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Credits & Workload
The course carries 6 ECTS credits and includes a total of 42 contact hours, all in the form of lectures with practical elements. There is no separate laboratory or project component specified. In addition, students are expected to complete approximately 120 hours of individual work over the semester.
Topics
Learning Outcomes - Knowledge
By the end of the course, students are expected to:
- Understand the principles underlying the solution of problems in science and natural sciences, and the mathematical models used to describe them.
- Consolidate and deepen their computational and calculation skills.
- Develop analytical thinking and the ability to reason, argue and draw conclusions.
- Prove statements and theorems using both deductive and inductive methods, and critically analyse and refute incorrect arguments through logical reasoning.
Learning Outcomes - Application of Professional Knowledge
- Use effective tools and modern problem-solving environments for mathematical tasks.
- Explain the concept of the limit of a sequence and a function, as well as continuity and the derivative, and understand their main applications.
- Compute limits by applying algebraic transformation rules, using graphs and applying limit-based approaches.
- Explain the relationship between continuity and limits and apply the fundamental theorems on continuity.
- Calculate derivatives of functions using standard differentiation rules.
Learning Outcomes - Transferable Skills
- Work confidently with professional mathematical literature.
- Formulate problems clearly and build step-by-step solution strategies.
- Recognize how general competences gained in mathematics can be transferred to other fields.
- Apply logical thinking systematically while solving problems.
- Strengthen analytical abilities by investigating and describing the behaviour of functions.
- Present mathematical arguments clearly and coherently, both orally and in writing.
Assessment & Grading
Assessment is based on written examinations, including an intermediate test and a final exam. All evaluations are individual. The intermediate exam usually combines a multiple-choice test with commentary and 3-4 typical problems with sub-questions. The final exam consists of 4-5 typical problems with several sub-questions each.
The final grade is composed of two written assessments:
- Short written test - 1 h 10 min, weight: 40%.
- Final written exam - 2 h, weight: 60%.
Each correct intermediate step is graded, even if the final numerical answer is not correct; such steps receive from 0.25 points upwards depending on 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 deduction of 0.25-0.5 points from the points allocated to the problem; if a numerical mistake does not affect the logic of the solution, no more than 0.5 points are subtracted. Logical errors lead to at least 0.5 points being deducted, depending on severity.
Teaching Methods & Prerequisites
Teaching combines theoretical explanations with a large number of worked examples and real-life-inspired problems. Students regularly solve diverse types of exercises in class, connecting abstract concepts with concrete applications.
To enrol in “Mathematics 1”, students should already have school-level knowledge of algebra and basic elements of mathematical analysis. These prerequisites ensure familiarity with the fundamental concepts and techniques that the course develops further.
Course Content
Topic 1 - Linear Function (9 hours)
Revision and formalisation of numerical sets, quadratic trinomials and basic elements of trigonometry. This block relies mainly on school mathematics textbooks and materials by G. G. Gevorgyan, A. A. Sahakyan, V. Kh. Musoyan, S. P. Stepanyan, A. E. Avetisyan and others.
Topic 2 - Functions, Sequences & Limits (24 hours)
Core material of mathematical analysis taught in this course, including:
- Definition of a function and inverse functions, with links to trigonometry.
- Power, exponential and logarithmic functions.
- Sequences and progressions; numerical sequences and their properties.
- The method of mathematical induction.
- Infinitesimal and infinite quantities; properties of convergent sequences.
- Limit of a function, derivative of a function, differential of a function, main theorems of differential calculus, and systematic investigation of functions.
Topic 3 - Integral Calculus (9 hours)
Introduction to integral calculus based on the previously studied differential calculus. Focus on the basic concepts and techniques of integration and their applications.
Literature & Resources
Required Literature
- V. Kh. Musoyan, Mathematical Analysis, Yerevan, 2018.
- S. P. Stepanyan, Fundamentals of Mathematical Analysis, Yerevan, 2023.
- A. E. Avetisyan et al., Problem Book in Higher Mathematics, Yerevan, 2014.
Additional Literature
- G. M. Fichtenholz, Fundamentals of Mathematical Analysis, Volumes 1-2, Lan Publishing, 2001.