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Sky lee

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The foundations: logic and proof

Atomic proposition,

Compound propositions,

Conditional contrapositive invers...

147
cards

Chapter one, Revision Examples.

Let s x be the predicate x is a s...,

Let s x be the predicate x is a s...,

Let s x be the predicate x is a s...

19
cards

Basic Structures: Sets, Functions, Sequences, Sums, and Matrices

Set intuitive definition,

Notations to represent set,

Roaster method

112
cards

2.4 Sequences and Summations

Sequence,

Notation of sequence,

How do we describe sequences

27
cards

2.5 Cardinality of Sets

Same cardinality,

What does cardinality of infinite...,

Define what it means for oneset t...

19
cards

2.6 Matrices

Matrix what are they when are the...,

Some terminology about matrices,

Matrix addition

29
cards

9.1 Relations and their properties

Binary relation,

Binary relation notation,

Representation of relations at en...

20
cards

9.2 n-ary Relations and their Applications

N ary relations and its degree an...,

A b mod m,

The time required to manipulate i...

34
cards

9.3 Representing Relations

Representing relations using matr...,

Representation of reflexive relat...,

What can u say about matrix of a ...

12
cards

9.4 Closure Of Relations

Closure of relation,

Reflexive closure,

Suppose that relations s and t bo...

19
cards

3.1 Algorithms

Algorithm,

Pseudocode,

Algorithm vs pseudocode

33
cards

Appendix 3 Pseudocode:

Pseudocode,

Procedure statements,

Assignment and other types of sta...

8
cards

3.2 The growth of functions

The time required to solve aprobl...,

The growth of functions is often ...,

What are the constants c and k in...

26
cards

3.3 Complexity Of Algorithms

How can the efficiency of an algo...,

What do you know about computaion...,

Time complexity how is it describ...

22
cards

4.1 Divisibility and Modular Arithmetic

Number theory,

Modular arithmetic,

Division definition and terms mul...

17
cards

4.2 Integer Representations and Algorithms

Theorem 1of allowed bases base b ...,

Common bases in comp sci,

Hexadecimal and binary interconve...

14
cards

4.3 Primes and Greatest Common Divisors

What is prime and composite whats...,

The fundamental theorem of arithm...,

Theorem 2 show given integer is p...

34
cards

4.4 Solving Congruences

Linear congruence,

Inverse of a modulo m,

Theroem 1 about inverse of a modu...

24
cards

4.5 Applications of Congruences

Hashing functions ideal hashing f...,

What is one unwanted charactersti...,

Linear probing function

14
cards

4.6 Cryptography

Encryption,

Caesar cipher,

Decryption

29
cards

5.1 Mathematical Induction

How is mathematical induction goi...,

Vocab warning use of words,

Principle of mathematical inducti...

17
cards

6.1 The Basics Of Counting

The product rule,

An extended version of the produc...,

The sum rule

12
cards

6.2 The Pigeonhole Principle

The pigeonhole principleand prove...,

Corollary about functions from pi...,

Show that for every integer n the...

10
cards

6.3 Permutations and Combinations

A permutation of a set of n disti...,

R permutation,

Theoremwe now use the product rul...

14
cards

6.4 Binomial Coefficients and Identities

Binomial expression,

Obtain expansion of x y 3 using c...,

Theorem 1 the binomial theorem

14
cards

6.5 Generalized Permutations and Combinations

Thm 1 the number of r permutation...,

Theorem 2 r combinations from a s...,

Permutations with indistinguishab...

16
cards

6.6 Generating Permutations and Combinations

Generating the next permutation i...,

Generating the next permutation i...,

Generating the next permutation i...

8
cards

9.5 Equivalence Relations

Equivalence relation when do they...,

Definition notion of equivalent e...,

For the notion of equivalent elem...

8
cards

9.6 Partial Orderings

Partial order poset,

Denote that a b r in an arbitrary...

2
cards

10.1 Graphs and Graph Models

Graph visualize it,

What is an edge,

Finite and infinite graphs

13
cards

10.2 Graph Terminology and Special Types of Graphs

Adjacent vertices incident edge,

Neighbourhood,

Degree of vertex

34
cards

10.3 Representing Graphs and Graph Isomorphism

When are 2 graphs isomorphic,

Representing graphs 1032,

Adjacency matrix for a graph how ...

12
cards

10.4 Connectivity

Definition 1 paths hints what is ...,

When it is not necessary to disti...,

Walk simple path and in this case...

27
cards

10.5 Euler and Hamilton Paths

Euler circuits and euler paths,

Necessary and sufficient conditio...,

Algorithm 1 constructing euler ci...

18
cards

10.6 Shortest-Path Problems

Weighted graphs length in these g...,

Theory of dijkstra s algorithmdo ...,

Algorithm 1 dijkstra s algorithm

7
cards

10.7 Planar Graphs

Planar graph planar representatio...,

The thickness of a graph crossing...,

Applications of planar graphs

13
cards

10.8 Graph Coloring

Dual graph of a map,

Graph coloring definition 1,

Definition 2 chromatic number

13
cards

11.1 Introduction to trees

Trees introduction,

Definition 1 tree,

Forests

23
cards

11.2 Applications of Trees

Binary search trees,

Algorithm 1 locating an item in o...,

The complexity of locating or add...

14
cards

7.1 An intro to Discrete Probability

Probability vocab,

Experiment,

Sample space and event

7
cards

7.2 Probability theory

Let s be the sample space of an e...,

What if the sample space is infinite,

Probability distribution

25
cards

7.3 Baye's theorem

Bayes theorem derive it solve exa...,

Generalized bayes theorem,

Bayesian spam filter

7
cards

7.4 Expected Value and Variance

What is expected value what infor...,

Definition 1 expected value,

When there are infinitely many el...

19
cards

11.3 Tree traversal

0
cards

discrete math, kenneth rosen

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