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What is programming? Commands are the smallest building blocks of your program. A single intruction to the computer to perform an action. A program is a collection of these individual ccommands put together in the right order to solve a problem, complete a task, or maybe interact with the user. The collection of commands you write for your program is called source code. 2D coordinate system * Computer screens are made up of tiny dots * Each one of these dots is called pixels * In p5.js we create an area of pixels on a webpage we can draw to: this is called the canvas * A canvas needs a width and height in pixels How you will be assessed?  * New topic every two weeks * This is your first topic (development environment) * Each topic will be divided into a series of lessons * In a lesson you will learn by watching videos * The game keeps a running total of your score which increases as you progress but fixed grades are taken at two points in the term. Each of...

Predicates and Quantifiers Introduction Until now, propositional logic cannot adequately express the meaning of all statements in mathematics and in natural language. For example, suppose that we know that "every computer connected to the university network is functioning properly" No rules of propositional logic allow us to conclude the trutth of the statement Predicates Statements involving variables, such as "x > 3", "x = y + 3" and "computer x is under attack by an intruder" are often found in mathematical assertions. These statements are neither true nor false when the values of the variables are not specified. There are ways that propositions can be produced from such statements. Consider "x is greater than 3" * has two parts * x, is the subject of the statement * "is greater than 3" refers to a property that the subject of the statement can have. * "x is greater than 3" can be denot...

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Propositional Equivalences An important type of step used in a mathematical argument is the replacement of a statement with another statement with the same truth value. Note that we will use the term “compound proposi- tion” to refer to an expression formed from propositional variables using logical operators, such as p ∧ q. Tautology: compound proposition that is always true Contradiction: compound proposition that is always false Contingency: compound proposition that is neither tautology nor a contradiction Logical Equivalences Compound propositions that have the same truth values in all possible cases are called logically equivalent. We can also define this notion as follows: > The compound propositions p and q are called logically equivalent if p ↔ q is a tautology. The notation p ≡ q denotes that p and q are logically equivalent. Propositional Satisfiability An unsatisfiable compound proposition happens when the negation is a tautology. A satisfiable...

Propositional Equivalences * Two formulas are equivalent when they have the same truth tables * We denote equivalence by ≡ * A ≡ B means that A and B always have the same truth values, regardless of how the variables are assigned. * Note that ≡ is a relation and NOT a connective De Morgan's Laws ¬(p∧q)≡¬p∨¬q  ¬(p∨q)≡¬p∧¬q It is similar to the process of algebra when you have a negative before a parenthesis. First law tells us also that the connective also changes.

Tautology: formula is a tautology when all scenarios are true Consistent: formula is consistent when at least 1 scenario is true Contradiction: formula is a contradiction when all scenarios are false