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Class Notes for 6.042J at Massachusetts Institute of Technology (MIT)

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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 19: Discrete Mathematics

OC9068083 Page
13 Apr 2016
6
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 3: Axiomatic System, Pythagorean Theorem, Angle

OC9068081 Page
13 Apr 2016
3
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 8: Public-Key Cryptography, Coprime Integers, Boolean Satisfiability Problem

OC9068082 Page
13 Apr 2016
27
In 1977, three professors at mit proposed a highly secure crypto-system, called rsa, based on number theory. The purpose of the rds scheme is to transm
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 1: Perfect Number, Number Theory, Linear Combination

OC9068083 Page
13 Apr 2016
8
Number theory underlies modern cryptography, which is what makes secure online communication possible. Number theory also provides an excellent environ
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 4: Binary Relation, Partial Function, Total Relation

OC9068082 Page
13 Apr 2016
5
A function assigns an element of one set (the domain) to an element of another set (the codomain) The notation : a > b indicated that is a function wit
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 20: Pigeonhole Principle, Bijection, Disjoint Sets

OC9068084 Page
13 Apr 2016
6
Number of operations to update a data structure. This is the same as saying how many comparisons are needed to sort n items. This is the same as saying
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 22: Partially Ordered Set, If And Only If, Antisymmetry

OC9068082 Page
13 Apr 2016
21
The properties of the walk relation in dags. For any digraph, g, the walk relations g+ and g* are transitive. A binary relation, r, on a set, a, is tra
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 26: Directed Acyclic Graph, Antichain, Partially Ordered Set

OC9068086 Page
13 Apr 2016
5
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 18: Cumulative Distribution Function, Bernoulli Distribution, Random Variable

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13 Apr 2016
6
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 7: Generating Function, Fibonacci Number, Pigeonhole Principle

OC9068087 Page
13 Apr 2016
10
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 11: Conditional Expectation, Random Variable, Sample Space

OC9068082 Page
13 Apr 2016
9
The expectation or expected value of a random variable is a single number that reveals a lot about the behavior of the variable. The expectation of a r
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MIT6.042JAlbert MeyerFall

6.042J Lecture Notes - Lecture 12: Mathematical Induction, If And Only If, Graph Coloring

OC9068082 Page
13 Apr 2016
9
A bipartite graph is a graph whose vertices can be partitioned into two sets, l(g) and r(g), such that every edges has one endpoint in l(g) and one end
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