Titlebook: Studying Mathematics; The Beauty, the Toil Marco Bramanti,Giancarlo Travaglini Book 2018 Springer International Publishing AG, part of Spri

大漩渦

Formulae and Indices (Level A)ath formulas? These issues are addressed first by explaining the use of summations (“sigma notation”) and products together with their properties and typical applications. Then we consider numerical functions and their compositions.

含水層

Saturation of Indices and Syntactic Consistency of a Formula (Level B)ritten in terms of syntactic consistency. This means that the two sides of an equality (an inequality) should be functions of the same variable(s). In order to introduce useful examples taken from mathematics in high school/college, we consider several mathematical objects and operations: e.g. seque

有雜色

悲痛

To Read a Definitiontion and to be able to deduce simple propositions related to the definition. Each exercise in this chapter introduces a definition and asks the reader to find some objects that satisfy the definition, to find some objects that do not satisfy the definition, and to establish the truth or the falsity

Optic-Disk

To Understand, i.e., to Know How to Apply one possible answer: when we are able to apply the above proof, argument, computational technique in a (slightly) different mathematical setting. In each exercise of this chapter, we propose the solution of a problem or the proof of a theorem (say Problem I or Theorem I). Then the reader is asked t

Anthropoid

Nausea

EXCEL

Majorizationsthematics, we often have to . an inequality, that is, to show that an inequality actually holds for every possible choice of certain parameters. Useful inequalities are normally proved combining several intermediate inequalities. At every step, we “l(fā)ook for an expression . greater than or equal to .

Amylase

Uniqueness Proofs (Level B)xcludes that a given problem may have more than one solution. From a logical point of view, the uniqueness issue is independent from the existence issue; the latter means that at least one solution to the problem actually exists. We deal with uniqueness proofs and some of their common features. The