13. Counting Using Recurrence Equations - Discrete Mathematics - Vol 2
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

13. Counting Using Recurrence Equations

13. Counting Using Recurrence Equations

The chapter introduces counting using recurrence equations, detailing how this technique simplifies counting problems in discrete mathematics and computer science. It explains the construction of recurrence relations and their solution methods, including iterative techniques. Furthermore, it explores linear homogeneous recurrence equations and emphasizes the uniqueness of solutions when provided with initial conditions.

10 sections

Enroll to start learning

You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

Navigate through the learning materials and practice exercises.

  1. 13
    Counting Using Recurrence Equations

    This section introduces the concept of counting through recurrence...

  2. 13.1
    Introduction To Counting Problems

    This section introduces the concept of using recurrence equations to solve...

  3. 13.2
    Example Of Bit Strings Without Consecutive 0's

    This section introduces the concept of counting bit strings that do not...

  4. 13.3
    Setting Up The Recurrence Equation

    This section introduces recurrence equations as a powerful counting...

  5. 13.4
    Initial Conditions For Recurrence Function

    This section introduces the concept of recurrence equations in counting...

  6. 13.5
    Solving Recurrence Equations

    This section introduces the concept of solving recurrence equations, a...

  7. 13.6
    General Methods For Solving

    This section introduces counting methods using recurrence equations and...

  8. 13.7
    Examples Of Linear Homogeneous Recurrence Equations

    This section discusses linear homogeneous recurrence equations, emphasizing...

  9. 13.8
    Uniqueness Of Solutions For Recurrence Equations

    This section focuses on the significance of uniqueness in the solutions of...

  10. 13.9
    Conclusion And Summary

    This section concludes the discussion on counting techniques using...

What we have learnt

  • Recurrence equations simplify many counting problems.
  • Various methods exist for solving recurrence equations, including iterative methods.
  • The uniqueness of solutions to recurrence equations depends on the provided initial conditions.

Key Concepts

-- Recurrence Equation
An expression that defines a sequence recursively by relating each term to preceding terms.
-- Initial Conditions
Specific values given at the start of a recurrence relation, which help to determine the unique solution of the equation.
-- Linear Homogeneous Recurrence Equation
A recurrence relation in which each term is a linear combination of previous terms, where the coefficients are constants.

Additional Learning Materials

Supplementary resources to enhance your learning experience.