Understanding Advanced Math

Advanced Math, General

Before we can jump to comprehending what is advanced math, we need to know the other two categories – Beginner and Intermediate. Till the time a child reaches high school, they are taught beginners’ mathematics. It includes:
· Arithmetic
· basic geometry
· trigonometry
· basic algebra
· basic calculus
After high school and at undergraduate level, a student it taught intermediate mathematics. The coursework for this may include:
· Calculus including vector/multivariable calculus
· Differential equations
· First courses in more theoretical topics like abstract algebra, analysis, topology and others.
Once an individual has crossed both these levels, they reach Advanced mathematics. It is taught during graduate school and the foremost way to differentiate it from other forms is that it is vague. Both beginner and intermediate level math offers problems that are bite-sized and are known to have a solid solution. The same logic doesn’t apply to advanced math. The problems at this junction can be highly trivial or worthy of an entire thesis. Advanced math also removes the boundaries between different topics and courses that were clearly demarcated in the other two levels.
The complications that arise with advanced math prove that it is not the cup of tea for everyone and should only be opted for with careful thought.

Which Student Should OptFor Advanced Math In College?

Advanced Math, General

A high school student in America who performs well on calculus BC or has taken classes on multi-variate calculus can choose advanced math at undergrad level. A course in both types of calculus prepares an individual to study any technical subject in college where the math is taken to a higher level of abstraction.
Also, students who were blessed with teachers and instructors who taught for more than for the tests can select higher studies in the math. Teachers who took the time to introduce proofs and provide better insight to concepts and theorems prepare a student for advanced math.
If both these above-mentionedconditions have not be met and person hopes to enrol in a course that incorporates advanced mathematics in the future, then they should look for competitions like AMC and USAMO. These competitions involve curriculum from number theory and proofs that help build the foundation for higher level learning of the subject. But a tale of caution would be to not take on the material only to have a feather in the cap. The last advice would be to judge the level of interest and capability the student has within before selecting a course that requires advanced math.