University of Debrecen -- Institute of Mathematics

College Geometry for Foundation students

Instructor: László Kozma, Associate Professor

Monday 14-16, Room M315 and Friday 14-16, Room M205 in the Math building

Compulsory/Recommended Readings:
L. Kozma, Cs. Vincze - College Geometry

Official Syllabus:

Topics: Elementary Geometry: triangles, right triangle, Pythagorean theorem, Thales theorem, height and leg theorems. Regular, equilateral triangles: symmetries. General triangles, triangle inequality, circumscribed, inscribed circles, sine and cosine theorem, calculations. Quadrilaterals: sum of angles, specials: parallelogram, rhombus, rectangle, square, kite: symmetries. Polygons: sum of angles, sum of diagonals, regular polygons: symmetries. Circles, tangent of a circle at a point of a circle, from outside point, length of the tangent segment. Geometrical transformation: planar transformation, reflection to an axis, reflection to a point, rotation around a point, translation, similarity, centro-similarity, theorem of parallels.
Coordinate geometry. Equations of lines, parallel and perpendicular lines. Equations of lines, touching lines, equations of ellipses, parabolas, and hyperbolas.

Exercises:
Week 1
Week 2
Week 3
Week 4
1st Sample Test
Week 6
Week 7
Week 8
Week 9
2nd Sample Test