What do people learn in university about math? (heard that there is less manipulation of numbers and more prov

Question

What do people learn in university about math? (heard that there is less manipulation of numbers and more proving)
What is the most interesting topic to you and why?
What is the most challenging topic to you and why?

Answer 1

I am copying and pasting this from another answer I gave:

A lot.

Differential equations usually follows calculus. Here you will learn important methods to solve equations that contain various derivatives. You will also cover some of the applications. This course sets you up for courses in partial differential equations (DEs with functions of more than one variable), calculus of variations (a new look on optimization problems), and mathematical modeling (how math applies to the real world).

There's also linear algebra - basically the study of matrices. This will probably be your first course that contains truly abstract material (lots of letters and deep thinking required). It also will be your first course involving rigorous proofs. Many colleges call this their "weeding-out" course for math majors, as it causes many math majors to switch majors.

Then there's all the pure math courses (not my forte, I should mention!), such as discrete math, proofs, and abstract algebra. I didn't take abstract algebra, but discrete math is a requirement for many colleges. You will learn about logic and set theory, which are very simple ideas. Then you progress into basic proofs involving induction, modulo arithmetic, and much more. You might also touch on graph theory (not the graphs many people think of but basically a set of a bunch of points connected) in discrete. If you don't talk about graph theory in discrete, there are courses in that too. In your first proofs course, you will review topics from discrete math and get deeper into how to write a good proof.

Also, there are computer-based courses such as numerical analysis (which is an extension of linear algebra) and solving differential equations numerically. These courses will teach you how to do problems that may go beyond pencil and paper. They will also teach you various algorithms that pertain to how computers handle math problems.

Finally, you have your probability and statistics courses. You will learn about discrete and continuous probability distributions in probability. In statistics you will take data, analyze it, and sometimes compare it with your knowledge from probability. There are, of course, many different types of statistics courses (such as regression and sampling), but I only took mathematical theory of statistics.

My hardest course was real analysis. Real analysis is the study of rigorous proofs of calculus theorems. By rigorous, I mean very particular proofs. You will see what I mean when you get there.

There's lots to discover. Good luck.


EDIT: I didn't include the most interesting course in my answer above. I would probably say calculus of variations and partial differential equations are the most interesting courses I have taken simply because they have so many applications to real-world problems. If you are interested in applied math, you would love these courses. They give you almost all the tools you need to model systems.

Answer 2

1)Yes, the university courses are different. It is more accent on theory. Students may find difficult to apply the theory to problems.
There are different courses: Calculus, Linear Algebra, Differential Geometry, Differential equations, Abstract Algebra, Real analysis, Numerical analysis, Statistics, Probability, Cryptography and many others. The topics in mathematics are numerous even if the common people don't have this impression. Each of the topics that I enumerated can branch into other more advanced and specialised topics.

Some more answers to a similar question here:
http://answers.yahoo.com/question/index;_ylt=AmozTaerMBSpfYvjNAJB2gHty6IX;_ylv=3?qid=20071128214418AA04wNs&show=7#profile-info-6yoUXjSGaa

2)The most interesting topic for me was and is algebra because some profs encouraged me to do it, I found it more close to logic and I think I have a good logic, or maybe I had to start somewhere. Now I like it more because I know it more. That is a principle: you enjoy more something that you know because you can see all the connections and structure of the theory, you are at ease with solutions and so on.


3) Right now I don't think I have something most challenging. I wish my brain developed so much that, given a sufficient amount of time, I can understand proofs from some topic or other.
Mathematicians in present times tend to be specialised in one area or other. They cannot grasp all mathematics topics like a Renaissence man since the math developed immensely.
When I was student though I found hard the differential equations course because the proofs and methods were intricated and long.

Answer 3

What is your intended degree? Does it require completion of specific math skills to graduate? If so, taking it either at the university or a community college would do little good. You'd be at different surroundings. But you'd still have the same dyscalculia. And if a particular degree requires a specific math skills set, asking for a course waiver/modification is an unreasonable modification. We have to show that we do have the same skills set as college students without disabilities. Your high school IEP does not have legal weight in college. I also have a learning disability with math. I knew I had not completed high school level algebra or geometry when I entered college. My degree did not specify I needed specific math courses. So I took a 'history of women in math' offered by the math department and listed as counting for the math core credit hours. And I earned an 'A' because the particular course utilized strengths rather than my disability.

Answer 4

It depends on the school and the major. You're right though that it's more about learning and applying the abstract and higher-level concepts of mathematics, rather than just "number crunching".

On one level you can find introductory courses like College Algebra (which cover not only what gets covered in a high school algebra course, but also some higher-level algebra, geometry, and trigonometry...all crammed into one semester). Engineering majors typically end up taking classes on differential equations and other mathematical models. Computer Science majors learn more about discrete mathematics and combinatorics. There are also those who focus on Statistics.

I myself majored in mathematics for both undergrad and graduate school, and ended up taking a number of different courses. I liked Linear Algebra a lot (which is certainly not to be confused with high school algebra), mainly because it was a whole new branch with countless fascinating applications. The class I found most challenging was probably my Real Analysis class in graduate school. It was working with things on such an abstract level, and the proofs seemed next to impossible to do. I did get by though.

Answer 5

The Best TOPIC IN MATHS is intergration and mechanics and abit of conics but my fav atm is Complex numbers.. but im not in uni im doing 4 unit maths which is the highest maths which can be done in a highschool and it rocks