Certificate of Achievement
has completed the following course:
Combinatorics: Strategies and Methods for Counting
Combinatorics is an area of mathematics primarily concerned with counting. This online course, allowed you to discover a simple and efficient method to translate a combinatorial problem into counting the elements of a reference mathematical structure. It also taught how to learn basic counting principles, and be able to explain the most frequent errors in their misuse.
4 weeks, 6 hours per week
Carlo Mariconda
Professor of Mathematical Analysis
University of Padova
Alberto Tonolo
Professor of Algebra
University of Padova
Transcript
Learning outcomes
- Apply the principles of combinatorics to solve the basic combinatorial problems
- Model some real life counting problems into that of counting precise mathematical structures
- Identify the mathematical structure which lies besides a combinatorial problem: sequences, collections, sharings, compositions, partitions, derangements.
- Identify the principle to face a combinatorial problem: bijiection, multiplication, division
- Calculate the probability of an event when the sample space is composed by equiprobable elementary events
- Calculate the number of possible outcomes of an aleatory experiment
- Calculate the number of sequences of prescribed length, with or without repetitions, from a given alphabet
- Calculate the number of sets of given cardinality
- Calculate the number of partitions of a given set in a prescribed number of subsets
- Calculate the number of permutations of a sequence without repetitions
- Calculate the number of distributions of distinguishable/indistinguishable objects in a given number of numbered boxes (possibly empty)
- Calculate the number of distributions of distinguishable/indistinguishable objects in a given number of numbered non-empty boxes
Syllabus
- Convert counting problems into precise mathematical models
- Count the basic combinatorial objects like sequences and collections
- Applications on counting anagrams, derangements of a sequence (hats problem)
- Count card shuffles and understand astonishing magic tricks
- Basic probabilities (birthday problem)
- Algebraic tools that allow to solve subtle combinatorial problems
Issued on 8th October 2023
The person named on this certificate has completed the activities in the transcript above. For more information about Certificates of Achievement and the effort required to become eligible, visit futurelearn.com/proof-of-learning/certificate-of-achievement.
This certificate represents proof of learning. It is not a formal qualification, degree, or part of a degree.