Mathematical Reasoning

Mathematical Reasoning is the branch of mathematics that uses logical thinking to analyze statements, determine their truth values, and draw valid conclusions using logical connectives, quantifiers, patterns, and proof techniques. It helps in developing problem-solving and decision-making skills and forms the foundation of mathematics and computer science.

Foundations

Basic concepts of logic, reasoning, statements, and proofs in mathematics.

• Introduction to Mathematical Reasoning
• Introduction to Mathematical Logic
• Logic Symbols

Statements & Compound Statements

Understanding simple statements and their combinations using logical connectives.

• Compound Statements
• Conjunction vs Disjunction
• Conditional Statements and Implications
• Converse, Inverse and Contrapositive of a Statement
• Quantifiers and Negation
• Tautology in Maths
• De Morgan's Law

Types of Reasoning and proofs

Methods used to logically prove and verify mathematical statements.

• Inductive Reasoning
• Deductive Reasoning
• Arithmetic Reasoning
• Principle of Mathematical Induction
• Introduction to Proofs