Lecture 1: What is Discrete Math?

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Taught by ArsDigita
  • Currently 4.0/5 Stars.
16245 views | 2 ratings
Lesson Summary:

In this introductory lesson on discrete math, the focus is on the common thread of counting that runs through disparate fields like graph theory, combinatorics, and logic. The class is about tackling hard counting problems, sometimes dealing with things that appear to be separate but are actually the same. The lecture concludes with an example of a proof by contradiction, a clever way to show that the square root of 2 can't be written as a fraction, and the importance of convincing others that something is true through a rigorous argument.

Lesson Description:

Learn what discrete math is, what problems are solved in this course, and what implications they have.

More information about this course:
http://www.aduni.org/courses/discrete
Licensed under Creative Commons Attribution ShareAlike 2.0:
http://creativecommons.org/licenses/by-sa/2.0/

Additional Resources:
Questions answered by this video:
  • What is discrete math?
  • What topics are covered in discrete math?
  • What are some example problems in counting or combinatorics?
  • How do you find the number of pins in a bowling alley lane with n rows??
  • How many possible binary trees are there with n nodes?
  • How many ways are there to multiply n square matrices?
  • What is the difference between continuous and discrete mathematics?
  • How can you show that two combinatorics problems are identical?
  • What is a proof and how do you prove things in discrete math?
  • What is the proof that the square root of 2 is irrational by contradiction?
  • What is Euclid's proof by contradiction that there are an infinite number of prime numbers?
  • How many pairs of people can you form in a group of n people?
  • What is the formula for the nth triangle number?
  • What is a proof by induction and how do you prove something by induction?
  • What is the geometric proof of the formula for the nth triangular number?
  • How do you add up all the numbers from 1 to 100 or 1 to n?
  • If you cut a pancake n times, how many pieces do you get?
  • Why does a proof by induction work?
  • What is Boolean Algebra?
  • How do you write formal logic statements?
  • How do and, or, not, and implies work in logic?
  • What is a truth table and how do you make one?
  • How do you write, simplify, and test compound logic statements?
  • What are some equivalence statements in logic?
  • What are the distributive, commutative, and associative rules of logic?
  • What are DeMorgan's Laws of logic?
  • How do you prove two logical statements are equivalent using truth tables?
  • Where can I find a Computer Science Discrete Math course?
  • Staff Review

    • Currently 4.0/5 Stars.
    This lecture does a great job of explaining exactly what discrete math is, what it means, and what types of problems will be tackled in this course. Some actual problems are shown, and the main ideas of this course are laid out very plainly as well as some basic, famous proofs. This is a wonderful introduction to Discrete Mathematics that every math major should watch.
  • JMP92

    • Currently 4.0/5 Stars.
    Great overview of the course.