Download School of Biology - Soran University

NAME
PRACTICAL/TUTORIAL GROUP
Unit Course book
Geometry
Course code:Mth 203 GM
Unit Coordinator
Haideh Lotfolla Ghaderi
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 2
Course Description:
The aim of the course:
Geometry is the first topic in mathematics which was established based on
axiomatic approach. The aim of the course is to enable the student to understand Euclidean
an non-Euclidean geometries in parallel and learn about their differences. The student is
expected to know the independence of parallel axiom and it's impact on philosophy and
science.
Course Description:
Initially Euclidean Geometry is reviewed in short. Axiomatic approach and logic
is discussed. Neutral geometry is presented in detail. The history of geometry ends each
chapter. The discovery of non-Euclidean geometry is presented along with it's history,
Hyperbolic geometry is proposed. A number of different models is introduce which enables
the student to appreciate the independence of parallel axiom. Finally numerous problems
ends each chapter which needs plenty of time to solve them.
Homework:
Solution of problem in geometry for each subject in this course. Presentation of
Problems: When you come into class, you should be prepared to it. One person will
present each problem and then we will all discuss it.
Quiz: Each quiz will be an equivalent percentage to one homework set.
Forms of Teaching:
Geometry forms of teaching will be used to reach the objectives of the course: the head
titles and definitions and summary of conclusions, classification of materials and any
other illustrations, There will be classroom discussions and the lecture will give enough
background to translate, solve, analyse, and evaluate problems sets, and different issues
discussed throughout the course.
Email:
E.mail:[email protected]
M: 07508954775
Staff associated with the unit:
Staff
Room Number
Dr Farhad Janati
Teaching room
Email
[email protected]
Soran University
Department of mathematics
Unit: Geometry
Credit 3
Method of Assessment:
1 x 3 h lectures per week.
Examination and grading
Month’s exam: 30%
Classroom participation and assignments and homework 10%
Final exam: 60%
Marking System
The grades for each piece of assessed work are as follows:




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90-100 % is excellent
80-89% is very good
70-79% is good
60-69% is a moderate pass
50-59% is a pass
<49% is a fail
Unit Timetable/Content
University
Academic
Lecture Title & Content
Week
1st week
Introduction, history of geometry, summary of Euclidean and
non-Euclidean geometry, hyperbolic and elliptic geometry
Assessments
Greek and Egyption geometry
2nd week
3rd week
4th week
Axiomatic method, logical implication, undefined terms,
undefined terms of plane geometry, canonical terms
Four postulates of Euclid, Fifth postulate of Euclid,
Legendre’s attempt to prove parallel axiom.
Problem solving sessions
Informal logic, logic rule 1, theorems and proof, logic rule 2,
negation
5th week
Logic rule 5, quantifiers, logic rules 6 and 7, rules of
detachment, law of
Excluded middle
Incidence geometry, axioms of Incidence geometry, models,
6th week
examples, 3, 4, and 5 points geometry
First examination
Canonical axioms, consistency, homomorphism of models,
7th week
danger of diagrams
Problem solving
8th week
Problem solving sessions
Hilbert axioms, introduction, betweenness axioms, proving
9th week
half line theorems,
Theorems of boundaries, Pash theorems.
Crossbar theorem plus three major theorems, congruence
10th week
theorem axioms, discussing 6 axioms in detail, superposition
proof, motion axioms, proof of SAS
11th week
Second examination
Proving 10 theorems about congruence
Continuity axioms, Archemid axioms, Dedekind axioms,
12th week
Euclid proof, circle
Continuity axioms, elementary continuity principle, parallel
axioms of Hilbert
13th week
Problem solving sessions
Neutral geometry, geometry without parallel axiom, angle
14th week
theorems, exterior angle theorems, Euclid proof, ASA proof,
measuring angles and segments, Sossre-legender theorem,
angle and segment sum theorems.
Convex rectangles, equivalence of parallel axioms, Euclid
15th week
and Hilbert, alternative forms of Hilbert axiom angle sum of
triangle triangles, existence of rectangle
16th week
17th week
18th week
19th week
Problem solving sessions
Problem solving session
Third examination
History of parallel axiom, Proclus, Valis, Soccre and
Lambert, Bulyai
Problem solving sessions
Discovery
20th week
of
non-Euclidean
geometry,
Gauss,
,
Lobachevosky, Hyperbolic geometry and it's axioms,
General theorem of hyperboline, , sum of angles, congruent
triangles
Parallel lines accepting a common perpendicular line,
21st week
proving six theorems in hyperbolic geometry, Asymptotic
parallel line. Theorems of asymptotic parallel lines,
categorizing parallel lines.
22nd week
Problem solving sessions.
Fourth examination
23rd week
Independence of parallel axiom, compatibility of hyperbolic
geometry, First theorem of metamathematics
Beltrami–klein model, incidence axioms in Klein model,
24th week
Proving Hilbert axioms in Poincare model, orthogonal lines
in this model, inversion in circles.
25th week
Proving 12 theorems about inversion in circles
26th week
27th week

A model of the hyperbolic geometry in physics, the projective nature of the
Beltrami–klein model
Problem solving
Fifth examination
Note that, Tutorials will be arranged by your lecturer during the class.
Tutorials & Assessments
Attendance at tutorials & Assessments is necessary in order to gain marks for the given
exercise.
Recommendation
Keeping a wall diary is recommended to enter all deadline dates so you can see what
assignments are due in. It is also essential to leave yourself sufficient time to complete
the work.
Recommended Reading &References:
1. Greenberg ,M.; " Euclidean and Non Euclidean Geometry" Freeman Inc. 1993
2.
Mcphee, I. ;" Euclidean or non Euclidean Geometry"
3. Shorme, H. & Robin; "Geometry: Euclidean and Beyond"
4. George, M.; "The foundation of geometry and the non-Eucllidean plane"
5. Heath & Li Thomas,S.;"The thirteen books of the elements"