥ 50% |
| F | ≥ 0% |
Teaching and learning philosophy
There are a few core beliefs that guide my teaching, and which I hope you will find useful in your learning process:
- The best way to learn math is by doing math - this means actively engaging with the material, and striving with problems. Mathematics is not a passive science, but rather requires active work on the ideas. I strongly encourage you to do as many problems from the textbook as you can (and to only check the solutions after you've seriously tried them!).
- Another important skill is communicating math. This takes many forms: discussions with your peers in and out of lecture, the written notes and homeworks that you create, and the explanations that you have on exams. Following this idea, there will be fully written proofs on each homework, as well as the oral presentation in class.
- It's also important to learn how to read and contextualize math. Reading a math textbook is very unlike the process of reading a novel or just about any other written material - it requires active engagement and work to understand the arguments and computations. As you read the book, you should take notes, write about your questions and their resolutions, and brainstorm ideas for how this material fits into the broader context of the math and science you've seen before.
- Learning math is also a community activity. Work along side your classmates! If doing math is the best way to learn math, then teaching math is the second best way; finding an explanation for someone else, or having a discussion about a difficult concept, or just comparing notes on homework can lead to new ideas and insights. It's okay to make mistakes, and is a fundamental and natural part of learning.
Resources, support, and learning strategies
There are many resources available to help you succeed in the course - remember that we are here to help you get the most possible out of your time here! Here are some suggestions:
- Come to class. Not only will I talk about the day's material, there will be time for us to learn actively. Guided discussions and problem solving with your peers are great opportunities to learn (and explain your own knowledge to others), as well as to ask questions.
- Come to office hours. I have drop-in office hours scheduled throughout the week; talking about math is an important way of learning, and a brief discussion or picture might give you exactly the right idea to grasp a concept. If none of the standard times work for your schedule, please contact me
- Email me. If you have shorter questions about a concept, the homework or exams, or any other things that come up, please feel free to email me at tyler.bongers@wustl.edu. I do my best to respond quickly (that is, within a few hours; almost surely by the end of the day) to emails that are sent before 8 pm during weekdays. However, I will generally be unavailable by email on Thursdays or weekends. I strongly encourage you to also schedule time off for yourself throughout the week, since mental health is such an important part of life; this brings us to...
- University resources. The university has numerous resources available for counseling and health and wellness.
- Calculators can be extremely helpful in developing visualizations and computational skills (or just for verification purpose). Although they will not be allowed on exams, you're encouraged to use them on homework to help explore the concepts. In particular, I recommend Sage and Octave as free and open-source software with visualization packages built in. Other alternatives include Matlab, Mathematica, and WolframAlpha.
Other Course Policies and Helpful Information
- Washington University is committed to providing accommodations and/or services to students with documented disabilities. Students who are seeking support for a disability or a suspected disability should contact Disability Resources at 935-4153. Disability Resources is responsible for approving all disability-related accommodations for WU students, and students are responsible for providing faculty members with formal documentation of their approved accommodations at least two weeks prior to using those accommodations. I will accept Disability Resources VISA forms by email and personal delivery. If you have already been approved for accommodations, I request that you provide me with a copy of your VISA within the first two weeks of the semester.
- Adherence to the university's academic integrity policy is expected and required. In particular, your homework submissions must be written up separately and individually - copying is never allowed, and will be treated as an act of plagiarism.
