BSc: Analytic Geometry And Linear Algebra I.f22
Analytical Geometry & Linear Algebra – I
- Course name: Analytical Geometry & Linear Algebra – I
- Code discipline: CSE202
- Subject area: Math. Computer Science
Short Description
This is an introductory course in analytical geometry and linear algebra. After having studied the course, students get to know fundamental principles of vector algebra and its applications in solving various geometry problems, different types of equations of lines and planes, conics and quadric surfaces, transformations in the plane and in the space. An introduction on matrices and determinants as a fundamental knowledge of linear algebra is also provided.
Course Topics
Section | Topics within the section |
---|---|
Vector algebra |
|
Line and Plane |
|
Quadratic curves and surfaces |
|
Intended Learning Outcomes (ILOs)
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 ...
- explain the geometrical interpretation of the basic operations of vector algebra,
- restate equations of lines and planes in different forms,
- interpret the geometrical meaning of the conic sections in the mathematical expression,
- give the examples of the surfaces of revolution,
- understand the value of geometry in various fields of science and techniques.
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 ...
- perform the basic operations of vector algebra,
- use different types of equations of lines and planes to solve the plane and space problems,
- represent the conic section in canonical form,
- compose the equation of quadric surface.
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 ...
- list basic notions of vector algebra,
- recite the base form of the equations of transformations in planes and spaces,
- recall equations of lines and planes,
- identify the type of conic section,
- recognize the kind of quadric surfaces.
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
- What is the characteristic property of trees?
- How to find an Euler tour?
- What is a Hamilton path?
- Why are K3 and K5,5 not planar?
- What is the difference between undirected and directed graphs?
- Why do we consider weighted graphs?
- What practical problems are solved using Dijkstra's algorithm?
- What is the maximum flow problem?
Final assessment
Section 1
- What is the difference between Categorical and Propositional Logic?
- How does Predicate Logic differ from Categorical and Propositional Logic?
- Why is Predicate Logic so important?
- What are Truth-Functions and why do we use them?
- Compute True Tables for Propositions
- Compute True Tables for Arguments
Section 2
Section 3
- Explain handshaking lemma.
- Give necessary and sufficient conditions for the existence of an Euler tour.
- Give sufficient conditions for the existence of a Hamilton path (theorems of Dirac and Ore).
- Explain Kuratowski’s theorem.
- Explain the difference between undirected and directed graphs.
- Give the definition of weighted graphs?
- Explain Dijkstra's algorithm?
- What is the solution of the maximum flow problem (the Ford-Fulkerson algorithm)?
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.