Which course should I take: Discrete Math or Bridge to Advanced Mathematics?

[Ric-Veda]

Hi, I am currently an undergraduate student and I plan on taking advanced math courses such as Abstract Algebra, Real Analysis, Complex Analysis, etc. There are two courses which I think could help me prepare for the courses above as they are proof intensive: discrete math and bridge to advance mathematics

Discrete math (3 credits):
This course introduces students to the foundations of discrete mathematics. The topics of study include propositional logic, methods of proof, set theory, relations and functions, mathematical induction and recursion, and elementary combinatorics.

Bridge to advanced mathematics (4 credits):
This course explores the logical and foundational structures of mathematics, with an emphasis on understanding and writing proofs. Topics include set theory, logic, mathematical induction, relations and orders, functions, Cantor's theory of countability, and development of the real number system.

So which will help me prepare for advance mathematics? I can only pick one.

BTW, I also took an introduction to Linear Algebra course (called "Matrix Algebra" at my college) which was 3 credits and covered:
Matrices and systems of equations, Determinants, Vector spaces, Orthogonality, Eigenvalues,
Just mentioning this if that helps. There were proofs in this class (especially on vector spaces), though they are nothing like on a real proof based math course

 

[fresh_42]

I'm a bit confused as to how the two courses differ. I would have expected something completely different in discrete math: primes, finite groups, rings and / or fields, algorithms, and more than just elementary combinatorics, e.g. sort algorithms. At least they have recursions. In general, discrete mathematics is more relevant to applied mathematics and computing, whereas the other course looks like a bit fundamental on how mathematics works. So I'd say, it again depends on what you intend to be, learn or aim for. I'd rather take a course in topology or differential geometry as this bridge course. Discrete math on the other hand can provide you with some basic tools which might be useful on a wider range, except you want to improve in mathematics without regard to the rest of your study. In this case, both are equally worth studying it.

 

[Ric-Veda]

I'm a bit confused as to how the two courses differ. I would have expected something completely different in discrete math: primes, finite groups, rings and / or fields, algorithms, and more than just elementary combinatorics, e.g. sort algorithms. At least they have recursions. In general, discrete mathematics is more relevant to applied mathematics and computing, whereas the other course looks like a bit fundamental on how mathematics works. So I'd say, it again depends on what you intend to be, learn or aim for. I'd rather take a course in topology or differential geometry as this bridge course. Discrete math on the other hand can provide you with some basic tools which might be useful on a wider range, except you want to improve in mathematics without regard to the rest of your study. In this case, both are equally worth studying it.

These courses are at two different colleges that I plan on going to (whichever picks me). I think that discrete math is more relevant for Computer Scientists and the other for Math majors. But both look similar (for the bridge to advance math course, it does teach you to write proofs, something that probably won't be taught at a discrete math, IDK)

But what I want to achieve is to be know and be comfortable with proofs since courses like abstract algebra, analysis, topology are proof intensive. I want to learn these courses because I feel like I need to start learning math all over again, but in a different way, and know how and why math works (If all of that makes any sense). I did take an intro to Linear Algebra course and it had some proofs (vector spaces) though not really that intensive, rather basic.

 

[fresh_42]

Well, from a mathematical point of view, "Bridge to Advanced Mathematics" would be preferable.
"Discrete Mathematics" hopefully also contains proofs and is a bit more useful for computer science.
However, my guess is, that you will encounter many of the concepts in discrete mathematics anyway, not necessarily within one course.

 

[Ric-Veda]

Just a question, do all universities require students (especially math majors) to take an intro to mathematical proof class in order to take advanced, proof based math classes?

 

[fresh_42]

Just a question, do all universities require students (especially math majors) to take an intro to mathematical proof class in order to take advanced, proof based math classes?

I don't think so and it depends on the curriculum and who determines this. As mathematics is basically a sequence of proofs and arguments, you automatically will learn those techniques. I don't even think it's especially useful. What is it good for, to know which tools there are, if you don't know how to use them? In addition real proofs are often a combination of various techniques, e.g. an induction can be embedded in an indirect proof. Some proofs even require an entire field of mathematics to be developed first, as in the case of FLT.

 

[vela]

As mathematics is basically a sequence of proofs and arguments, you automatically will learn those techniques.

Some students can automatically learn the techniques, and they are the one, who in the past, would succeed and the rest would quit math.

I don't even think it's especially useful. What is it good for, to know which tools there are, if you don't know how to use them?

This is kind of like asking, why do kids need to learn how to write a sentence properly when they still won't be able to write a good paragraph.

Ideally, students learn how to write simple proofs in lower-division classes, but the reality is many do not. I think explicit emphasis on proof-writing was introduced to ease the transition between lower-division classes and upper-division classes (at least in the US).

 

[fresh_42]

This is kind of like asking, why do kids need to learn how to write a sentence properly when they still won't be able to write a good paragraph.

I don't think so. To me it's more as if someone knew ZFC back and forth but not what it means. We use it all the time, no need to think about it, except one is especially interested in the subject.