If you are thinking of taking a class in number theory next semester, you might be wondering how difficult the class will be. This post will show you how hard number theory is and how you can make it easier.
Generally, number theory is considered to be an easy class when compared to other high-level math classes such as abstract algebra or real analysis. However, being a high-level math class, it will still require a lot of work.
There are actually many factors that will influence how hard the class 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 number theory can be a hard class
An introductory class in number theory tends to focus on things such as modular arithmetic, prime numbers and additivity. 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, number theory tends to be a class involving lots of proofs. So, if you have not got much experience with proofs, you will likely find number theory to be a difficult class. With that being said, the proofs are not that difficult, so if you do have experience with proofs, you should be ok with the proofs in introductory number theory.
Reasons why number theory can be an easy class
While there can be some difficult aspects of number theory, there are also some things that make it an easier class compared to its alternatives.
The topics that are usually introduced in an introductory number theory class tend to be relatively straight forward topics. If you have already taken a class in discrete math and you did not have too much trouble, it is likely that you will be able pick up the concepts in number theory relatively easily.
In addition, the proofs in number theory do not tend to be very difficult when compared to proofs in abstract algebra or real analysis.
It depends on the professor
How difficult the class is 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, abstract algebra or real analysis, it is likely that you will be fine in number theory.
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 number theory easier
Below are some options you have that will help you to have an easier time in number theory (and most other math classes).
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 number theory. Here is one playlist.
It would also help to work through a number theory 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.