recurrence relations
Sequence-defining equations recursively
A recurrence relation defines each term in a sequence using previous terms: the Fibonacci sequence follows the recurrence relation F(n) = F(n-1) + F(n-2).
Solving recurrence relations—finding a closed-form formula—is fundamental in computer science for analyzing algorithm efficiency and in mathematics for modeling growth patterns.
The recurrence relation for factorial is n! = n × (n-1)!
Pisan mathematician, numeral importer
- geometric progressionSeries multiplying by constant
- factorialDescending multiplication of integers
- Stirling numbersCounts set partitions or permutation cycles
- generating functionsPower series encoding sequences
Alike in composition throughout
- nonhomogeneousNot uniform in structure
- initial conditionsState at time zero
- boundary conditionsValues specified at limits
- iterationRepeated procedural pass
Organizing data systematically
- divide and conquerOvercome by fragmenting opposition
- bottom-upStarting from fundamentals
- top-downDirected from highest level
- quicksortRecursive partitioning sort method
Recursion's stopping condition
- well-orderingOrdering with guaranteed minimums
- verificationProving something accurate
Fibonacci
Pisan mathematician, numeral importer
- geometric progressionSeries multiplying by constant
- factorialDescending multiplication of integers
- Stirling numbersCounts set partitions or permutation cycles
homogeneous
Alike in composition throughout
- nonhomogeneousNot uniform in structure
- initial conditionsState at time zero
- boundary conditionsValues specified at limits
tabulation
Organizing data systematically
- divide and conquerOvercome by fragmenting opposition
- bottom-upStarting from fundamentals
- top-downDirected from highest level
base case
Recursion's stopping condition
- well-orderingOrdering with guaranteed minimums
- verificationProving something accurate
- combinatoricspermutation, combinations, combination, counting, arrangements
- discrete mathcombinatorics, graph theory, set theory, number theory, proofs
- Algorithm Analysisruntime, running time, growth rate, complexity, linear
- mathematical functionssine function, exponential function, logarithm, trigonometric functions, linear functions
- continued fractions
- finite differences
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