Intoductory Mathematics 390-FS1-1WDM
Study profile: general academic
Form of study: full-time
Subject type: compulsory
Field and discipline of study: Field of exact and natural sciences, Discipline of physical sciences.
Level of education: first-cycle studies
Year of study/semester: 1st year/1st Semester
ECTS Credits: 4
Student Workload Balance:
- Participation in tutorials (60 hours),
- Participation in consultations (15 hours),
- Student's own work at home (25 hours),
Quantitative Indicators:
- Student workload related to classes requiring direct teacher involvement - 3 ECTS;
- Student workload related to independent work - 1 ECTS.
Principles of Artificial Intelligence (AI) Use:
During classes, the use of AI systems is permitted for:
1. Machine translation of source texts from foreign languages.
2. Searching for and organizing scientific sources.
3. Creating simulations and modeling of physical phenomena discussed in lectures.
If a student is found to have violated the above principles, he or she may be held accountable under separate disciplinary regulations.
Topics covered during the seminar:
1. Basic topics in mathematical logic and set theory; mathematical induction.
2. Elementary functions. Polynomials. The exponential function. Logarithms. Trigonometric and inverse trigonometric functions.
3. Complex numbers. Polar and exponential forms – De Moivre’s formula. Roots of complex numbers.
4. Two- and three-dimensional vector and affine spaces: fixed (position) vectors and free vectors. Bases and coordinates, dot product, cross product. Orthogonal projection. Reflections across lines and planes.
5. Elements of analytic geometry. Equations of lines and planes. Equations of selected plane curves.
6. Elements of combinatorics, probability theory, and mathematical statistics. (Discrete) random variables, distribution functions, expected values.
|
Term 2024:
None |
Type of course
Mode
Prerequisites (description)
Course coordinators
Term 2024: | Term 2025: |
Learning outcomes
Knowledge: The graduate knows and understands:
KP6_WG2 advanced knowledge of elements of higher mathematics and mathematical methods used in physics;
Skills: The graduate is able to:
KP6_UW6 learn independently, finding necessary information in professional literature, databases, and other sources, and critically evaluate information from unverified sources;
KP6_U01 organize their own work and that of their team;
KP6_UU1 engage in lifelong learning and inspire and organize the learning process of others.
Social Competencies: The graduate is ready to:
KP6_KK1 critically evaluate their knowledge and the content they receive;
KP6_KK2 recognize the importance of knowledge in solving cognitive and practical problems;
KP6_KK3 collaborate with experts when faced with difficulties in independently solving problems.
KP6_KO1 fulfill social obligations and reject disinformation regarding acquired knowledge;
Assessment criteria
Two in-class tests covering the material previously introduced during classes, each consisting of approximately 6–10 problems of varying difficulty. An activity component is added to the final result (up to +12%, proportionally to the number of contributions). The final grade is determined on the basis of the sum of the arithmetic mean of the percentage scores from two tests and the activity component.
Grading scale:
0% - 50% - unsatisfactory grade 2 (failed)
51% - 60% - satisfactory grade 3
61% - 70% - satisfactory grade plus 3.5
71% - 80% - good grade 4
81% - 90% - good grade plus 4.5
91% - 100% - very good grade 5
Bibliography
1) B.Gdowski, E.Pluciński, Zbiór zadań z rachunku wektorowego i geometrii analitycznej, Oficyna Wydawnicza PW 2000,
2) H.Rasiowa, Wstęp do matematyki współczesnej, PWN 1972
3) K.Kuratowski, Wstęp do teorii mnogości i topologii, PWN 1970
4) T. Gerstenkorn, T.Śródka, Kombinatoryka i rachunek prawdopodobieństwa PWN 1972,
5) A. Birkholz, Analiza matematyczna dla nauczycieli, PWN 1980
|
Term 2024:
None |
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: