Course: Geometry 1

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Course title Geometry 1
Course code KMA/G1
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 2
Semester Winter and summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Lávička Miroslav, Doc. RNDr. Ph.D.
  • Výrut Radek, Mgr.
Course content
Affine space, affine coordinate system and its transformations. Subspaces and their descriptions. Mutual position of subspaces, specially for hyperplanes. Ratio of lengths, linear (specially convex) combination of points, subsets of affine subspaces. Euclidean space and its subspaces, Cartesian coordinate system and its transformations (mainly translation and rotation). Cross and scalar triple products, their generalizations and geometric meaning. Orthogonality and distances of subspaces, angles of lines and hyperplanes. Conics in the plane, quadrics in the space ? definitions, properties, applications.

Learning activities and teaching methods
Interactive lecture, Lecture supplemented with a discussion, E-learning, Cooperative instruction, Discussion, Task-based study method, Students' self-study, Textual studies, Lecture, Practicum
  • Contact hours - 39 hours per semester
  • Preparation for an examination (30-60) - 50 hours per semester
  • Preparation for formative assessments (2-20) - 10 hours per semester
  • Preparation for comprehensive test (10-40) - 10 hours per semester
prerequisite
professional knowledge
vysvětlit základní poučky z rovinné, eventuálně prostorové analytické geometrie na úrovni střední školy
popsat a vysvětlit základní postupy pro řešení geometrických úloh
popsat a vysvětlit základní principy z lineární algebry a vektorového počtu
popsat a vysvětlit základní principy z kalkulu
professional skills
aplikovat osvojené postupy na elementární geometrické úlohy na úrovni střední školy
počítat s vektory, maticemi a determinanty a řešit soustavy lineárních a kvadratických rovnic
používat aparát kalkulu na základní i středně pokročilé úlohy
general eligibility
N/A
N/A
N/A
N/A
learning outcomes
professional knowledge
definovat afinní prostor a zavést vhodnou soustavu souřadnic, rozumět problematice afinních podprostorů, odvozovat jejich rovnice a určovat jejich vzájemnou polohu
definovat eukleidovský prostor, zavést kartézskou soustavu souřadnic jakožto specializaci obecné afinní soustavy souřadnic, sestavovat rovnice ortogonálních podprostorů, určovat vzdálenosti a odchylky eukleidovských podprostorů
definovat a klasifikovat kuželosečky v eukleidovské rovině, převést jejich vyjádření na kanonické tvary a rozpoznávat je
definovat a klasifikovat kvadriky v trojrozměrném eukleidovském prostoru, převést jejich vyjádření na kanonické tvary a rozpoznávat je a aktivně je používat
professional skills
aktivně používat analytickou metodu při řešení matematických i aplikačních problémů
řešit geometrické úlohy s lineárními a kvadratickými objekty
aktivně používat analytickou metodu při vizualizaci nejrůznějších matematických konceptů
nalézat a využívat aplikační možnosti nejen v geometrii a dalších matematických disciplínách, ale i v přírodních vědách, počítačové grafice atd
general eligibility
N/A
N/A
teaching methods
professional knowledge
Lecture
Lecture supplemented with a discussion
Interactive lecture
Practicum
E-learning
Task-based study method
Textual studies
Cooperative instruction
Students' self-study
Discussion
professional skills
Lecture
Lecture with visual aids
Interactive lecture
Practicum
E-learning
Task-based study method
Textual studies
Cooperative instruction
Students' self-study
Discussion
general eligibility
Lecture
Lecture with visual aids
Interactive lecture
Practicum
E-learning
Task-based study method
Textual studies
Cooperative instruction
Discussion
assessment methods
professional knowledge
Combined exam
Test
Seminar work
professional skills
Combined exam
Test
Seminar work
general eligibility
Combined exam
Test
Seminar work
Recommended literature
  • Budinský, B. Analytická a diferenciální geometrie. 1. vyd. Praha : SNTL, 1983.
  • Ježek, František; Míková, Marta. Maticová algebra a analytická geometrie. 2., přeprac. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-996-6.
  • Mahel a kol. Sbírka úloh z lineární algebry a analytické geometrie. ČVUT, 1980.
  • Sekanina, M. a kol. Geometrie. 1. díl..
