In Fall 2017, I taught Modern Algebra (aka “Abstract Algebra”) for the first time in many years. For the next time I teach this class, I am considering putting here a version of my notes, instead of just distributing them in class. Whether I do or not, I am providing here now a kind of “Learning Algorithm” or “Study Algorithm”, or as you may call it, a set of “Study Guidelines”, for every class you take, especially problem solving oriented classes, like this Modern Abstract Algebra class.

The overall plan is to use a textbook, but also I will use notes from when I took the course, augmented with things I’ve learned since then, and augmented with my thoughts on the textbook. In Fall 2017, I used the text by Pinter (see Pinter’s Abstract Algebra Book), which is the same text that was used by my predecessor for quite a few years.

Here are some general study, learning, and course-taking recommendations:

- Plan to read the textbook more than once, and then execute that plan, for instance, according to the remainder (see steps 2, 3, … below) of this algorithm.
- Learn any suggested software (e.g. PROLOG, MathCAD, Maple, UACalc, Mathematica, MatLAB, Fortran, C++, LaTeX, Mathematica, Wolfram Alpha, etc), or online systems (e.g. Quora, StackExchange, Proceedings of the American Mathematical Society, Instructure Canvas, MyMathLab, GAP, Par GP, etc) to assist your learning of the material.
- On the first reading of the textbook, give the problems only a cursory glance. “Read it like a novel.”
- Ask your classmates questions that you have about the reading. Take notes about their answers. Keep these notes organized. When asking or answering questions, treat your classmates with the same respect that you think you deserve.
- Participate in class and take notes during every class meeting. Keep your daily notes organized. Respectfully ask questions about the class lectures.
- Form a study group (not a homework solution group). Discuss within your study group your daily notes and the notes you take of the answers given by your classmates about the reading, and the questions that they pose to you, and your answers to their questions. When asking or answering questions, treat your study group colleagues with the same respect that you think you deserve.
- Later (see below), when working (unassigned or assigned) problems, use a fresh page for each problem (or type your solutions using a mathematics friendly document preparation system like LaTeX or LyX, which allows you to insert space as needed).
- Prepare to write your solutions to problems, and to write your course notes, in complete sentences, using “English with Embedded Mathematics”.
- On the second reading, solve on your own the first problem from each section of the textbook, long before any homework is assigned by your instructor. File your solutions, so that if they are assigned later, you have them ready for proofreading, editing, correction, and submission.
- Ask your questions about the reading in class or in an online forum as indicated by your instructor. Repeat as instructed or as invited.
- Anytime in this process of reading, learning, and participating in class, when you are assigned problems to turn in, go through your files of problems you already worked, and edit out any errors, and then submit the corrected solutions, but solve all other assigned problems as instructed also; then continue this “learning algorithm” on your own pace.
- Visit your instructor during office hours to ask questions about the reading, and about the notes you took in class. Take notes in these office hour meetings, and file your notes for later use. Use them to help revise misunderstandings that you have developed during the course.
- Anytime in this process, if someone provides you a solution to a problem that you should do on your own, make a note of that fact when you write your own version of the solution. If the problem is assigned to turn in, cite your source (in fact, for your further understanding of the subject, it will usually be helpful to cite the sources in your filed problems, even for problems not to be submitted), and ask the instructor if you should do an extra problem, to compensate for the fact that you did not actually solve that problem on your own. In fact, attempt to make up a new related problem (hopefully of similar difficulty to you) yourself, and solve that problem, and explain why you are doing this.
- When graded work is returned, rework any problems for which your attempted solutions were incorrect, and take notes about your errors (keep the erroneous work as well as the correct work, so that you can remind yourself not to make the same errors later).
- With instructor approval (because your instructor may allow you to resubmit solutions, and may require that you do this revision work on your own as well), discuss in your study group the solutions to problems that have been graded.
- On your third reading of the textbook, solve on your own the second and third problems from each section of the textbook.
- Continue to meet with your study group to learn more. If exams are part of the graded component of the course, practice problem-solving potential exam questions in your study group. Keep notes about any errors or correct solution methods or correct problem solutions.
- Determine which sections you feel you understand well. In all subsequent readings, skip these sections, and only solve the associated problems (on your own). Continue to do this planning and task list revision after each subsequent reading of the textbook.
- On your fourth reading (of the sections that you still feel you need to read), solve (on your own) the fourth, fifth, and sixth problems of each section.
- Continue to meet with your study group to learn more. If project proposals, projects, or project reports are part of the graded component of the course, brainstorm in your study group about possible project ideas and how to write proposals or reports. Keep notes about any errors or correct writing methods or correct document preparation methods, etc. Plan to not do a project on the same topic as any of your classmates, unless expected by your instructor.
- Visit your instructor during office hours to ask questions about the reading, and about the notes you took in class, and, if project proposals, projects, or project reports are part of the graded component of the course, discuss the appropriateness of potential topics for your assignment. Take notes in these office hour meetings, and file your notes for later use. Use them to help guide you in your preparation for that assignment.
- On your fifth reading, solve (on your own) all remaining problems in each section.
- Continue to meet with your study group to learn more. If presentations (in person or on video) are part of the graded component of the course, discuss in your study group about possible presentation ideas and perhaps how to script and video record your presentations, as well as how to upload or submit them. Keep notes about any technical questions or issues that arise. Plan to
**not**do a project on the same topic as any of your classmates, unless expected by your instructor. - Visit your instructor during office hours to ask questions about the reading, and about the notes you took in class, and, if presentations (in person or on video) are part of the graded component of the course, discuss the appropriateness of potential topics for your assignment, and discuss any technical questions or issues that arose for your study group in understanding how to present or video record or upload/submit your presentations. Take notes in these office hour meetings, and file your notes for later use. Use them to help guide you and your group in your preparation for that assignment.
- Enjoy learning!!