Course Language:
İngilizce
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
| COURSE CONTENT | ||
| Week | Topics | Study Materials |
| 1 | Basic connectives and truth tables | Textbook |
| 2 | Logical equivalence: The laws of logic | Textbook |
| 3 | Logical implication: The rules of inference | Textbook |
| 4 | The use of quantifiers | Textbook |
| 5 | Formal thinking: Methods of proof | Textbook |
| 6 | Sets, operations on sets | Textbook |
| 7 | Ordered pairs and Cartesian product | Textbook |
| 8 | Relations | Textbook |
| 9 | Ordering relations | Textbook |
| 10 | Equivalence relations | Textbook |
| 11 | Functions | Textbook |
| 12 | Equinumerous sets, Finite sets | Textbook |
| 13 | Countable sets | Textbook |
| 14 | Uncountable sets | Textbook |
Recommended Sources
| RECOMMENDED SOURCES | |
| Textbook | Intro. to Mathematical Structures, Steven Galovich. HBJ |
| Additional Resources | |
Material Sharing
| MATERIAL SHARING | |
| Documents | |
| Assignments | |
| Exams | |
Assessment
| 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’s Contribution to Program
| 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
| ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION | |||
| 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 | 10 | 20 |
| Quizzes | - | - | - |
| Assignments | - | - | - |
| Final examination (Including self study) | 1 | 15 | 15 |
| Total Work Load | 175 | ||
| Total Work Load / 25 (h) | 7 | ||
| ECTS Credit of the Course | 7 | ||