That's the problem with college(and high school). Usually classes can be tough because your professor is a huge prick.

My last math class was 20 years ago, but I can still count to 100.
And backwards too, all you need to pass DUI tests!

I had some Algebra and Calculus, Differentials integration, Logic and stuff at University but honestly don't remember much. My professors were very disinterested in teaching. Stupid rule that anyone that wants to continue exploring their fields at university has to teach. Most people make lousy teachers, basically teaching tricks to pass exams instead of showing the how and why of mathematics.

Well, in Norway we don't have directly equivalent courses to what you have in the US (or many other parts of the world).

Basically, when you start high school, you choose between practical math and theoretical math. I have taken the first two years of theoretical math (well, I still have the Probability part of year 2 left). Not sure how they'd directly compare to the courses in the US for instance. We have had a lot of Calculus though, a lot of Algebra, Trigonometry, Geometry, Vectors, etc.

Calculus 1, 2, 3; Differential Equations, Linear Algebra 1,2; Elementary Analysis 1,2; Abstract Algebra 1,2; Probablity/Statistics, Elementary Proof Techniques, Modern Geometry, History of Mathematics, Cryptology, Complex Analysis.

Next semester: Just Number Theory.

Best book is my book for abstract algebra. http://www.amazon.com/Book-Abstract-Algebra-Second-Mathematics/dp/0486474178/ref=sr_1_1?ie=UTF8&qid=1459706620&sr=8-1&keywords=abstract+algebra

I'm more into Analysis (when I understand it). Learning integration, I've found has been a real tedious task and the epsilon delta language is really hard to grasp (for me) at first. I liked abstract algebra when it was mostly groups, but once they talked about rings, and quotient rings is where I've gotten confused. Cryptology (codes and ciphers) I've found pretty interesting.

It all depends in University how and where it's taught. I'm not a fan of one of my professor's methods of teaching, while I like the other one.

I loved Calculus though! I don't have any plans for grad school. I majored in math because it's something I'm good at and hope to find a high enough paying job with it. 

Source: Math major.

Nice! I was going to ask you your questions, but directed at you. You're a math major as well? 

It's all relative (difficulty) depending on your school. I go to a state school so it's not THAT hard in terms of grades. My GPA is like 3.8 which is pretty good for a math major. 

That book is really good because it explains things well, but I just wish it did more examples. Because you learn through doing the examples, they give you useful tools for solving other examples. It's also dirt cheap for a math text and covers everything from groups, rings, to Galois theory. 

The only issue with that class, for me, is how it's taught. It's taught by the Moore method, which is when the class has to present problems. The professor doesn't always explain things well and some of the material should be taught with more formal lecture than Moore method, especially quotient rings, but it's good if you're looking to one day become a teacher, as he has you explain the problems. Again it's all relative to the course. 

For abstract algebra, it's a lot of definitions that you have to know and relate back constantly to previous definitions. 
For that book you'll be using cosets, group operations, and certain theorems all throughout the course. Just be sure to know definitions and relate them to problems. 

Enough to know there's a lot more I want to know. I've studied mathematics at university, about 60 ECTS credits total, and then some that weren't technically under mathematics. My studies include calculus (including multivariable calculus), ordinary differential equations, linear algebra, abstract algebra, and measure and integration theory. I also know a bit about complex numbers, automata theory, and basics of programming languages (the formalism is pure mathematics, e.g. Lambda calculus). I have an idea about some other subjects too but I guess that's the most important areas I'm more or less familiar with.

Those are the beginning of your proof based classes, I presume. That's the true heart of being a math major. The computational stuff is what they expect you to know and apply, the theory behind it is what's difficult. But I'm sure you'll do fine though. 

It takes time writing up formal proofs, but a lot of it just takes practice like everything else. It gets harder as there isn't much help online as for like the computational stuff. 

Enjoy!

Oh they are great. I collect them, even if I don't read all of them thoroughly.  I self-studied some basic Graph Theory from this one for fun. It was actually a great way to get into a subject which I probably won't use, but I was interested about nevertheless. I have a few others that I read from time to time, one on Engineering Mechanics (which is quite a different approach to forces and physical systems than I am used to as a physics major), a Theoretical Physics reference book which is handy when I need to look up a particular topic/formulation, "The Philosophy of Space & Time" by Hans Reichenbach which is a great way to learn about what philosophers of science do, and the ideas behind many of the ideas presented in relativity; Mathematics for Non-Mathematicians which I read when I want to describe a topic to somebody without mathematics experience, an upper level undergraduate Geometry book  which I have yet to go through thoroughly, and a book on Fourier Series which I have also yet to go through thoroughly. 

When I was in fifth grade we started learning how to solve the most basic algebraic equations (that was in the 2004/2005 school year.) I wouldn't call that "learning algebra" though, it was just basic computational stuff which we had no conceptual knowledge of. Depending on our scores on the state mathematics exam (which at the time was called the P.S.S.A) in fifth grade, we would either be put on an accelerated track in 7th grade (in which we took the class "Pre-Algebra) or remain in a normal track which was called generically "Math." Those of us who were put on the accelerated track learned Algebra I (8th grade), Geometry (9th grade), Algebra II (10th grade), Trigonometry + assorted Pre-Calc topics (11th grade), and AP Calculus AB (or we took Calculus I and II at the community college) our senior year of high school. Students who weren't in the accelerated track could do this same thing, but they'd have to double up on math classes in 9th grade (Algebra I + Geometry.) The state of Pennsylvania required that everyone took three math courses in high school. Some people took Probability and Statistics instead of Algebra II. 

From what I gather, people who went to private schools and schools in other states had much more rigorous math training, but not too much more. 

@Pi guy.
I used that book for my ODE class and I was thinking of buying that Topology book, as I have a project in History of math that relates music to topology, and I never took a class on that.