Course Identification
“Analytic Geometry & Algebra” is a first-year, first-semester course in the 2025–2026 academic year within the Informatics Bachelor / Licence en Informatique program at the French University in Armenia. The course belongs to the Informatics specialization and is assigned to the ICM Faculty, Department of Mathematics, as Bloc 1, Module 1.
Credits & Workload
The course carries 4 ECTS credits and includes a total of 42 contact hours, divided equally into 21 hours of lectures and 21 hours of tutorials / practical sessions. There is no separate laboratory or project component specified. In addition, students are expected to complete approximately 80 hours of individual work over the semester.
Aim of the Course
The aim of “Analytic Geometry & Algebra” is to provide students with the basic tools of algebra and analytic geometry needed for subsequent study of mathematical analysis and applied disciplines. The course develops skills in working with vectors, coordinates, matrices and systems of linear equations, and introduces polynomial techniques. It strengthens logical and algorithmic thinking and the ability to model and solve quantitative problems that appear in computer science and related fields.
Learning Outcomes – Knowledge
By the end of the course, students are expected to:
- Know the basic concepts and objects of analytic geometry (points, vectors, lines, circles and conics) in the plane and space.
- Understand coordinate methods for representing geometric objects and relationships.
- Master fundamental notions of linear algebra: matrices, determinants, rank, eigenvalues and eigenvectors at an introductory level.
- Know the basic theory of systems of linear equations and the structure of their solution sets.
- Understand key properties of polynomials, including factorisation and root multiplicity.
Learning Outcomes – Application of Professional Knowledge
- Use coordinate and vector methods to describe and solve geometric problems in the plane and in three-dimensional space.
- Set up and solve systems of linear equations arising from practical or application-oriented problems.
- Perform basic matrix operations, compute determinants and apply them to analyse linear systems and transformations.
- Use eigenvalues and eigenvectors in simple situations to understand properties of linear operators and matrices.
- Manipulate polynomials, factorise them and interpret the multiplicity of roots in algebraic problems.
Learning Outcomes – Transferable Skills
- Develop structured and rigorous mathematical reasoning.
- Translate real-world or applied tasks into algebraic and geometric models using coordinates and equations.
- Design step-by-step solution strategies for multi-stage quantitative problems.
- Strengthen algorithmic thinking through systematic procedures for solving systems of equations and working with matrices.
- Present mathematical arguments clearly and coherently in written form and in classroom discussions.
Assessment & Grading
Assessment is based on written examinations, including an intermediate test and a final exam. All evaluations are individual. The intermediate exam typically combines short questions or multiple-choice tasks with commentary and several standard problems with sub-questions. The final exam consists of a set of typical problems with multiple sub-questions.
The final grade is composed of two written assessments:
- Short written test – weight: 40%.
- Final written exam – weight: 60%.
Each correct intermediate step is graded, even if the final numerical answer is not correct; such steps receive partial credit depending on their importance. Copying only the problem statement or solving a different problem than the assigned one results in 0 points for that task.
Numerical errors typically result in a small deduction from the points allocated to the problem; if a numerical mistake does not affect the logic of the solution, only a limited penalty is applied. Logical errors lead to a larger deduction, depending on the severity of the mistake and its impact on the solution.
Teaching Methods & Prerequisites
Teaching combines theoretical explanations with many worked examples and practical exercises. Students regularly solve diverse types of problems in tutorials, applying algebraic and geometric methods to concrete situations and developing confidence in symbolic computations.
To enrol in “Analytic Geometry & Algebra”, students should have school-level knowledge of algebra and geometry. These prerequisites ensure familiarity with basic equations, inequalities and geometric constructions on which the course builds.
Course Content
Topic 1 – Elements of Analytic Geometry
Introduction to coordinate systems and vectors in the plane. Representation of points, directed segments and basic geometric objects in coordinates. Distance and angle formulas. Main reference chapters from A. K. Poghosyan and H. S. Arakelyan.
Topic 2 – Lines and Conics in the Plane
General and parametric equations of a line in the plane, relative position of two lines, and distance from a point to a line. Equations of a circle and other conic sections (ellipse, parabola, hyperbola), their basic properties and geometric interpretation via coordinates.
Topic 3 – Vectors, Matrices & Linear Systems
Vectors in the plane and space, linear combinations and linear dependence. Matrices and matrix operations; determinants and rank. Systems of linear equations, Gaussian elimination and classification of solution sets. Eigenvalues and eigenvectors in simple settings.
Topic 4 – Linear Systems & Polynomials
Structure of solutions of homogeneous and non-homogeneous linear systems. Polynomial algebra: basic operations, factorisation, roots of a polynomial and multiplicity. Applications to solving equations and understanding algebraic structures that will be used in later courses.
Literature & Resources
Required Literature
- Yu. M. Movsisyan, Higher Algebra and Number Theory, Yerevan, 2008.
- H. S. Arakelyan, H. M. Khosrovyam, V. A. Mirzoyan, Analytic Geometry and Linear Algebra, Yerevan, 2003.
- A. K. Poghosyan, V. R. Davtyan, Analytic Geometry and Linear Algebra, Yerevan, 2005.
Additional Literature
- V. A. Philippossyan, H. H. Ohnikyan, Analytic Geometry, Yerevan, 2018.