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Combinatorics: Strategies and Methods for Counting

University of Padova via FutureLearn

Overview

See combinatorics made simple and how to avoid errors in counting principles

Combinatorics is an area of mathematics primarily concerned with counting. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry.

On this free online combinatorics course, you’ll discover a simple and efficient method to translate a combinatorial problem into counting the elements of a reference mathematical structure.

You’ll learn basic counting principles, and be able to explain the most frequent errors in their misuse. Ultimately, you’ll discover that combinatorics isn’t as difficult as it seems.

Hear from our courses team

You can sign up at any time. However, if you’d like to take advantage of feedback from the educators and your mentors, you can do so within the following periods:

June 1 - July 15

December 1 - January 15

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

Syllabus

  • How and what to count
    • Welcome to the course
    • The basic objects of combinatorics
    • Distribution of objects
    • The basic principles of combinatorics
    • Uniform probability
    • Test yourself
  • Counting sequences and collections
    • Counting sequences
    • Counting collections without repetitions
    • Counting arbitrary collections and compositions
    • Constraints on collections, compositions, and sequences
    • Test yourself
  • The Inclusion/Exclusion Principle and its applications
    • The inclusion/exclusion principle
    • The inclusion/exclusion principle for intersection of sets
    • Distribution of distinct objects into distinguishable boxes and derangements
    • Distribution of distinct objects into undistinguishable boxes.
    • Test yourself
  • Counting with formal power series
    • Formal power series
    • Advanced Combinatorics
    • Test yourself

Taught by

Carlo Mariconda

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