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Course info
KMA / G1-A
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Course description
Department/Unit / Abbreviation
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KMA
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G1-A
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Geometry 1
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
2
[Hours/Week]
Tutorial
1
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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English
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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English
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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KMA/G1
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The main aim of this course is to give students a thorough introduction to the analytic geometry in n-dimensional affine and Euclidean spaces. The course also aims at giving the student a firm understanding of analytic method in the visualization of mathematical concepts, it develops the student's skills to solve problems using the analytic method and finally it shows several applications not only in mathematical disciplines but also in other sciences. In addition, since the course is taught in English, students will master the basic English terminology of the studied theory.
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Requirements on student
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During semester, students have to write two assignments (10 points each) - it is necessary to obtain at least 11 points from both.
The final examination is in the form of a written exam (70% of the grade) which is supplemented by an oral examination (30% of the grade). All assessment tasks will assess the learning outcomes, especially, the ability to provide logical and coherent proofs of chosen theoretical results and to use the analytic method on solving given problems.
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Content
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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.
This course is lectured in English, its content is equivalent to KMA/G1.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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-
Recommended:
Budinský, B. Analytická a diferenciální geometrie. 1. vyd. Praha : SNTL, 1983.
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Recommended:
Sekaninová, A. a Janyška, J. Analytická teorie kuželoseček a kvadrik. Alfa, Bratislava, 1984.
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Recommended:
Boček, Leo. Geometrie. I. Praha : Univerzita Karlova, 1982.
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Recommended:
Sekanina, M. a kol. Geometrie. 1. díl..
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Recommended:
Sekanina, M. a kol. Geometrie. 2. díl.. 1. vyd. Praha : Státní pedagogické nakladatelství, 1988.
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Recommended:
Boček, L., Šedivý J. Grupy geometrických zobrazení. SPN Praha, 1980.
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Recommended:
Ježek, František; Míková, Marta. Maticová algebra a analytická geometrie. 2., přeprac. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-996-6.
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Recommended:
Pomocné studijní texty na KMA/G1 - sekce "Materiály pro studenty"
(Lávička, M.)
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Recommended:
Příklady na cvičení z KMA/G1
(Holub, P.)
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Recommended:
Mahel a kol. Sbírka úloh z lineární algebry a analytické geometrie. ČVUT, 1980.
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Recommended:
Coxeter, Harold Scott MacDonald. The beauty of geometry : twelve essays. 1st pub. Mineola : Dover Publications, 1999. ISBN 0-486-40919-1.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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39
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Preparation for comprehensive test (10-40)
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20
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Preparation for formative assessments (2-20)
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15
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Preparation for an examination (30-60)
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60
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Total
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134
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
A good knowledge of linear algebra and vector calculus (KMA/LA or equivalent). Basic knowledge of space analytic geometry at the secondary school level. Skills in computing with vectors, matrices and determinants and in solving systems of linear and quadratic equations. In case of insufficient background knowledge, the teachers will suggest reading material to make up for it.
Since this course is taught in English, the active understanding of English language is presumed. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
Upon completion of the course a student will be able to:
- give the definition of affine space and introduce a suitable coordinate system;
- understand affine spaces, write down their descriptions and determine their mutual position;
- give the definition of Euclidean space and introduce Cartesian coordinate system as the specialization of affine coordinate system;
- determine equations of orthogonal subspaces, compute distances and angles of Euclidean subspaces;
- define and classify conics in Euclidean plane. Rewrite their equations on canonical form, identify and use them;
- define and classify quadrics in 3-dimensional Euclidean space. Rewrite their equations on canonical form, identify and use them;
- independently use the analytic method for solving problems from mathematics a from praxis;
- understand and use the English terminology of the theory stated above. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Test |
Seminar work |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Lecture supplemented with a discussion |
Interactive lecture |
Practicum |
E-learning |
Task-based study method |
Textual studies |
Cooperative instruction |
Self-study of literature |
Discussion |
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