Titlebook: Cool Math for Hot Music; A First Introduction Guerino Mazzola,Maria Mannone,Yan Pang Textbook 2016 Springer International Publishing Switze

含糊

储备

艰苦地移动

Functions and RelationsThe elements of a set can be written in any order, and we don’t yet have a way to define ordered structures. So we now develop the theory of ordered structures. It also allows us to define the central concept of a function.

假设

Natural NumbersNatural numbers are the first topic studied by all students in first years of elementary school. Here, the classic definitions of ordinal and natural numbers are entirely derived from set theory. The well-known five Peano axioms that define natural numbers are now presented as a theorem.

NAVEN

Natural ArithmeticIn the previous chapter, we defined natural numbers. Now, we are interested in how to combine these numbers to obtain other natural numbers. In this chapter, we will define three operations: addition, multiplication, and exponentiation.

顾客

上下倒置

subacute

Roots, Logarithms, and Normal FormsCorollary 2 in Chapter 12 is crucial for the construction of some important structures for real numbers, such as general roots and logarithms. These are introduced in this chapter. We also discuss musical applications to pitch theory.

Anemia

Universal Propertiesing arrows. We also introduce exponentials and subobject classifiers. These concepts are broadly used in modern mathematics, because they describe constructions that appear everywhere in mathematical creativity.

漂泊