Combinatorics Unit
The first combinatorial problems were studied by ancient Indian, Arabian, and Greek mathematicians. Interest in the subject increased during the 19th and 20th century, together with the development of graph theory and problems like the four color theorem. Some of the leading mathematicians to study combinatorics included Blaise Pascal (1623 – 1662), Jacob Bernoulli (1654 – 1705) and Leonhard Euler (1707 – 1783).
Combinatorics also has many applications in other areas of mathematics, including graph theory, coding and cryptography, and probability. 
Lecture Notes & Other Resources
TENTATIVE SCHEDULE FOR THE UNIT
Combinatorics  Day 1
Introduction to the Partition Function P(n)
The HardyRamanujan Asymptotic Partition Formula
An Online Partition Number Generator
G.H. Hardy and Ramanujan Research Project
MOVIE TRAILER: The Man Who Knew Infinity
The Man Who Knew Infinity: A Life of the Genius Ramanujan is a biography of the Indian mathematician Srinivasa Ramanujan. The movie gives a detailed account of his upbringing in India, his mathematical achievements, and his mathematical collaboration with English mathematician G. H. Hardy.
Combinatorics  Day 1
Introduction to the Partition Function P(n)
The HardyRamanujan Asymptotic Partition Formula
An Online Partition Number Generator
G.H. Hardy and Ramanujan Research Project
MOVIE TRAILER: The Man Who Knew Infinity
The Man Who Knew Infinity: A Life of the Genius Ramanujan is a biography of the Indian mathematician Srinivasa Ramanujan. The movie gives a detailed account of his upbringing in India, his mathematical achievements, and his mathematical collaboration with English mathematician G. H. Hardy.
Combinatorics  Day 2
Introduction to Series and Summation Notation
VIDEO: Brief Introduction to Summation Notation
VIDEO: Summation (Sigma) Notation on the TI84 Graphing Calculator
Series and Summation Worksheet
Combinatorics  Day 3
Introduction to Factorials, Double Factorials, Triple Factorials, Quadruple Factorials, and Superfactorials
Factorials Worksheet
Combinatorics  Day 4
Permutations & Combinations
VIDEO: Factorials, Permutations, and Combinations on the TI84 Graphing Calculator
Sierpinski Triangle and Fibonacci Sequence Research Project
Combinatorics  Day 5
A Look At Pascal's Triangle
Pascal's Triangle
A Blank Pascal's Triangle
VIDEO: The Mathematical Secrets of Pascal's Triangle
VIDEO: Dissecting Hypercubes with Pascal's Triangle
Combinatorics  Day 6
Sequences Research Project
Combinatorics  Day 7 The Lazy Caterer's Sequence Activity Large Circles Small Circles A Visual of The Lazy Caterer's Sequence 

