CSE 1400 Applied Discrete Mathematics Handouts
Department of Computer Sciences College of Engineering Florida Tech Spring 2011
Abstract This file contains handouts covering topics in the class. Numbers Numeral Systems Conversion Modular Numbers Sets Boole
CSE 1400 Applied Discrete Mathematics Permutations
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Permutations
1
2 2 2
Cyclic Notation
Permutations Re-Order a Sequence Stirling Numbers of the First Kind Problems on Permutati
CSE 1400 Applied Discrete Mathematics Polynomials
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Polynomials
Constants
1
1 2 2
Linear Polynomials Quadratic Polynomials The Power Basis 3 The Binomial Theorem Taylor Polynomial
CSE 1400 Applied Discrete Mathematics Predicates
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Predicate Logic
1
7 7
Predicate Logic Inference Rules
Negation of Quantified Predicate Statements Reasoning about Quantification
CSE 1400 Applied Discrete Mathematics Recurrences
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Recurrence Equations
1
1 2 3 5 5 6 7
The Alice Recurrence Equation The Gauss Recurrence Equation
The Triangular Recurrence Equa
CSE 1400 Applied Discrete Mathematics Relations
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Relations and Their Graphs A Sampling of Relations
Equality Less than Divides 3 4 5 3 3
1 2
A Relation's Domain, Co-domain, and R
CSE 1400 Applied Discrete Mathematics Sets
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Set Basics Common Sets
1 3 3
4
Operations On Sets Cartesian Products Subset of a Set Cardinality of a Set Power Set of a Set 6
Binomia
CSE 1400 Applied Discrete Mathematics or MTH 2051 Discrete Mathematics Class Syllabus
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Abstract Student Name Attributes 1.* Calendar Events Type Includes Learns from Material Rea
CSE 1400 Applied Discrete Mathematics Orders
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Abstract Placing things in order is a common activity. Ordinal numbers: first, second, third, fourth, and so on are used to describe
A Course On Computing For Computing Student Learning Objective1
William Shoaff January 5, 2010
Name, Values, and Types: A name is a string over a finite alphabet. The name is used to write, pronounce, or call the value of something. Values can be organize
CSE 1400 Applied Discrete Mathematics Numbers
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Numbers
Integers
1
1
Natural Numbers 2 2 Integers Mod n Rational Numbers The Real Numbers Complex Numbers
3 5
Floating Point Number
WILLIAM SHOAFF
A COURSE O N M AT H E M AT I C S FOR COMPUTING
FLORIDA TECH
" A N D O U T O F T H E G RO U N D T H E L O R D G O D F O R M E D E V E RY B E A S T O F T H E F I E L D, A N D E V E RY F O W L O F T H E A I R ; A N D B R O U G H T T H E M U N
CSE 1400 Applied Discrete Mathematics Boolean Logic
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Control Structures Boolean Logic
Normal Forms
1
3
4 5 6
The Conditional Operator Complex Propositions Truth Tables 8 10 Logic
Theoretical Computer Science Cheat Sheet Definitions f (n) = O(g(n) f (n) = (g(n) f (n) = (g(n) f (n) = o(g(n)
n
Series
n
iff positive c, n0 such that 0 f (n) cg(n) n n0 . iff positive c, n0 such that f (n) cg(n) 0 n n0 . iff f (n) = O(g(n) and f (n) = (g
CSE 1400 Applied Discrete Mathematics Conversions Between Number Systems
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Conversion Algorithms: Decimal to Another Base
Conversion of Natural Numbers Conversion of Integers 3 4
CSE 1400 Applied Discrete Mathematics Equivalences
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Abstract Establishing equivalences is a common activity. When two things have a common property they can be called equivalent.
CSE 1400 Applied Discrete Mathematics Functions
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Functions
1
2 3 3 4 4 4
Counting Functions Onto Functions Cardinality Defined Inverse Function Function Composition One-to-One Fu
CSE 1400 Applied Discrete Mathematics Mathematical Induction
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Induction
1
1 7 8 10
Summations
The Tower of Hanoi and Mersenne Numbers
Rabbit Population Growth and Fibonacci Numbe
CSE 1400 Applied Discrete Mathematics Integer Functions
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Integer Functions
1 1
Floor, Ceiling, and Related Functions Number Theoretic Functions Problems on Integer Functions
Abst
CSE 1400 Applied Discrete Mathematics Logarithms and Exponents
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Logarithms
1
2 3
Properties of Logarithms Change of Base Formula
Computing the Logarithm of a Number Calculating t
CSE 1400 Applied Discrete Mathematics Modular Numbers
Department of Computer Sciences College of Engineering Florida Tech Fall 2011
Conversion Between Units Modular Numbers
Division mod n
1
3
5 6
Linear Congruence Equations Relatively Prime Numbers Extend
CSE 1400 Applied Discrete Mathematics Algorithms
Department of Computer Sciences College of Engineering Florida Tech Spring 2011
1
1.1 1.2
Algorithms
Basic Sums
1
1 2
Abstract
Horner's Rule
There are many algorithms useful in computing.
1
Algorithms
1.1 H