Download EinfГјhrung in die Mathematik: HintergrГјnde der by Helmut Koch PDF

By Helmut Koch

Diese Einführung besticht durch zwei ungewöhnliche Aspekte: Sie gibt einen Einblick in die Mathematik als Bestandteil unserer Kultur, und sie vermittelt die Hintergründe der Mathematik vom Schulstoff ausgehend bis zum Niveau von Mathematikvorlesungen im ersten Studienjahr. Die Stoffdarstellung geht vom Aufbau der natürlichen Zahlen aus; der Schwerpunkt liegt aber in den exakten Begründungen der Zahlenbegriffe, der Geometrie der Ebene und der Funktionen einer Veränderlichen. Dabei werden alle Sätze bis hin zum Hauptsatz der Algebra vollständig bewiesen. Der klare Aufbau des Buches mit Stichwortregister wichtiger Begriffe erleichtert das systematische Lernen und Nachschlagen. Die zweite Auflage enthält teilweise ausführliche Darstellungen für die Lösungen der zahlreichen Übungsaufgaben. Da viele Aspekte zur Sprache kommen, die so weder im Unterricht noch im Studium behandelt werden, ergänzt die Einführung excellent den Vorlesungsstoff für Lehramtskandidaten und Diplomstudenten.

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Given that p and q are contradictories, p and r are contraries, p and s are subcontraries, and p and t are subalterns, what are the relations subsisting between q, r, s, and tf If p and q are contraries, q and r are contradictories, and r and s are contraries, what are p and s7 GROUP C 1. by determining whether they are or transitive. Classify the following relations reflexive, symmetrical, "is "is higher than" the cousin of" "is parallel to" "works for" "has a greater velocity than" the king of" "is "Some —— is a part of" "is a factor of" (in mathematics) "is "belongs underneath" "All—is— "loves" "No—is— "is an analogue of" "Some — is not — Give a relation which is reflexive, symmetrical, and transitive; one (other than "implies") which is reflexive and transitive, but not symmetrical; one which is neither reflexive, symmetrical, nor transitive; one which is only symmetrical; one which is only reflexive; one which is only transitive; one which is reflexive and symmetrical, but not transitive.

E) /) Two d) is a number obtained by adding one and g) Gravity is that force ter of the earth. 3. and A sculpin is a fish of the group Loricati of the family Cottidae. A maxim is a statement embodying a general truth. A bonfire is a large fire made in the open air. c) which attracts all bodies one. towards the cen- Place in their genera and species the following: man, logic, pleasure, triangle. 4. 5. What are the principal species of the following genera: number, element, literature, trade. What are the indefinables in the following set of definitions: X is an immediate cause of y, if x is the cause of y and there is nothing which is caused by x and causes y.

Define by dichotomy the following terms: furniture, house, flower, goat. 2. Designate the genus, species, and differentia in the following defi- nitions: a) A farce b) Geography is a light dramatic composition of a satirical nature. is the science of the earth its life. e) /) Two d) is a number obtained by adding one and g) Gravity is that force ter of the earth. 3. and A sculpin is a fish of the group Loricati of the family Cottidae. A maxim is a statement embodying a general truth. A bonfire is a large fire made in the open air.

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