A transition to advanced mathematics

(bq) part 1 book "a transition to advanced mathematics" has contents: propositions and connectives, propositions and connectives, quantifiers, basic proof methods i, additional examples of proofs, basic concepts of set theory, equivalent forms of induction, cartesian products and relations,...and other contents.

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(bq) part 2 book "a transition to advanced mathematics" has contents: infinite sets, countable sets, the ordering of cardinal numbers, comparability of cardinal numbers and the axiom of choice, algebraic structures, operation preserving maps, completeness of the real numbers, the bounded monotone sequence theorem,...and other contents.

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One of the major advances of science in the 20th century was the discovery of a mathematical formulation of quantum mechanics by Heisenberg in 1925 [94].1 From a mathematical point of view, this transition from classical mechanics to quantum mechanics amounts to, among other things, passing from the commutative algebra of classical observables to the noncommutative algebra of quantum mechanical observables. To understand this better we recall that in classical mechanics an observable of a system (e.g. energy, position, momentum, etc.

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