If you are thinking of taking abstract algebra soon, you might be wondering if it will be a hard class. This post will show you how hard you can expect it to be and what you can do to make it easier.
Overall, abstract algebra is generally considered one of the hard undergraduate math classes. The reason for this is that it is a proof heavy class and most students take it without significant experience in proof heavy classes.
There are actually many factors that will influence how hard abstract algebra will be for you. However, there are also a number of things you can do that will make your time in the class much easier.
Reasons why abstract algebra can be a hard class
An introductory class in abstract algebra tends to focus on things such as groups, rings and fields. These tend to be reasonably abstract concepts and it can be hard to see their usefulness like you can in a class such as calculus or linear algebra. This can cause some students to struggle to motivate themselves to study for the class and, in turn, cause them to have a hard time.
In addition to this, abstract algebra tends to be a class involving lots of proofs. The proofs in abstract algebra can be hard proofs (but usually easier than those in real analysis). So, if you have not got much experience with proofs, you will likely find abstract algebra to be a difficult class.
Reasons why abstract algebra can be an easy class
Even though abstract algebra can be difficult, there are some things that can make it a less difficult class.
As in most math classes, the topics in abstract algebra build on themselves. If you can put a consistent effort into the class right from the start of the semester, making sure that you understand each theorem and definition as you go, and you are reasonably comfortable with proofs, you should be able to do well in the class.
However, if you allow yourself to fall behind, early on, you will likely have a hard time in the class. This is why it is very important to make sure to dedicate time to the class from the beginning of the semester.
In addition, the topics covered in the class do actually have real-world applications. If you take the time now to see why the class is useful, it could help motivate you to study for the class. You can read about its uses here and here.
It depends on the professor
How difficult abstract algebra will be for you will largely depend on the professor.
Some professors will cover the material quickly, expect you to know everything from the book, ask tough proofs and give you little idea of what will be on the exam.
While, other professors will not rush through the book, ask simpler proofs and let you know what you can expect to see on the exam.
Before choosing the class, it would be recommended to see how other students have rated the professor that will be teaching it.
It depends on your own background
The difficulty of the class will also depend largely on your own background in mathematics. If you have taken classes involving proofs before such as discrete math or real analysis, it is likely that you will be fine in abstract algebra as long as you study from the start.
How much you can expect to study
Generally, you should expect to spend around 15 hours per week on the class. You might need to spend more or less time on the class than that, depending on other factors influencing how difficult the class is for you such as the professor, how demanding your college is and your own background.
Ways to make Abstract algebra easier
Below are some things you can do in order to make the class easier for yourself.
Plan the schedule for the semester early on
It is important to plan the entire semester out during the first week of classes. By doing so you will be able to spot potentially difficult weeks, before they come, avoid missing due dates and know when you need to start focusing on a certain class.
Prepare for it ahead of time
Another thing you can do that will greatly improve your chances of success, in the class, would be to prepare for it ahead of time. I personally graduated with a 3.8 GPA in mathematics and I put most of it down to preparing for the classes before actually taking them.
My recommended way of preparing for the class would be to watch a Youtube playlist teaching abstract algebra. Here is one playlist.
It would also help to work through an abstract algebra textbook. You’ll likely be able to find a cheap one from Dover books on mathematics.
Pick a well-reviewed professor
As mentioned above, the professor will have a big impact on the difficulty of the class. It would help to try to choose your professor for the class as early as possible and to look at what other students have said about them.
Read the book before skipping to the problems
Many students will jump to the problems before reading the relevant chapter from the textbook because they want to save time. The problem with this is that the problems will be based on what is in the textbook and the professor will often skip over sections from it.
Instead of jumping straight to the problems, you will likely have a much easier time if you read the chapter before jumping to them.
Prioritize the material given to you by the professor
If the professor gives you any material then make sure to prioritize understanding it especially if it is a study guide. This material tends to be very likely to appear on the exam.