Intoductory Mathematics 390-FS1-1WDM

Study profile: general academic
Mode of study: full-time
Type of course: compulsory
Field and discipline of science: Field of exact and natural sciences, discipline: physical sciences.
Level of study: first-cycle studies
Year of study/semester: 1st year/1st semester
ECTS credits: 4

Student workload:
- participation in classes – 60 hours,
- participation in consultations – 15 hours,
- individual study at home – 25 hours,

Quantitative indicators:
- student workload related to classes requiring direct participation of the instructor – 3 ECTS;
- student workload related to independent study – 1 ECTS.

Rules for the use of artificial intelligence (AI) systems:

During classes, the use of AI systems is permitted for:
1. translating source texts from foreign languages;
2. searching for and organizing scientific and educational sources;
3. supporting the explanation of mathematical concepts and generating additional examples and solution methods.

The student is required to independently verify the correctness of information and results obtained with the use of AI systems.

The use of AI systems during written tests and other forms of assessment is prohibited unless the instructor explicitly specifies the permitted scope of their use.

The use of AI systems is governed by Ordinance No. 31 of the Rector of the University of Bialystok of 11 April 2025.

Topics covered during the classes:

1. Number sets, operations and relations. Basic properties of natural, integer, rational, real and complex numbers. Operations in number sets. Relations and their properties, in particular equivalence and order relations.

2. Fundamentals of mathematical logic and set theory. Propositions, logical connectives, quantifiers, implication and equivalence. Operations on sets. Writing definitions and theorems.

3. Methodology of mathematical reasoning. Basic methods of mathematical reasoning. Direct proof, proof by contradiction, and counterexample. Formulating conclusions and assessing the correctness of reasoning.

4. Complex numbers. Algebraic, trigonometric and exponential forms of a complex number. Geometric interpretation. De Moivre’s formula. Powers and roots of complex numbers.

5. Vector and affine spaces and elements of analytic geometry. Vectors, bases and coordinates. Scalar product and vector product. Lines and planes. Orthogonal projection. Relative positions of lines and planes. Selected plane curves.

6. Elements of combinatorics, probability theory and mathematical statistics. Basic counting methods. Random events and probability. Discrete random variables and their distributions. Expected value. Basic statistical characteristics and interpretation of data.

7. Elements of differential and integral calculus – supplementary topics. The concept of a derivative and its interpretation as a rate of change. Derivatives of basic functions and simple applications. The concepts of the indefinite and definite integral and simple computational examples.