I. Introduction to Logic and Algorithms Logic and algorithms defined: Logic is the study of reasoning and argumentation; algorithms are step-by-step procedures for solving problems. Importance: Logic underpins sound decision-making, while algorithms are fundamental to computer science and problem-solving. II. Propositional Logic Propositions and Connectives: Proposition: A statement that is either true or false. Connectives: AND, OR, NOT, IMPLIES, IF AND ONLY IF. Truth tables for connectives. Logical Equivalence: Two propositions are logically equivalent if their truth values are the same for all possible inputs. De Morgan's Laws. Inference Rules: Modus Ponens, Modus Tollens, Disjunctive Syllogism. Using rules for valid reasoning. Page 2 III. Predicate Logic Predicates and Quantifiers: Predicates: Statements with variables (e.g., "x is greater than 5"). Quantifiers: Existential (∃) and Universal (∀). Expressing statements with quantifiers.
Logical Equivalence in Predicate Logic: Negating quantified statements. De Morgan's Laws in predicate logic. Inference Rules in Predicate Logic: Universal instantiation, universal generalization, existential instantiation, existential generalization. Using rules for valid reasoning in predicate logic. IV. Algorithms Definition and Characteristics: Algorithms are step-by-step procedures for solving problems. Characteristics: Input, output, definiteness, finiteness, effectiveness. Algorithm Analysis: Time complexity: Measure of the time an algorithm takes to run. Space complexity: Measure of the memory space used by an algorithm. Algorithm Design Paradigms: Divide and conquer, dynamic programming, greedy algorithms. Choosing the right paradigm for a problem. Page 3 V. Sorting and Searching Algorithms Sorting Algorithms:
Bubble sort, selection sort, insertion sort, merge sort, quicksort. Time and space complexity analysis. Searching Algorithms: Linear search, binary search, hash tables. Efficiency and applicability of each. VI. Recursion Recursive Functions: A function that calls itself. Base case and recursive case. Recursive Algorithms: Examples: Fibonacci sequence, factorial calculation. Analyzing recursion depth and time complexity. VII. Algorithmic Problem Solving Problem-Solving Strategies: Understanding the problem, breaking it down, devising a plan, implementing the solution, testingand refining. Importance of problem-solving in computer science. Pseudocode and Flowcharts: Tools for representing algorithms visually. Creating clear and detailed algorithmic descriptions.