Discrete Mathematics - Vol 2 | 13. Counting Using Recurrence Equations by Abraham | Learn Smarter
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge
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.

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

  • 13

    Counting Using Recurrence Equations

    This section introduces the concept of counting through recurrence equations, highlighting their significance in simplifying counting problems in discrete mathematics.

    Learning Practice

  • 13.1

    Introduction To Counting Problems

    This section introduces the concept of using recurrence equations to solve counting problems in discrete mathematics.

    Learning Practice

  • 13.2

    Example Of Bit Strings Without Consecutive 0's

    This section introduces the concept of counting bit strings that do not contain two consecutive zeros using recurrence equations.

    Learning Practice

  • 13.3

    Setting Up The Recurrence Equation

    This section introduces recurrence equations as a powerful counting technique in discrete mathematics, illustrated through examples and problem-solving strategies.

    Learning Practice

  • 13.4

    Initial Conditions For Recurrence Function

    This section introduces the concept of recurrence equations in counting problems and establishes the necessary initial conditions for their solutions.

    Learning Practice

  • 13.5

    Solving Recurrence Equations

    This section introduces the concept of solving recurrence equations, a crucial tool in counting problems within discrete mathematics.

    Learning Practice

  • 13.6

    General Methods For Solving

    This section introduces counting methods using recurrence equations and provides foundational techniques for solving these equations in discrete mathematics.

    Learning Practice

  • 13.7

    Examples Of Linear Homogeneous Recurrence Equations

    This section discusses linear homogeneous recurrence equations, emphasizing their formulation and solving techniques through examples.

    Learning Practice

  • 13.8

    Uniqueness Of Solutions For Recurrence Equations

    This section focuses on the significance of uniqueness in the solutions of recurrence equations, particularly in the context of linear homogeneous equations with appropriate initial conditions.

    Learning Practice

  • 13.9

    Conclusion And Summary

    This section concludes the discussion on counting techniques using recurrence equations, summarizing the key points about recurrence equations and their applications in discrete mathematics.

    Learning Practice

References

ch35.pdf

Class Notes

Memorization

What we have learnt

  • Recurrence equations simpli...
  • Various methods exist for s...
  • The uniqueness of solutions...

Final Test

Revision Tests