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.

Find available tutors

Understanding Abstract Math

What Is Abstract Math?

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.

Math Vocabulary

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.
Proof
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.
Function
The relationship between a set of integers. It might look something like f(x) = x^2.

How to Approach Abstract Math Problems

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.

Did you find this useful? If so, please let others know!

Other Articles You May Be Interested In

  • More Blog Articles
    Creating Your Own Math Problems and Worksheets

    Supplementing your child's math lessons with a few problems and worksheets of your own will help you become better acquainted with his or her curriculum, and will help your child perform better in the classroom. Here are some tips for creating them.

  • More Blog Articles
    Sample Math Worksheet - Simple Addition

    This simple addition worksheet is only a sample to help you format your own practice math problems. Includes answers.

We Found 7 Tutors You Might Be Interested In

Huntington Learning

  • What Huntington Learning offers:
  • Online and in-center tutoring
  • One on one tutoring
  • Every Huntington tutor is certified and trained extensively on the most effective teaching methods
In-Center and Online

K12

  • What K12 offers:
  • Online tutoring
  • Has a strong and effective partnership with public and private schools
  • AdvancED-accredited corporation meeting the highest standards of educational management
Online Only

Kaplan Kids

  • What Kaplan Kids offers:
  • Online tutoring
  • Customized learning plans
  • Real-Time Progress Reports track your child's progress
Online Only

Kumon

  • What Kumon offers:
  • In-center tutoring
  • Individualized programs for your child
  • Helps your child develop the skills and study habits needed to improve their academic performance
In-Center and Online

Sylvan Learning

  • What Sylvan Learning offers:
  • Online and in-center tutoring
  • Sylvan tutors are certified teachers who provide personalized instruction
  • Regular assessment and progress reports
In-Home, In-Center and Online

Tutor Doctor

  • What Tutor Doctor offers:
  • In-Home tutoring
  • One on one attention by the tutor
  • Develops personlized programs by working with your child's existing homework
In-Home Only

TutorVista

  • What TutorVista offers:
  • Online tutoring
  • Student works one-on-one with a professional tutor
  • Using the virtual whiteboard workspace to share problems, solutions and explanations
Online Only

Our Commitment to You

  • Free Help from Teachers

  • Free Learning Materials

  • Helping Disadvantaged Youth