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This course aims to provide learning of fundamental
concepts of mathematics which are essential for mathematical
thinking. The course includes concepts and theories such as
logic, mathematical statements, mathematical implications,
proof, elementary set theory, induction, relations,
mappings, functions, images and inverse images, elementary
number theory. In mathematical reasoning, logical arguments
are using to deduce the consequences of basic assumptions.
The course provides most common methods of proof and
illustrate each technique with examples.
By the end of this
course students are expected to
- describe proof methods,
- conclude validity of propositions,
- apply concepts of logic to proof methods,
- formulate and develop mathematical
statements,
- distinguish mathematical implications.,
- use proof techniques such as direct
proof,induction,contrapositive,contradiction
effectively,
- adapt proof techniques to fundamental
topics:set theory, relations, functions,construct sets
and relations of given property,
- compare sets (cardinality),compare
functions (injection, surjection, bijection, inverse,
preimage),demonstrate basic abstract structures.
In this course symbolic logic, set theory, cartesian
product, relations, functions, equivalence relations,
equivalence classes and partitions, order relations: partial
order, total order and well ordering will be discussed.
Mathematical induction and recursive definitions of
functions will be taught. |
