Matrices
Matrices
Rosen 5th ed., 2.7
09/30/15
(c)2001-2003, Michae
1
Matrices
2.7 Matrices
A matrix is a rectangular array of
objects (usually numbers).
An mn (m by n) matrix has exactly m
Not
our
horizontal rows, and n vertical columns.
meaning!
Plura

Equivalence Relations
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,
and transitive.
Two elements that are related by an
equ

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
MCS 2010
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)

Functions
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
natural

Proof Methods
Basic Proof Methods
Rosen 5th ed., 1.5 & 3.1
09/30/15
(c)2001-2003, Michae
1
Proof Methods
Nature & Importance of Proofs
In mathematics, a proof is:
a correct (well-reasoned, logically valid) and complete
(clear, detailed) argument that ri

Week_3_Combinatorics
Combinatorics
Rosen 5th ed., 4.1-4.3, 4.6, & 6.5
21 slides, 1 lecture
Week_3_Combinatorics
Combinatorics
The study of the number of ways to put
things together into various combinations.
E.g. In a contest entered by 100 people,
how

Mathematics for
Computer Sciences
IF 11211
Course overview
Yaya Setiyadi
Course Description
This
is an introductory course in Discrete
Mathematics oriented toward Computer
Science. The course divides roughly into two:
Fundamental concepts of Mathematics:

Finite State Machines
(FSM)
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.
Al