# Logic: Difficulty for Students vs Analysis & Algebra

• LordCalculus
In summary, the difficulty of a course in Logic depends on its type and structure. At the undergraduate level, it can be an easy introduction to Symbolic Logic or a more challenging Mathematics course. The latter type, which builds on topics like Set Theory, is important for laying the groundwork for the study of the Foundations of Mathematics. This course can be difficult for some, but it also has deep connections to Philosophy. Overall, the main difficulty lies in understanding the formal and abstract approach to the subject, which is similar to other advanced math courses.

#### LordCalculus

Do most students find it more difficult than analysis and abstract algebra?

It depends on the type of Logic and the structure of the course.

Normally, at the undergraduate level, a course in Logic is one of two things: a very easy introduction to Symbolic Logic taught out of the Philosophy Dept. or a Mathematics course that can act as a transition to other advanced courses. Typically the later will contain the former and use it to build such topics like Set Theory.

This type of the course (the Mathematics led one) is important as it will usually rigorously define things like functions, relations, etc.. and lay the groundwork for the study of the Foundations of Mathematics. It can be a difficult topic for some, but then again so could Analysis and Algebra. My course in Logic and Set Theory was the best course I'd ever taken as an undergrad and I learned more from it than I'd ever imagined I would -- it was also a springboard for me into the Foundations, which is a topic that holds most of my attention and energy right now. For what it's worth, Mathematical Logic is not a subject for the weak at heart. It has very deep connections to Philosophy and I think one of the reasons that I personally took to it was because of this connection. Good luck.

I think the main difficulty with either type of course that Discrete* mentioned, is that you need the mathematical maturity to see that you are playing a "game" according to fixed "rules", and the rules are not quite the same as the common-sense "logic" you use every day outside of your math class.

But the same is true about all of math once you get beyond the elementary level (for example abstract algebra and analysis, compared with arithmetic and calculus). I expect for many people, the "hardest math course" is the first one which uses this more formal and "abstract" approach, indepedent of what topic the course is about.