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Proof and Fundamentals

This course introduces problem solving techniques used throughout the mathematics curriculum. Each class combines a lecture describing the common tricks and techniques used in a particular field, together with a problem solving session where the students work together using techniques to tackle some concrete problems. Among the topics of the course are the problems of the classical mathematical logic (statements; relations between statements, arguments, quantifiers) and problems of strategies for mathematical proofs (direct proofs; proofs by contrapositive and contradiction, proofs by cases, " If and Only If" theorems, quantifiers in theorems). Fundamentals of mathematics are presented to be a set theory of elements, cardinality of sets; cardinality of the number systems, mathematical induction; recursion. The course also deals with complex numbers, elements of combinatorics, matrices and elements of calculus which allow us to discuss fractal geometry and consider its widespread beautiful applications in art and music.

Credits: 6/3

Course ID: MATH_D_100

Programm Complex System

Taught this semester: No

Complies with general requirements: Yes

Course Type: General Course

Language: English