CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content...
Transcript of CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content...
![Page 1: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/1.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
CSI2101 Discrete Structures: Introduction
Lucia Moura
Winter 2010
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 2: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/2.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:
I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 3: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/3.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structures
I designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 4: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/4.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithms
I reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 5: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/5.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithms
I solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 6: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/6.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computer
I in particular, solving problems in information technology,i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 7: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/7.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 8: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/8.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 9: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/9.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking
2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 10: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/10.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking
3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 11: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/11.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking
4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 12: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/12.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)
5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 13: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/13.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking
6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 14: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/14.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 15: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/15.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Discrete Mathematics is essential to Computer Science!
The various aspects of discrete mathematics form the foundation for:I modelling computing structuresI designing programs and algorithmsI reasoning about programs and algorithmsI solving real-world problems using the computerI in particular, solving problems in information technology,
i.e. problems involving computers, communication, information.
Aspects of discrete mathematics: (David J. Hunter, Essential of Discrete Mathematics, 2009)
1 logical thinking2 relational thinking3 recursive thinking4 quantitative thinking (counting)5 analytical thinking6 applied thinking
Question: How these 5 aspects appear in the the activities listedabove?
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 16: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/16.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Logical Thinking
formal logic(symbolic manipulation of notation; logical not-thinking :-)))) )
propositional logicpropositional calculus allows us to make logical deductions formally
predicate logicmake a proposition to depend on a variable and we get a predicate;here the logical deductions include quantifiers (for all, there exists) infront of the predicates)
methods of proof: direct, by contraposition, by contradictionuse what you learned in formal/symbolic logic, to guide yourreasoning on mathematical proofs (written in paragraph form)
logic in programmingimperative programming: conditional statements (if-then-else, do-while)
logic programming languages (e.g. prolog): uses the rules of predicate logic
logic in circuits
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 17: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/17.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Logical Thinking
formal logic(symbolic manipulation of notation; logical not-thinking :-)))) )
propositional logicpropositional calculus allows us to make logical deductions formally
predicate logicmake a proposition to depend on a variable and we get a predicate;here the logical deductions include quantifiers (for all, there exists) infront of the predicates)
methods of proof: direct, by contraposition, by contradictionuse what you learned in formal/symbolic logic, to guide yourreasoning on mathematical proofs (written in paragraph form)
logic in programmingimperative programming: conditional statements (if-then-else, do-while)
logic programming languages (e.g. prolog): uses the rules of predicate logic
logic in circuits
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 18: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/18.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Logical Thinking
formal logic(symbolic manipulation of notation; logical not-thinking :-)))) )
propositional logicpropositional calculus allows us to make logical deductions formally
predicate logicmake a proposition to depend on a variable and we get a predicate;here the logical deductions include quantifiers (for all, there exists) infront of the predicates)
methods of proof: direct, by contraposition, by contradictionuse what you learned in formal/symbolic logic, to guide yourreasoning on mathematical proofs (written in paragraph form)
logic in programmingimperative programming: conditional statements (if-then-else, do-while)
logic programming languages (e.g. prolog): uses the rules of predicate logic
logic in circuits
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 19: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/19.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Logical Thinking
formal logic(symbolic manipulation of notation; logical not-thinking :-)))) )
propositional logicpropositional calculus allows us to make logical deductions formally
predicate logicmake a proposition to depend on a variable and we get a predicate;here the logical deductions include quantifiers (for all, there exists) infront of the predicates)
methods of proof: direct, by contraposition, by contradictionuse what you learned in formal/symbolic logic, to guide yourreasoning on mathematical proofs (written in paragraph form)
logic in programmingimperative programming: conditional statements (if-then-else, do-while)
logic programming languages (e.g. prolog): uses the rules of predicate logic
logic in circuits
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 20: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/20.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Logical Thinking
formal logic(symbolic manipulation of notation; logical not-thinking :-)))) )
propositional logicpropositional calculus allows us to make logical deductions formally
predicate logicmake a proposition to depend on a variable and we get a predicate;here the logical deductions include quantifiers (for all, there exists) infront of the predicates)
methods of proof: direct, by contraposition, by contradictionuse what you learned in formal/symbolic logic, to guide yourreasoning on mathematical proofs (written in paragraph form)
logic in programmingimperative programming: conditional statements (if-then-else, do-while)
logic programming languages (e.g. prolog): uses the rules of predicate logic
logic in circuits
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 21: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/21.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Logical Thinking
formal logic(symbolic manipulation of notation; logical not-thinking :-)))) )
propositional logicpropositional calculus allows us to make logical deductions formally
predicate logicmake a proposition to depend on a variable and we get a predicate;here the logical deductions include quantifiers (for all, there exists) infront of the predicates)
methods of proof: direct, by contraposition, by contradictionuse what you learned in formal/symbolic logic, to guide yourreasoning on mathematical proofs (written in paragraph form)
logic in programmingimperative programming: conditional statements (if-then-else, do-while)
logic programming languages (e.g. prolog): uses the rules of predicate logic
logic in circuits
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 22: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/22.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functionsI relationsI partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.I Graphs: networks (communication, roads, social),
conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 23: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/23.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I sets
I functionsI relationsI partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.I Graphs: networks (communication, roads, social),
conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 24: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/24.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functions
I relationsI partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.I Graphs: networks (communication, roads, social),
conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 25: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/25.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functionsI relations
I partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.I Graphs: networks (communication, roads, social),
conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 26: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/26.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functionsI relationsI partial orderings
I graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.I Graphs: networks (communication, roads, social),
conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 27: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/27.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functionsI relationsI partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.I Graphs: networks (communication, roads, social),
conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 28: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/28.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functionsI relationsI partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.I Graphs: networks (communication, roads, social),
conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 29: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/29.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functionsI relationsI partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.I Graphs: networks (communication, roads, social),
conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 30: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/30.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functionsI relationsI partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tuple
I Dependency of task executions (partial ordering);topological sorting: order tasks respecting dependencies.
