Course Code:
MATH 101
Semester:
Fall
Course Type:
Core
P:
3
Lab:
2
Laboratuvar Saati:
0
Credits:
4
ECTS:
8
Course Language:
English
Course Objectives:
To teach the usage of analytical tools for mathematical thinking.
Course Content:

Propositional and predicate calculus. Introduction to logic. Methods of proof. Axioms of set theory. Cartesian product, relations and functions. Partial and total orderings. Zorn's lemma. Cardinality, finite, countable and uncountable sets. Arithmetic of cardinals and ordinals.

Course Methodology:
1: Lecture, 2: Problem Solving, 3:Question-answer, 4: Homework
Course Evaluation Methods:
A: Written examination, B: Homework

## Vertical Tabs

### Course Learning Outcomes

 Learning Outcomes Program Learning Outcomes Teaching Methods Assessment Methods 1) Thinks like a mathematician. 1,2,3,4 A 2) Applies laws of logic in reasoning. 1,2,3,4 A 3) Tests the validity of an argument by using laws of logic. 1,2,3,4 A 4) Identifies the properties of a given function, relation or an ordering. 1,2,3,4 A 5) Understands that there are different sizes of infinity. 1,2,3,4 A 6) Applies set theory axioms to deduce results about denumerable and uncountable sets. 1,2,3,4 A

### Course Flow

 Week Topics Study Materials 1 Intro. to propositional logic, logical equivalence and tautologies Textbook 2 Rules of inference Textbook 3 Proof techniques Textbook 4 Mathematical induction Textbook 5 Predicates and quantifiers Textbook 6 The Algebra of sets Textbook 7 Arbitrary unions and intersections Textbook 8 Product sets, functions Textbook 9 Compositions, bijections and inverse functions Textbook 10 Images and inverse images of sets Textbook 11 Relations, equivalence relations Textbook 12 Partially ordered sets Textbook 13 The cardinality of finite sets Textbook 14 The cardinality of infinite sets Textbook

### Recommended Sources

 Textbook Introduction to Advanced Mathematics, William Barnier- Norman Feldman. Additional Resources

### Material Sharing

 Documents Assignments Exams

### Assessment

 IN-TERM STUDIES NUMBER PERCENTAGE Mid-terms 2 100 Quizzes - - Assignments - - Total 100 CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE 40 CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE 60 Total 100

 COURSE CATEGORY Core Courses

### Course’s Contribution to Program

 No Program Learning Outcomes Contribution 1 2 3 4 5 1 The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) x 2 Acquiring fundamental knowledge on fundamental research fields in mathematics x 3 Ability form and interpret the relations between research topics in mathematics x 4 Ability to define, formulate and solve mathematical problems x 5 Consciousness of professional ethics and responsibilty x 6 Ability to communicate actively x 7 Ability of self-development in fields of interest x 8 Ability to learn, choose and use necessary information technologies x 9 Lifelong education x

### ECTS

 Activities Quantity Duration (Hour) Total Workload (Hour) Course Duration (14x Total course hours) 14 5 70 Hours for off-the-classroom study (Pre-study, practice) 14 5 70 Mid-terms (Including self study) 2 15 30 Quizzes - - - Assignments - - - Final examination (Including self study) 1 20 20 Total Work Load 190 Total Work Load / 25 (h) 7.60 ECTS Credit of the Course 8