If you are thinking of taking real analysis soon, you might be wondering if it is a hard class. This post will show you how hard real analysis is and what you can do to make it easier.
Overall, real analysis is generally considered as being one of the hardest undergraduate math classes. This is mainly because it is a proof heavy class and the proofs are not always obvious.
There are actually many factors that will influence how hard real analysis 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 real analysis can be a hard class
In real analysis you will be mostly proving the stuff you learned in calculus. However, real analysis will be much less computational than calculus and the theorems and definitions in real analysis are often quite general. It can be difficult to see where they fit in to the proofs and this can cause the proofs in real analysis to be challenging.
In addition to this, the concepts taught in real analysis can be quite abstract and difficult understand despite being based on what you used in calculus. This can further cause difficulty in making use of them in the proofs.
Reasons why real analysis can be an easy class
Despite real analysis having many difficult aspects, there are some things that it has going for it as well.
While the concepts can be difficult to understand at first, since they based on what you did in calculus, it should still be apparent that they are useful concepts to know. For me, this helped motivate me to study for the class since I was able to see the usefulness of what I was learning.
In addition, you will be given many definitions in real analysis. These definitions are what you will be using to prove things. If you can learn all of the definitions by heart, the proofs will become much easier.
It depends on the professor
As with most math classes, the difficulty of the class with have a lot to do with the professor.
Some professors will ask difficult proofs on the exams, give you very little idea of what will be on the exam and will go through the book quickly.
While others will give you an idea of what will be on the exams, not ask the most difficult proofs and not go through the book as fast.
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 abstract algebra, you will be better prepared for real analysis.
If you have not taken a class on proofs before, I would strongly recommend that you take an introduction to proofs class before taking real analysis.
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 real analysis easier
Below are some things you can do in order to make real analysis easier.
Take a class on proofs first
As mentioned above, real analysis is a proof heavy class. If you have not taken an introduction to proofs class already, it would be strongly recommended that you take one before real analysis. If it will not be possible for you to do that, you should at least work through an intro to proofs book before taking real analysis.
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 real analysis. Here is one playlist.
It would also help to work through a real analysis textbook.
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.