BSc: Logic and Discrete Mathematics
Logic and Discrete Mathematics (Philosophy 1)
- Course name: Logic and Discrete Mathematics (Philosophy 1)
- Code discipline: CSE113
- Subject area: Math. Computer Science
Short Description
This course consists of two distinct but overlapping parts: i. Logic; and ii. Discrete Mathematics. The first part of the course is an introduction to formal symbolic logic. Philosopher John Locke once wrote that ``logic is the anatomy of thought. This part of the course will teach students to analyse and evaluate arguments using the formal techniques of modern symbolic logic. The second part of the is designed for students to teach them basic notions of graph theory, discrete optimization and dynamic programming. This part will give practical experience with basic algorithms in discrete mathematics.
Course Topics
| Section | Topics within the section |
|---|---|
| Basic of Logic |
|
| Set Theory & Finite combinatorics |
|
| Basic of Graphs |
|
Intended Learning Outcomes (ILOs)
What is the main purpose of this course?
This calculus course will provide an opportunity for participants to:
- understand key principles involved in differentiation and integration of functions
- solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities
- become familiar with the fundamental theorems of Calculus
- get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.
ILOs defined at three levels
We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
Level 1: What concepts should a student know/remember/explain?
By the end of the course, the students should be able to ...
- know the categorical logic
- know the propositional logic
- know the predicate logic
- explain the difference between deduction and induction
- know the trees and spanning trees
- remember the Euler and Hamilton graphs
- know what is planar graphs
- explain the Dijkstra’s algorithm
Level 2: What basic practical skills should a student be able to perform?
By the end of the course, the students should be able to ...
- use Venn diagrams
- calculate truth values
- analyse formal structures of some arguments
- differ the deduction and induction
- build spanning trees
- find Euler tour and Hamilton path
- use Dijkstra’s algorithm
- solve maximum flow problem
Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
By the end of the course, the students should be able to ... ...
Grading
Course grading range
| Grade | Range | Description of performance |
|---|---|---|
| A. Excellent | 90-100 | - |
| B. Good | 75-89 | - |
| C. Satisfactory | 60-74 | - |
| D. Fail | 0-59 | - |
Course activities and grading breakdown
| Activity Type | Percentage of the overall course grade |
|---|---|
| Midterm | 40 |
| Final exam | 40 |
| In-class participation | 20 |
Recommendations for students on how to succeed in the course
- Participation is important. Attending lectures is the key to success in this course.
- Review lecture materials before classes to do well.
- Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.
Resources, literature and reference materials
Open access resources
- K.H. Rosen, Discrete Mathematics and Its Applications (7th Edition). McGraw Hill, 2012.
- Lehman, E., Leighton, F. T., Meyer, A. R. (2017). Mathematics for Computer Science. Massachusetts Institute of Technology Press.
Software and tools used within the course
- No.
Activities and Teaching Methods
| Teaching Techniques | Section 1 | Section 2 | Section 3 |
|---|---|---|---|
| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 1 | 1 | 1 |
| Project-based learning (students work on a project) | 0 | 0 | 0 |
| Modular learning (facilitated self-study) | 0 | 0 | 0 |
| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1 |
| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0 |
| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0 |
| Inquiry-based learning | 0 | 0 | 0 |
| Just-in-time teaching | 0 | 0 | 0 |
| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0 |
| Studio-based learning | 0 | 0 | 0 |
| Universal design for learning | 0 | 0 | 0 |
| Task-based learning | 0 | 0 | 0 |
| Learning Activities | Section 1 | Section 2 | Section 3 |
|---|---|---|---|
| Lectures | 1 | 1 | 1 |
| Interactive Lectures | 1 | 1 | 1 |
| Lab exercises | 1 | 1 | 1 |
| Experiments | 0 | 0 | 0 |
| Modeling | 0 | 0 | 0 |
| Cases studies | 0 | 0 | 0 |
| Development of individual parts of software product code | 0 | 0 | 0 |
| Individual Projects | 0 | 0 | 0 |
| Group projects | 0 | 0 | 0 |
| Flipped classroom | 0 | 0 | 0 |
| Quizzes (written or computer based) | 1 | 1 | 1 |
| Peer Review | 0 | 0 | 0 |
| Discussions | 1 | 1 | 1 |
| Presentations by students | 0 | 0 | 0 |
| Written reports | 0 | 0 | 0 |
| Simulations and role-plays | 0 | 0 | 0 |
| Essays | 0 | 0 | 0 |
| Oral Reports | 0 | 0 | 0 |
Formative Assessment and Course Activities
Ongoing performance assessment
Section 1
- Solve Truth Tables
- Use Truth Tables to analyse arguments
- Use Quantifiers to assess inferences
- What is Propositional Logic used for?
- What is Predicate Logic used for?
Section 2
Section 3
Final assessment
Section 1
- Apply the appropriate differentiation technique to a given problem.
- Find a derivative of a function
- Apply Leibniz formula
- Draw graphs of functions
- Find asymptotes of a parametric function
Section 2
- Apply the appropriate integration technique to the given problem
- Find the value of the devinite integral
- Calculate the area of the domain or the length of the curve
Section 3
- Find a limit of a sequence
- Find a limit of a function
The retake exam
Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.