Types of Problem

Types of Problem

Pure Problems

  • Pure problems consider mathematical theory, abstract motivation and proof.
  • Cover areas such as analysis, algebra, number theory and geometry.
  • Require a thorough understanding of mathematical concepts and principles.

Applied Problems

  • Applied problems involve mathematics applied to real-world scenarios.
  • Domain includes physics, engineering, economics, population dynamics, and more.
  • Understanding of context and assumptions often critical to solve these types of problems.

Open Problems

  • Open problems are unsolved mathematical issues.
  • Can be categorised as pure or applied problems.
  • The nature of open problems requires a high level of originality and creativity.

Recursive Problems

  • Recursive problems solve something based on previous results within the problem.
  • Useful in series, sequences and mathematical induction.
  • Understanding recursion is fundamental to solving these types of problems.

Geometric Problems

  • Geometric problems revolve around geometric figures and properties.
  • Can be purely theoretical or depend on measurements and the application of formulas.
  • Familiarity with geometric terms, concepts, theorems, and postulates is crucial.

Constraint Problems

  • Constraint problems involve conditions or limitations within the problem.
  • Evaluation of options within set boundaries is key to solutions.
  • Understanding how to work within constraints is central to solving these problems.

Graphing Problems

  • Graphing problems involve visualising relationships between variables.
  • Require understanding of coordinate geometry, functions, and calculus.
  • Integration of graphical and algebraic methods often leads to solutions.

Equation-based Problems

  • Equation-based problems involve the formulation and solution of equations.
  • Knowledge of various types of equations and methods to solve them is vital.
  • Understanding how to interpret solutionsets is equally crucial.

Probability Problems

  • Probability problems involve predicting uncertain outcomes.
  • Require understanding of probability theory, statistics, and combinatorics.
  • Methods can vary from simple counting principles to sophisticated statistical techniques.