How to Approach Abstract Math Problems
Abstract math is very different from the more widely applicable math ideas you've seen before. It may take some getting used to, but try not to become frustrated - many people struggle with these advanced concepts. Here are some explanations to help you along.
A lot of math concepts can be applied to other fields. For example, engineering, astronomy, statistics, finance and economics all use mathematical principles to determine real-life structures. Abstract math (sometimes called 'pure' or 'higher' math) is based on abstract conceptualizations that usually aren't applied to any non-math setting. Abstract math involves a lot of theorems and proofs, and relies on fact-checking to prove statements.
In other words, abstract math is not connected to uses beyond the world of math. Applied math is math that you use in other ways, such as to build bridges or develop banking systems. Pure, or abstract, math can be seen as math's unapplied concepts.
Approaching Abstract Math Problems
You may have to begin by stating all the known facts related to the given problem. This will allow you to build an answer based on the evidence provided by the mathematical objects involved, such
as sets and numbers. Watch how your teacher handles abstract math problems on the blackboard, and take careful notes.
These words will probably come up when you are first learning about abstract math problems. Memorizing their meanings now may make your schoolwork easier.
- Number Theory
- The study of integers (usually of prime numbers, like 9 and 3). Number theory is a branch of abstract math that focuses exclusively on integers. A lot of the work in number theory deals with division, and the ways in which integers can be divided by one another.
- A proof is similar to a scientific hypothesis, or statement. It's a mathematical argument that needs to be backed up with data and empirical evidence. Abstract math is largely built on proofs and their supporting statements.
- The relationship between a set of integers. It might look something like f(x) = x^2.
Abstract math problems can often be made easier if you approach them with concrete methods. For instance, if you have trouble visualizing a problem, you can use manipulatives, or objects, to solve it. Examples of manipulatives might include coins, candy or marbles. Drawings can also help you solve abstract math problems.