University Discrete Math Recurrence Relations and Advanced Counting — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 4 definitions and 5 theorems, 5 worked examples, 1 diagram, in 11 printable pages. This page lists what the notes cover. The notes themselves come with the University Discrete Math bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Recurrence Relations and Advanced Counting — what the notes cover
6 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Modelling a count by a recurrence
- Definition — Recurrence relation and initial conditions
- Theorem — Counting a set by a case split
Also in this section: 1 worked example, 1 note on method and common errors.
Linear recurrences with distinct characteristic roots
- Definition — Linear homogeneous recurrence with constant coefficients
- Theorem — Solving a degree-two recurrence with distinct roots
Also in this section: 1 worked example, 1 note on method and common errors.
Linear recurrences with a repeated characteristic root
- Definition — Repeated characteristic root
- Theorem — Solving a degree-two recurrence with a repeated root
Also in this section: 1 worked example, 1 note on method and common errors.
The inclusion-exclusion principle
- Theorem — The inclusion-exclusion principle
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Derangements and onto functions
- Definition — Derangement
- Theorem — Counting onto functions and derangements
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Discrete Math Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Recurrence Relations and Advanced Counting practice worksheet is free and stays free.
Every University Discrete Math topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Discrete Math units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
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Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Recurrence Relations and Advanced Counting practice worksheet About the Recurrence Relations and Advanced Counting unit test