General principles before algebra Any mathematical statement does not necessarily need symbols to be considered general. It can be stated through words, diagrams , tables, or examples. Ancient Babylonians used to practice mathematics like this in their culture. Is mathematics all about generalization and abstraction Mathematics is not only generalization and abstraction. Mathematical activity also includes: Solving real life problems . Studying patterns. Measuring and comparing quantities. Making predictions. Making diagrams. Making procedures. Communicating. Studying why a method works. Abstract ideas to focus on real results , mathematics often develops through movement between the concrete and the abstract. Therefore, mathematics is both particular and general, as well as both practical and abstract. General ideas without algebra Number theory A general number-theory principle could be stated verbally: When an even number is added to another even number, it will give...
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