• GIT: source code development, versioning, distribution and submission

  • Online tutorial
  • Download git
  • Git Service

• RUBY: an object-oriented programming language used for experimentation

  • Live online, Download
  • Tutorial, Introduction, Online course

• LaTeX: documentation platform to produce PDF files

  • Online service
  • Thai tutorial, Thai manual
  • LaTeX software

• yEd: Diagram editor for illustrating concepts, relationships and networks

  • Download yEd
  • Online version

git clone https://gitlab.com/rbatzing/discretemathclass.git
git add -A
git commit -am "added new files"
git push origin master
git pull origin master

• Sign up for an account with https://gitLab.com
• Download and install Git on your computer
• Do the Git tutorial at Online tutorial
• Create the web interfaces to GitLab to create a test project
• Follow the instructions provided by GitLab to clone the project and configure Git on your computer.

git config --global user.name "Ajarn Bob"
git config --global user.email "robert_b@payap.ac.th"
git clone git@gitlab.com:rbatzing/mytest.git
cd mytest
touch README.md
git add README.md
git commit -m "add README"
git push -u origin master

• Use A text editor to add content to README.md on your computer
• Add the file to your git system using git add -A
• Commit the changes using git commit -am "ReadMe file"
• Push the changes to your GitLab account using git push origin master
• Use the web interface to GitLab to verify the updates

• Create a project on GitLab called DiscreteMath
• Clone this project to your computer and configure your Git settings.
• Add rbatzing as a member of your class project
• Pull the course files from the Git repository https://gitlab.com/rbatzing/DiscreteMathClass on to your computer.
• Commit the files and push to your GITLAB account.
• Verify the update with the web interface to your GitLab account

• Interpreted scripting language:

  • can call operating system directly
  • powerful string operations and regular expressions
  • immediate feedback during development

• Quick and easy:

  • no variable declarations, typing
  • syntax is simple and consistent
  • automatic memory management
  • multithreaded process management

• Object oriented programming:

  • everything is an object
  • classes, methods, inheritance, iterators and closures
  • singleton methods, “mixin” functionality

• Advanced features:

  • multiple precision integers
  • convenient exception processing
  • dynamic loading
  • symbol processing
  • multi-threading support

When you finish the tutorial, answer the following questions:

• What is the class defined in this program?

• What is the meaning of the attributes of this class?

• What do the various methods do?

• Which lines invoke and use an object of this class?

• How were the global data for the survey stored?

• How were the results stored? And in what format?

• Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values.
• Discrete mathematics contrasts with continuous mathematics which uses real values to produce smooth variations
• Computer science is built almost entirely on discrete math especially combinatorics and graph theory.
• Discrete mathematics is a required skill for pursuing a successful career in IT.

• Mathematics Reasoning: ability to apply mathematical logic, proofs, and induction to read, comprehend and construct mathematical arguments.
• Combinatorial Analysis: ability to count or enumerate objects and combinations.
• Discrete Structures: Use of discrete structures to represent objects and relationships between them. Includes sets, permutations, relations, graphs, trees, and finite-state machines.
• Algorithmic Thinking: Ability to specify an algorithm, verify correctness and analysis time and resources.
• Applications and Modeling: Ability to apply principles to solve problems

1. How many unique pairs of ducks and eggs can be made?
2. How many unique combinations of ducks and eggs are there?

• How many license plates can be made using 3 Thai letters and 3 digits?
• What is the shortest path between Payap University and the airport?
• What is the fastest way to sort a list with limited memory?
• What is the best way to randomize a list?
• What is the best way to color a map with the fewest colors?

Atomic

cannot be divided into smaller statements

Molecular

can be divided into smaller statements

• a molecular statement of the form \( P \rightarrow Q \)
• P is the hypothesis (or antecedent statement).
• Q is the conclusion (or consequent statement).
• The only way for \( P \rightarrow Q \) to be false is for \( P=T \) and \( Q = F \)
• To prove an implication \( P \rightarrow Q \) :

It is enough to assume P, and from it, deduce Q

• Conjunction: means (P AND Q), written as \( P \cap Q \) or \( P \land Q \)
• Disjunction: means (P OR Q), written as \( P \cup Q \) or \( P \lor Q \)
• Implication or conditional: means (IF P THEN Q), written as \( P \rightarrow Q \)
• Biconditional: means (P IF AND ONLY IF Q), written as \( P \leftrightarrow Q \)
• Negation: means (NOT P), written as \( \neg P \) or \( !P \)

Negation:

\[ \begin{array}{r|c|} \neg P& Outcome\\ \hline P=T & F \\ P=F & T \\ \hline \end{array} \]

Given the implication \( P \rightarrow Q \) :

\( Q \rightarrow P \) (can be false)

For \( numbers > 2 \) :
\( Prime \rightarrow Odd\ number \) (True)
\( Odd\ number \rightarrow Prime\ \) (Often False)

Given the implication \( P\rightarrow Q \) :

\( \neg Q \rightarrow \neg P \) (always True)

For \( numbers > 2 \) :
\( Prime \rightarrow Odd\ number \) (True)
\( \neg Odd\ number \rightarrow \neg Prime\ \) (True)

• P is necessary for Q means \( Q \rightarrow P \)
• P is sufficient for Q means \( P\rightarrow Q \)
• P is necessary and sufficient for Q means \( P\leftrightarrow Q \)

• You can fool some people all of the time.
• You can fool everyone some of the time.
• You can always fool some people.
• Sometimes you can fool everyone.

Existential quantifier means “there exists” or “there is.”

\[ \exists x (x < 0) \]

There exists at least one number < 0

Universal quantifier means “for all” or “every.”“

\[ \forall x (x > 0) \]

Asserts that every number > 0

\[ \forall x \exists y ( y < x) \]

\[ \exists x \forall y (y < x) \]

Assuming \( P(x) \) means x is a prime number

\[ \neg \forall x P(x) \equiv \exists x \neg P(x) \]

\[ \neg\exists x P(x) \equiv \forall x \neg P(x) \]

• Either you win the lottery or else you are not rich.
• Either you don’t win the lottery or else you are rich.
• You will win the lottery and be rich.
• You will be rich if you win the lottery.
• You will win the lottery if you are rich.
• It is necessary for you to win the lottery to be rich.
• It is sufficient to win the lottery to be rich.
• You will be rich only if you win the lottery.
• Unless you win the lottery, you won’t be rich.
• If you are rich, you must have won the lottery.
• If you are not rich, then you did not win the lottery.
• You will win the lottery if and only if you are rich

\[ \begin{matrix} \bf Conjunction & \land & \verb '\land' & \verb '&&' \\ \bf Disjunction & \lor & \verb '\lor' & \verb'||' \\ \bf Implication & \rightarrow & \verb '\rightarrow' & \verb'->'\\ \bf Biconditional & \leftrightarrow & \verb '\leftrightarrow' & \verb'<-->' \\ \bf Negation & \neg & \verb '\neg' & \verb'!' \\ \end{matrix} \]

• Do each and every activity and exercise in this Unit.
• Record and label your results in a text file.