I Graphs: networks (communication, roads, social),conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 31: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/31.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functionsI relationsI partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.
I Graphs: networks (communication, roads, social),conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 32: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/32.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Relational Thinking
It deals with the following type of structures:
I setsI functionsI relationsI partial orderingsI graph theory
Question 1: what are each of these structures?
Question 2: give examples of situations where they can be applied incomputer science.
I Databases: table=relation; record=n-ary tupleI Dependency of task executions (partial ordering);
topological sorting: order tasks respecting dependencies.I Graphs: networks (communication, roads, social),
conflicts (timetabling, coloring maps),hierarquies (rooted trees), diagrams (binary relations).
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 33: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/33.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Recursive Thinking
Recurrence relationsRecursively defined sequences of numbers. e.g. Fibonacci sequence.
Recursive definitionse.g. binary trees, recursive geometry/fractals
Proofs by inductionProve that P (n) is true for all n ≥ 0:basis: P (0) is true + induction step P (n)⇒ P (n + 1)Recursive data structurese.g. binary search trees
Recursive algorithmse.g. binary search, mergesort, solving towers of Hanoi.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 34: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/34.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Recursive Thinking
Recurrence relationsRecursively defined sequences of numbers. e.g. Fibonacci sequence.
Recursive definitionse.g. binary trees, recursive geometry/fractals
Proofs by inductionProve that P (n) is true for all n ≥ 0:basis: P (0) is true + induction step P (n)⇒ P (n + 1)Recursive data structurese.g. binary search trees
Recursive algorithmse.g. binary search, mergesort, solving towers of Hanoi.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 35: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/35.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Recursive Thinking
Recurrence relationsRecursively defined sequences of numbers. e.g. Fibonacci sequence.
Recursive definitionse.g. binary trees, recursive geometry/fractals
Proofs by inductionProve that P (n) is true for all n ≥ 0:basis: P (0) is true + induction step P (n)⇒ P (n + 1)
Recursive data structurese.g. binary search trees
Recursive algorithmse.g. binary search, mergesort, solving towers of Hanoi.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 36: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/36.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Recursive Thinking
Recurrence relationsRecursively defined sequences of numbers. e.g. Fibonacci sequence.
Recursive definitionse.g. binary trees, recursive geometry/fractals
Proofs by inductionProve that P (n) is true for all n ≥ 0:basis: P (0) is true + induction step P (n)⇒ P (n + 1)Recursive data structurese.g. binary search trees
Recursive algorithmse.g. binary search, mergesort, solving towers of Hanoi.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 37: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/37.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Recursive Thinking
Recurrence relationsRecursively defined sequences of numbers. e.g. Fibonacci sequence.
