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Combinatorics: Strategies and Methods for Counting

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$10

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Course Features

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Duration

4 weeks

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Delivery Method

Online

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Available on

Lifetime Access

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Accessibility

Mobile, Desktop

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Language

English

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Subtitles

English

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Level

Intermediate

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Effort

6 hours per week

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Teaching Type

Self Paced

Course Description

Combinatorics refers to mathematics that focuses primarily on counting. Combinatorial problems can arise in many areas, including algebra, probability theory and topology. This free online course in combinatorics will show you how to convert a combinatorial problem into the counting of elements in a reference mathematical structure. You will learn the basics of counting and how to identify common errors in their misuse. You'll find that combinatorics doesn't seem as hard as you think.

Course Overview

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International Faculty

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Instructor-Moderated Discussions

Skills You Will Gain

What You Will Learn

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Apply the principles of combinatorics to solve the basic combinatorial problems

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Model some real life counting problems into that of counting precise mathematical structures

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Identify the mathematical structure which lies besides a combinatorial problem: sequences, collections, sharings, compositions, partitions, derangements

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Identify the principle to face a combinatorial problem: bijiection, multiplication, division

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Calculate the probability of an event when the sample space is composed by equiprobable elementary events

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Calculate the number of possible outcomes of an aleatory experiment

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Calculate the number of sequences of prescribed length, with or without repetitions, from a given alphabet

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Calculate the number of sets of given cardinality

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Calculate the number of partitions of a given set in a prescribed number of subsets

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Calculate the number of permutations of a sequence without repetitions

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Calculate the number of distributions of distinguishable-indistinguishable objects in a given number of numbered boxes (possibly empty)

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Calculate the number of distributions of distinguishable-indistinguishable objects in a given number of numbered non-empty boxes

Target Students

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This course is ideal for anyone interested in mathematical problems, with a basic background in precalculus

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It would be useful for anyone wanting to study or work in mathematics, or anyone who wants to develope their critical thinking and problem-solving skills

Course Instructors

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Alberto Tonolo

Instructor

I am a professor of algebra at the University of Padova and I teach at the science and engineering faculties. I like very much math and classical music.
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Carlo Mariconda

Instructor

I am professor of mathematical analysis at the University of Padova. Among my interests: magic, tango, photography, innovative teaching, technology and e-learning.
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$10

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