1. CSC 1300 – Discrete Structures
CSC Dr Papalaskari - Villanova University

2. CSC 1300 - Dr Papalaskari - Villanova University
Discrete Structures
Mathematical concepts that support computing:
sets
functions and relations
sequences
summations
logic
proofs, including mathematical induction
recurrences
elementary combinatorics
matrices
trees
graphs
Much of the teaching and activities aim to develop the ability to read and write valid mathematical arguments.
CSC Dr Papalaskari - Villanova University

3. What is “discrete” about Discrete Structures?
The word "discrete” by definition means distinct or separate entity. Therefore, Discrete Mathematics deals mainly with the analysis of a finite collections of objects. In other words, it is used whenever objects are counted and when a process involving a finite number of steps areanalyzed. Discrete Math is often referred to as Finite Mathematics.
Listed below are just some of the computing topics that are finite by nature and require the concepts of Discrete Mathematics:
Algorithms
Data structures
Databases
Operating Systems
Computer Security
Digital imaging
Unlike Calculus, Discrete Mathematics is not concerned with infinite processes and does not support the notion of continuity. While in computing we sometimes "witness" infinite processes, in reality the need is for finite processing.
CSC Dr Papalaskari - Villanova University

4. Examples of problems solved using discrete structures
How many ways are there to choose a valid password?
How can it be proven that a sorting algorithm correctly sorts a list?
Is there a link between two computer systems in a network?
How many habitats do you need to create in a zoo so that animals don’t eat each other?
CSC Dr Papalaskari - Villanova University

5. CSC 1300 - Dr Papalaskari - Villanova University
Course organization
Approximately one chapter/week
Before Tuesday:
write up solutions to problems assigned the previous week
read intro section of next Chapter, do practice exercises
Tuesday in class: do more exercises, in groups
Before Thursday: read rest of chapter, do “Try this” exercises
Thursday in class: present and discuss solutions
CSC Dr Papalaskari - Villanova University

6. CSC 1300 - Dr Papalaskari - Villanova University
Course organization
Before the first day (typically a Tuesday), you will read assigned sections of the text and do the "Check Yourself" problems.
You may work with your friends and you may (should!) post questions on Piazza. Active participation includes following the discussions on Piazza asking questions, and also answering questions when you can. If a question is raised and does not get a complete answer online, it will be addressed in the following class. However, if you come to class without understanding something, but have not posted or commented on the question, you are neglecting part of your responsibility. 
At the beginning of each class period, we will address any questions posed on Piazza and not sufficiently answered. Then, a random member of the class will present a problem from the set that were to have been done before class.
Next, the class will work in groups of 3 or 4 on problems from the book.
Finally, there will be an introduction to the next topic and an assignment of the next reading and problem set. 
Once a week, you will be assigned a problem set. These assignments will consist of problems similar to the ones we worked on in class and will be due the following week. 
CSC Dr Papalaskari - Villanova University

7. Four short exams (about 40 minutes):
Tuesday, September 17
Thursday, October 10
Tuesday, November 5
Thursday, December 5
CSC Dr Papalaskari - Villanova University

8. CSC 1300 - Dr Papalaskari - Villanova University
An old quote
A priest asked: What is Fate, Master?  And he answered:  It is that which gives a beast of burden its reason for existence.  It is that which men in former times had to bear upon their backs.  It is that which has caused nations to build byways from City  to City upon which carts and coaches pass, and alongside which inns have come to be built to stave off Hunger, Thirst and Weariness.  And that is Fate? said the priest.  Fate...I thought you said Freight, responded the Master.  That's all right, said the priest. I wanted to know what Freight was too.  - Kehlog Albran
Source unknown: This quote appeared as one of the “fortunes” displayed by the fortune cookie program on old unix systems (“fortune” was a program that ran automatically every time you logged out of the system and displayed a random, pithy saying.
CSC Dr Papalaskari - Villanova University