Recursive definitionse.g. binary trees, recursive geometry/fractals
Proofs by inductionProve that P (n) is true for all n ≥ 0:basis: P (0) is true + induction step P (n)⇒ P (n + 1)Recursive data structurese.g. binary search trees
Recursive algorithmse.g. binary search, mergesort, solving towers of Hanoi.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 38: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/38.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Quantitative Thinking
counting,
combinations, permutations, arrangements,
the pigeonhole principle,
discrete probability,
counting operations in algorithms,
estimating growth of functions, big-Oh notation.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 39: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/39.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Quantitative Thinking
counting,
combinations, permutations, arrangements,
the pigeonhole principle,
discrete probability,
counting operations in algorithms,
estimating growth of functions, big-Oh notation.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 40: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/40.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Quantitative Thinking
counting,
combinations, permutations, arrangements,
the pigeonhole principle,
discrete probability,
counting operations in algorithms,
estimating growth of functions, big-Oh notation.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 41: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/41.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Quantitative Thinking
counting,
combinations, permutations, arrangements,
the pigeonhole principle,
discrete probability,
counting operations in algorithms,
estimating growth of functions, big-Oh notation.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 42: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/42.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Quantitative Thinking
counting,
combinations, permutations, arrangements,
the pigeonhole principle,
discrete probability,
counting operations in algorithms,
estimating growth of functions, big-Oh notation.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 43: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/43.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Quantitative Thinking
counting,
combinations, permutations, arrangements,
the pigeonhole principle,
discrete probability,
counting operations in algorithms,
estimating growth of functions, big-Oh notation.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 44: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/44.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Analytical Thinking
Apply previous tools to analyze problems of interest such as:
I Writing programs that are correct.software engineering tools: testing versus verification.
F loop invariants,F program correctness and verification.
I Writing algorithms that are efficient.
F algorithm complexity,F analysis of algorithms.
Question: How previous tools can be applied in each of the aboveareas?
I This question will be answered more fully by the studies in this course.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 45: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/45.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Analytical Thinking
Apply previous tools to analyze problems of interest such as:
I Writing programs that are correct.software engineering tools: testing versus verification.
F loop invariants,F program correctness and verification.
I Writing algorithms that are efficient.
F algorithm complexity,F analysis of algorithms.
Question: How previous tools can be applied in each of the aboveareas?
I This question will be answered more fully by the studies in this course.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 46: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/46.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Analytical Thinking
Apply previous tools to analyze problems of interest such as:
I Writing programs that are correct.software engineering tools: testing versus verification.
F loop invariants,
F program correctness and verification.
I Writing algorithms that are efficient.
F algorithm complexity,F analysis of algorithms.
Question: How previous tools can be applied in each of the aboveareas?
I This question will be answered more fully by the studies in this course.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 47: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/47.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Analytical Thinking
Apply previous tools to analyze problems of interest such as:
I Writing programs that are correct.software engineering tools: testing versus verification.
F loop invariants,F program correctness and verification.
I Writing algorithms that are efficient.
F algorithm complexity,F analysis of algorithms.
Question: How previous tools can be applied in each of the aboveareas?
I This question will be answered more fully by the studies in this course.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 48: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/48.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Analytical Thinking
Apply previous tools to analyze problems of interest such as:
I Writing programs that are correct.software engineering tools: testing versus verification.
F loop invariants,F program correctness and verification.
I Writing algorithms that are efficient.
F algorithm complexity,F analysis of algorithms.
Question: How previous tools can be applied in each of the aboveareas?
I This question will be answered more fully by the studies in this course.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 49: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/49.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Analytical Thinking
Apply previous tools to analyze problems of interest such as:
I Writing programs that are correct.software engineering tools: testing versus verification.
F loop invariants,F program correctness and verification.
I Writing algorithms that are efficient.F algorithm complexity,
F analysis of algorithms.
Question: How previous tools can be applied in each of the aboveareas?
I This question will be answered more fully by the studies in this course.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 50: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/50.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Analytical Thinking
Apply previous tools to analyze problems of interest such as:
I Writing programs that are correct.software engineering tools: testing versus verification.
F loop invariants,F program correctness and verification.
I Writing algorithms that are efficient.F algorithm complexity,F analysis of algorithms.
Question: How previous tools can be applied in each of the aboveareas?
I This question will be answered more fully by the studies in this course.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 51: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/51.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Analytical Thinking
Apply previous tools to analyze problems of interest such as:
I Writing programs that are correct.software engineering tools: testing versus verification.
F loop invariants,F program correctness and verification.
I Writing algorithms that are efficient.F algorithm complexity,F analysis of algorithms.
Question: How previous tools can be applied in each of the aboveareas?
I This question will be answered more fully by the studies in this course.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 52: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/52.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Analytical Thinking
Apply previous tools to analyze problems of interest such as:
I Writing programs that are correct.software engineering tools: testing versus verification.
F loop invariants,F program correctness and verification.
I Writing algorithms that are efficient.F algorithm complexity,F analysis of algorithms.
Question: How previous tools can be applied in each of the aboveareas?
I This question will be answered more fully by the studies in this course.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 53: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/53.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Applied Thinking
Making the bridge between the mathematical tools and problems weneed to solve.
