ma312: Abstract Algebra I - f24

Daniel Rowe
darowe{at}nmu{dot}edu

I'm an associate professor of mathematics in the Mathematics and Computer Science Department at Northern Michgan University. I've been a professor at NMU for nine years, and I am very passionate about the praxis of doing mathematics and teaching it. I grew up on a fishing camp in Northwestern Ontario, Canada.

• Office Hours
• W 1-2, R 10-11, F 11-12
• JXJ 2228
• zoom link - passcode 809390
• read the relevant section(s) of our materials
• study all posted solutions
• re-watch the recorded lectures
• math tutor lab

• hybrid-flexible, in-person and over zoom
• recordings available 2-3 days after each class
• strive for in-person attendance
• avoid becoming reliant on zoom and recordings!
• use them for extenuating circumstances only
• engagement is vital to learning mathematics (or anything)

• (30%)   Homework
• (10%)   Collaborative In-Class Quizzes
• (30%)   Traditional In-Class Midterm Exam
• (30%)   Traditional In-Class Final Exam

This course is an introduction to the vast area of mathematics referred to as algebra. This semester will focus on a small subset of topics from algebra, but will introduce students to the important themes of symmetry, transformation, and representation that underly the subject. At the end of the class, a student will be able to understand and apply:

• matrices and permutations
• groups, subgroups, order, generators and relations, homomorphisms
• particular finite groups: such as S_n, C_n, D_n, Z/_n, (Z/_n)^x.
• particular linear groups: such as GL_n, SL_n, O(n), SO(n)
• group actions, orbits, stabilizers, Frobenius' counting formula
• applications: elementary number theory, orbit counting problems, symmetries of objects.

• the instructor's job is to ensure the course content is clear, organized, and interesting


• your job is to attend as many classes as you can, engage your mind, ask questions, read, and budget (at least) 1-2 focused hours every week to work on the course content

In the spirit of academic honesty, credit for this section is due to Asher Auel, as this is an adapted form of their discussion of academic honesty in mathematics.

• Working with others on mathematics, and using electronic resources is both highly encouraged and fun. You may work with anyone (e.g. classmates, non-classmates, tutors, etc.) If this is done well, you'll learn more effectively and efficiently.
  
  Here's the fundamental rule:

  Work with anyone or anything to develop your own personal understanding of the ideas required to solve your homework problem, but always write-up the final draft by yourself and in your own words.

• Writing up the final draft is just as important as figuring out the problems on scratch paper with your friends, using the internet, ChatGPT, etc. If you work with people, or use electronic resources on a particular homework:

You must list your collaborators and electronic sources at the top of the very first page. This makes the process completely transparent and honest.

A Note About Copying Mathematics

Mathematical writing is idiosyncratic; if your assignments are copied, it is quite easy to tell. You will not learn by copying solutions from others, or from external sources such as internet forums (e.g. math.stackexchange) and generative AI (e.g. ChatGPT). Regarding internet forums, you are free to look at them and use any understanding you've gained from them. Be warned that internet forums often contain incorrect or circuitous solutions, misleading discussions, use of techniques outside of the course material, and other material that may be detrimental to your learning process. Even the time that it takes to repeatedly search for solutions and read through dozens of forum posts could be better spent learning the material on your own or composing a question to the instructor or classmate. Regarding generative AI (e.g. ChatGPT), you are free to experiment with asking questions, but be warned that these systems are currently still very bad at deductive reasoning, and that the output may contain a mix of correct, incorrect, and unverified statements. Ask them to prove something false, they will work hard to do so, often giving contradictory answers. Therefore, I would be very careful with using these tools as learning resources on your own.

Punishments

In this modern world of online resources, cheating, copying, copy-and-pasting, ChatGPT, etc.; it is now more important than ever that citizens develop the intelligence to use their own brain to solve problems. I want my classes to be a postive force in this regard, by promoting the principles of academic honesty, and punishing those who disrespect those principles. The first infraction will result in a 0% on the entire assigment and a stern warning. If there is a second infraction, I will pursue sanctions through the Dean of Students office.

If you have a need for disability-related accommodations or services, please inform the Coordinators of Disability Services in the Dean of Students Office at 2001 C. B. Hedgcock Building (227-1737 or disability@nmu.edu). Reasonable and effective accommodations and services will be provided to students if requests are made in a timely manner, with appropriate documentation, in accordance with federal, state, and University guidelines.

• here are my hand-written notes on abstract algebra
• the following is a good, free, open textbook on abstract algebra
• Abstract Algebra: Theory and Applications, Thomas W. Judson, 2020.
• how do I read the text to follow the flow of our class?
• 1.1 → 1.2 → 5.1 → 3.1 → 3.2 → 3.4 → 4.1 → 11.1 → 9.1 →
• here are some (ungraded) practice problems and their solutions

• hw1 (due 9/8 @ 11:59PM) → sol (9/12 @ 11:00am)
• hw2 (due 9/22 @ 11:59PM) → sol (9/26 @ 12:40pm)
• hw3 (due 10/9 @ 11:59PM) → sol (10/14 @ 9:30pm)
• hw4 (due 10/20 @ 11:59PM) → sol (10/22 @ 1:30pm)
• hw5 (due 11/13 @ 11:59PM) → sol (11/19 @ 2:00pm)
• hw6 (due 12/8 @ 11:59PM)


• quiz1 (9/23 @ 10:00AM-4:00PM) → sol
• quiz2 (10/16 @ 10:00AM-4:00PM) → sol


• practice_midterm → sol
• midterm_exam → sol


• practice_final
• final_exam

• list of extra credit problems
• (please read the instructions before you submit)


• repository of solved extra credit problems
• (check which problems have been solved before trying one)

• for quizzes, midterm, final: physical paper in-class


• for extra credit: email me a .pdf (read instructions in the link above)


• for homework: put a .pdf file inside our shared google folder
• the shared google folder will be titled f24_ma312_yourlastname
• I will share it with you within first two weeks of class
• please don't submit anything via email attachment
• name your files in an organized manner, for example: hw1_Jane_Smith.pdf
• always show your work and keep it organized
• indicate/circle/highlight your answers
• answer the questions in the correct order