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Course Information

Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
ABSTRACT MATHEMATICS I	MAT1105		0 + 0	3.0	6.0

Prerequisites

None

Language of Instruction	Turkish
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery
Course Coordinator
Instructors
Assistants
Goals	It is a reality that a subtantial number of students who do well in the calculus courses have difficulty with their first theoretical upper-division course.The transition from the rather routine problem solving involved in the study of calculus to abstract proof-oriented advanced courses is too abrupt for these students. The aim of this course is to bridge the gap referred to above,to teach what a valid proof is, and to enable the student to construct simple proofs.
Course Content	Communicating mathematics and using symbols Sets, subsets and set operations Indexed collection of sets, partitions of sets and cartesian products of sets Statements, the negation of statement, the disjunction and conjuction of statements The implication, the biconditional, tautologies and contradictions Logical equivalence, some fundamental properties of logical equivalence, characterization of statements Direct proof Proof by contrapositive Existence Proof by contradiction Prove or disprove Eqivalence relations Partial order and total orders Maximum, maximal, minimum, minimal elements of ordered sets
Learning Outcomes	1) To learn how to translate a given expression into the language of mathematics using the correct symbols. 2) To be able to determine the maximum, maximal, minimum and minimal elements of the cluster according to the given order relation. 3) To prove the truth of a proposition directly, to learn to prove the right of non-proprietary methods by using the appropriate one.