SubjectsSubjects(version: 945)
Course, academic year 2023/2024
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Geometry I - NMUM203
Title: Geometrie I
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Mgr. Zdeněk Halas, DiS., Ph.D.
doc. RNDr. Jarmila Robová, CSc.
Class: M Bc. MZV
M Bc. MZV > Povinné
M Bc. MZV > 2. ročník
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility : NMTM203, NMUM808, NUMP010
Interchangeability : NMTM203, NMUM808, NUMP010
Is incompatible with: NUMP010, NMUM808, NMTM203
Is interchangeable with: NMUM808, NMTM203, NUMP010
Annotation -
Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (08.09.2013)
Analytical geometry of affine and Euclidean spaces and their subspaces. Sets of points defined by distance. This subject provides the high-school analytical geometry with theoretical base using linear algebra.
Course completion requirements -
Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (29.10.2019)
Credit
Attendance at seminars is compulsory for full-time students, maximum 3 absences are allowed.

Possible absences above the limit will be solved by additional homework.

There will be 2 tests, one in the middle of the semester, one at the end of the semester, 2 correction terms are allowed.

Both tests will have the same score, from each test individually the student must earn at least 50% of the points, for both tests together they must obtain at least 2/3 of the total of points.

Exam
The requirements of the exam correspond to the syllabus of the subject to the extent that was presented at the lecture, including everything that was ordered for individual study.

The exam can be taken after obtaining the credit.

The examination consists of a written and an oral part, which are consecutive (they cannot be divided into two terms).

Successful completion of the written part is a prerequisite for admission to the oral part.

Literature -
Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (08.09.2013)
  • Sekanina, M. a kol. Geometrie I. SPN, Praha, 1986.
  • Lávička, M. Geometrie I. Pomocný učební text. Plzeň, 2008. Dostupné z < http://home.zcu.cz/~lavicka/subjects/G1/texty/G1_texty.pdf>.
  • Jennings, G. A. Modern Geometry with Applications. Springer, 1996.
  • Bennett, M. K. Affine and Projective Geometry. John Wiley et sons, 1995.
Syllabus -
Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (08.09.2013)
Affine space
  • Affine space, subspace.
  • Coordinates and their transformation.
  • Linear combination of points. Definition of basic geometrical figures in plane, segment of line and its center, triangle, center of gravity.
  • Parametric equations of subspace.
  • (n-1)-dimensional subspace and its equation.
  • Subspace as intersection of (n-1)-dimensional subspaces.

Euclidean space

  • Vector spaces with scalar product, geometrical interpretation of scalar product.
  • Outer and vector product, geometrical interpretation. Axioms of measure.
  • Euclidean space and subspace, equation of (n-1)-dimensional subspace.
  • Cartesian coordinates.
  • Orthogonal subspaces.
  • Distance from a point to a subspace, distance of two subspaces.
  • Angle and its measure, angle of a line and a subspace.

Set of points satisfying a given property

  • Set of points defined by distance; axis of a segment of line, angle, belt.
  • Circle of Apollonios; power of a circle with respect to the point, chordal of two circles, chordal center of three circles.
  • General equation of a conic section, classification, singular and regular conic sections. Equations of regular conic sections and their properties. Conic sections as sections of a cone.
 
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