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Maths › 00. General Mathematics ›

09.1 Algorithmic Thinking

9.1 Algorithmic Thinking Algorithmic thinking means solving a problem by describing a clear sequence of steps that always leads from input to output. Instead of relying on intuition, we make the method explicit so that anyone can follow it and obtain the same result. From answers to procedures When you compute $27 + 48$, you do not guess. You follow a method. First add the ones: $7 + 8 =...
mathematics algorithms computation methods May 2, 2026
Maths › 00. General Mathematics ›

08. Problem Solving Strategies

Chapter 8. Problem Solving Strategies Mathematics is not only a collection of results, but a practice of solving problems. While proof establishes correctness, problem solving determines how one arrives at a solution. This chapter gives an overview of the main strategies used to approach unfamiliar or complex problems. A problem rarely yields directly. It must be transformed. One of the most common strategies is reduction. A difficult problem is rewritten...
mathematics problem-solving methods strategy May 2, 2026
Maths › 00. General Mathematics ›

07. Proof Techniques

Chapter 7. Proof Techniques Proof is the method by which mathematics separates assertion from knowledge. A statement becomes a theorem only when it follows from accepted assumptions by valid reasoning. This chapter introduces the main proof techniques used across mathematics. A proof technique is not a trick. It is a disciplined pattern of argument. Each technique is suited to a different kind of statement and a different kind of structure....
mathematics proof reasoning methods May 2, 2026
Maths › 00. General Mathematics ›

00. Preface

This volume defines the ground layer of mathematics. It focuses on how mathematics is expressed, structured, and practiced before any specialization. The scope follows MSC 00 and concentrates on classification, exposition, philosophy, and general methods that recur across all fields . Mathematics operates as a language, a system of structures, and a method of reasoning. Each of these aspects appears in every branch, whether one studies algebra, analysis, geometry, or...
mathematics foundations philosophy methods May 2, 2026
Maths ›

00. General Mathematics

This volume establishes the meta-layer of mathematics. It covers language, structure, methodology, and cross-cutting tools that apply across all branches. The scope follows MSC 00: classification, exposition, philosophy, and general methods. Part I. What Mathematics Is Chapter 1. Nature of Mathematical Objects 1.1 Abstract objects and structures 1.2 Sets, types, and universes 1.3 Equality, identity, and equivalence 1.4 Finite vs infinite objects 1.5 Constructive vs classical viewpoints Chapter 2. Mathematical...
mathematics foundations philosophy methods May 2, 2026