I problem solving skillsI modelling
Before using tools we need to learn the language and methods.
A lot of the course will focus on acquiring the mathematical skills.But we don’t want to lose sight of their use in applications.
Here we discuss some application problems illustrated in the followingslides by Prof. Zaguia (2008): IntroZaguia2008.pdf
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 54: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/54.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Applied Thinking
Making the bridge between the mathematical tools and problems weneed to solve.
I problem solving skills
I modelling
Before using tools we need to learn the language and methods.
A lot of the course will focus on acquiring the mathematical skills.But we don’t want to lose sight of their use in applications.
Here we discuss some application problems illustrated in the followingslides by Prof. Zaguia (2008): IntroZaguia2008.pdf
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 55: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/55.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Applied Thinking
Making the bridge between the mathematical tools and problems weneed to solve.
I problem solving skillsI modelling
Before using tools we need to learn the language and methods.
A lot of the course will focus on acquiring the mathematical skills.But we don’t want to lose sight of their use in applications.
Here we discuss some application problems illustrated in the followingslides by Prof. Zaguia (2008): IntroZaguia2008.pdf
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 56: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/56.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Applied Thinking
Making the bridge between the mathematical tools and problems weneed to solve.
I problem solving skillsI modelling
Before using tools we need to learn the language and methods.
A lot of the course will focus on acquiring the mathematical skills.But we don’t want to lose sight of their use in applications.
Here we discuss some application problems illustrated in the followingslides by Prof. Zaguia (2008): IntroZaguia2008.pdf
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 57: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/57.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Applied Thinking
Making the bridge between the mathematical tools and problems weneed to solve.
I problem solving skillsI modelling
Before using tools we need to learn the language and methods.
A lot of the course will focus on acquiring the mathematical skills.But we don’t want to lose sight of their use in applications.
Here we discuss some application problems illustrated in the followingslides by Prof. Zaguia (2008): IntroZaguia2008.pdf
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 58: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/58.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Why Discrete Mathematics ?
Applied Thinking
Making the bridge between the mathematical tools and problems weneed to solve.
I problem solving skillsI modelling
Before using tools we need to learn the language and methods.
A lot of the course will focus on acquiring the mathematical skills.But we don’t want to lose sight of their use in applications.
Here we discuss some application problems illustrated in the followingslides by Prof. Zaguia (2008): IntroZaguia2008.pdf
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 59: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/59.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Course Content Overview
Calendar description:
CSI2101 Discrete Structures (3,1.5,0) 3 cr. Discrete structures as theyapply to computer science, algorithm analysis and design. Predicate logic.Review of proof techniques; application of induction to computingproblems. Graph theory applications in information technology. Programcorrectness, preconditions, postconditions and invariants. Analysis ofrecursive programs using recurrence relations. Properties of integers andbasic cryptographical applications. Prerequisite: MAT1348.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 60: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/60.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Course Content Overview
Objectives:
Discrete mathematics form the foundation for computer science;it is essential in every branch of computing.
In MAT1348 (discrete mathematics for computing) you have beenintroduced to fundamental problems and objects in discretemathematics.
In CSI2101 (discrete structures) you will learn:I more advanced concepts in discrete mathematicsI more problem solving, modelling, logical reasoning and writing precise
proofsI how to apply concepts to various types of problems in computing:
analyse an algorithm, prove the correctness of a program, model anetwork problem with graphs, use number theory in cryptography, etc.
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 61: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/61.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Course Content Overview
Textbook
References:
Kenneth H. Rosen, Discrete Mathematics and Its Applications, SixthEdition, McGraw Hill, 2007.(same textbook as normally used for MAT1348; we will use differentsections!)
CSI2101 Discrete Structures, Winter 2010 Lucia Moura
![Page 62: CSI2101 Discrete Structures: IntroductionDiscrete Mathematics and Discrete Structures Course Content Overview CSI2101 Discrete Structures: Introduction Lucia Moura Winter 2010 CSI2101](https://reader034.fdocuments.us/reader034/viewer/2022052423/5f04e6bc7e708231d4104620/html5/thumbnails/62.jpg)
Discrete Mathematics and Discrete Structures Course Content Overview
Course Content Overview
Topic by topic outline: (approximate number of lectures, order may vary)
1 Introduction (1)
2 Propositionl logic (2)
3 Predicate logic (2)
4 Rules of inference/proof methods (2)
5 Basic number theory and applications (4)
6 Induction and applications. (4)Program correctness and verification (1)
7 Solving recurrence relations. Complexity of divide-and-conqueralgorithms. (3)
8 Graphs (3)
CSI2101 Discrete Structures, Winter 2010 Lucia Moura