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. Finite, countable and uncountable sets.
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. | 3,4,5 | 1,2,3,4 | A |
| 2) Applies laws of logic in reasoning. | 3,7,9 | 1,2,3,4 | A |
| 3) Tests the validity of an argument by using laws of logic. | 7,9 | 1,2,3,4 | A |
| 4) Identifies the properties of a given function, relation or an ordering. | 3,7,9 | 1,2,3,4 | A |
| 5) Understands that there are different sizes of infinity. | 3,4,5 | 1,2,3,4 | A |
| 6) Applies set theory axioms to deduce results about denumerable and uncountable sets. | 4,5,7 | 1,2,3,4 | A |
Course Flow
| 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 | Formel 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
| Textbook | Introduction to Mathematical Structures, Steven Galovich. HBJ |
| 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 | 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 |