  • Sekaninová, A. a Janyška, J. Analytická teorie kuželoseček a kvadrik. Alfa, Bratislava, 1984.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Education Physics in Education (16) Physics courses 2 Winter
Faculty of Education Biology in Education (15) Biology courses 3 Winter
Faculty of Education Geography in Education (13) Pedagogy, teacher training and social care 3 Winter
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 2 Winter
Faculty of Applied Sciences Geomatics (2012) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Geomatics (2015) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 2 Winter
Faculty of Applied Sciences Land-use Planning (2017) Special and interdisciplinary fields 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 2 Winter
Faculty of Education Chemistry in Education (16) Chemistry courses 2 Winter
Faculty of Education Biology in Education (16) Biology courses 2 Winter
Faculty of Education Chemistry in Education (13) Chemistry courses 3 Winter
Faculty of Education Biology in Education (13) Biology courses 3 Winter
Faculty of Applied Sciences Building Structures (2010) Construction industry, geodesy and cartography 2 Summer
Faculty of Applied Sciences Land-use Planning (2016) Special and interdisciplinary fields 2 Winter
Faculty of Education Physics in Education (17) Physics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 2 Winter
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 1 Winter
Faculty of Education - (16) Pedagogy, teacher training and social care 2 Winter
Faculty of Education Physical Education in Education (1) Physical education and sport 3 Winter
Faculty of Education Studies in Mathematics (16) Mathematics courses 2 Winter
Faculty of Education Biology in Education (17) Biology courses 2 Winter
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 2 Winter
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 2 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 2 Winter
Faculty of Education Chemistry in Education (15) Chemistry courses 3 Winter
Faculty of Education Biology in Education (14) Biology courses 3 Winter
Faculty of Education Information Technologies in Education (14) Informatics courses 3 Winter
Faculty of Education Physics in Education (13) Physics courses 3 Winter
Faculty of Education - (17) Pedagogy, teacher training and social care 2 Winter
Faculty of Applied Sciences Land-use Planning (2014) Special and interdisciplinary fields 2 Winter
Faculty of Education Studies in Mathematics (17) Mathematics courses 2 Winter
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 2 Winter
Faculty of Applied Sciences Scientific Computing and Modelling (2011) Mathematics courses 2 Winter
Faculty of Education Geography in Education (16) Pedagogy, teacher training and social care 2 Winter
Faculty of Education Physics in Education (15) Physics courses 3 Winter
Faculty of Education Physics in Education (14) Physics courses 3 Winter
Faculty of Education Chemistry in Education (14) Chemistry courses 3 Winter
Faculty of Education Geography in Education (15) Pedagogy, teacher training and social care 3 Winter
Faculty of Education Studies in Mathematics (15) Mathematics courses 3 Winter
Faculty of Education Geography in Education (1) Pedagogy, teacher training and social care 3 Winter
Faculty of Education Studies in Mathematics (1) Mathematics courses 3 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 2 Winter
Faculty of Education Information Technologies in Education (16) Informatics courses 2 Winter
Faculty of Education Information Technologies in Education (15) Informatics courses 3 Winter
Faculty of Education Geography in Education (14) Pedagogy, teacher training and social care 3 Winter
Faculty of Education Information Technologies in Education (17) Informatics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 2 Winter
Faculty of Education Information Technologies in Education (13) Informatics courses 3 Winter
Faculty of Education Studies in Mathematics (14) Mathematics courses 3 Winter
Faculty of Education Studies in Mathematics (13) Mathematics courses 3 Winter
Faculty of Applied Sciences Building Structures (2016) Construction industry, geodesy and cartography 2 Summer
Faculty of Applied Sciences Building Structures (2013) Construction industry, geodesy and cartography 2 Summer
Faculty of Education Chemistry in Education (17) Chemistry courses 2 Winter
Faculty of Education Geography in Education (17) Pedagogy, teacher training and social care 2 Winter
Faculty of Applied Sciences Land-use Planning (2013) Special and interdisciplinary fields 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 2 Winter
Faculty of Education Physical Education in Education (17) Physical education and sport 2 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 2 Winter
Faculty of Applied Sciences Building Structures (2017) Construction industry, geodesy and cartography 2 Summer