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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: 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"