Rosen 5th ed., 2.7
A matrix is a rectangular array of
objects (usually numbers).
An mn (m by n) matrix has exactly m
horizontal rows, and n vertical columns.
Equivalence relations are used to relate
objects that are similar in some way.
Definition: A relation on a set A is called an
equivalence relation if it is reflexive, symmetric,
Two elements that are related by an
The Fundamentals of Logic
Rosen 5th ed., 1.1
Foundations of Logic
(1.1-1.3, ~3 lectures)
Mathematical Logic is a tool for working with
elaborate compound statements. It includes:
A formal language for expressing them.
A concise notation for writing them
Predicate Logic and Quantifiers
5 Oktober 2010
Topic #3 Predicate Logic
Predicate Logic (1.3)
Predicate logic is an extension of
propositional logic that permits concisely
reasoning about whole classes of entities.
Propositional logic (recall)
Rosen 5th ed., 1.8
On to section 1.8 Functions
From calculus, you are familiar with the
concept of a real-valued function f,
which assigns to each number xR a
particular value y=f(x), where yR.
But, the notion of a function can also be
Basic Proof Methods
Rosen 5th ed., 1.5 & 3.1
Nature & Importance of Proofs
In mathematics, a proof is:
a correct (well-reasoned, logically valid) and complete
(clear, detailed) argument that ri
Rosen 5th ed., 4.1-4.3, 4.6, & 6.5
21 slides, 1 lecture
The study of the number of ways to put
things together into various combinations.
E.g. In a contest entered by 100 people,
is an introductory course in Discrete
Mathematics oriented toward Computer
Science. The course divides roughly into two:
Fundamental concepts of Mathematics:
Finite State Machines
Week 14 Session 1
January 8th 2008
Computers as Transition Functions
A computer (or really any physical system) can be
modeled as having, at any given time, a specific state
sS from some (finite or infinite) state space S.