Teaching Guide 2021 Fall - 11829 Euclidean and Non-Euclidean Geometry I Online Mode
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Euclidean and Non-Euclidean Geometry I
Teaching Guide 2021 Fall
11829 Euclidean and Non-Euclidean Geometry I
Online Mode
Universidad Católica San Antonio de Murcia – Tlf: (+34) 968 278 160 info@ucam.edu – www.ucam.edu
Mathematics - Tlf: (+34) 902 102 101Euclidean and Non-Euclidean Geometry I
11829 Euclidean and Non-Euclidean Geometry I
Course Information
Module: Euclidean and Non-Euclidean Geometry I
Field: Mathematics
Character: Introductory Training
Credits: 4
Course Instructor Information
Teacher: TBA
Online hours: 55 Hours
Student’s attention timetable: Monday to Friday, 10h - 12h
Module coordinator teacher: To Be Assigned
Brief Description
This course offers an introduction to the history, development and
philosophical implications of elementary Euclidean and the
discovery of Non-Euclidean geometry. The main topics such as the
origins of geometry, parallel postulate, Hilbert’s axioms,
hyperbolic geometry, geometric transformations, the discovery of
non-Euclidean geometry will be discussed. After learning this
course, students will develop the skills of applying geometric
concepts to real-world situations.
Previous Requisite(s)
11801 Calculus I; 11804 Linear Algebra
Mathematics - Tlf: (+34) 902 102 101Euclidean and Non-Euclidean Geometry I
Competences and Learning Results
1. Cross Curricular Competences
(1) Analysis and synthesis skills;
(2) Planning and organizational skills;
(3) Problem solving skills;
(4) Decision making skills;
(5) Information management skills;
(6) Computer science knowledge related to the field of study;
(7) Capacity for critical thinking;
(8) Autonomous learning;
(9) Motivation for quality;
(10) Reflection ability.
2. Learning Results
Having successfully completed this course, students will be able to:
1. Understand the concepts and theories of Euclidean geometry,
non-Euclidean geometry, and parallel postulate;
2. Get acquainted with the history and development of geometry
(Euclidean and non-Euclidean);
3. Develop technological skills in using Geometer’ s Sketchpad to
explore geometry;
4. Work independently and with others to identify and
communicate geometric truths.
Mathematics - Tlf: (+34) 902 102 101Euclidean and Non-Euclidean Geometry I
3. Specific Competences
1. Develop the ability to write careful mathematical proofs;
2. Have the ability to apply the knowledge to the practice;
3. Use regularly information and communication technology in
the professional performance;
4. Communicate fluently within the work environment and work
in team;
5. Follow or provide step by step instructions for geometric
construction.
Methodology
Hours of work Hours of work
Methodology Hours
Face-to-face Non Face-to-face
Online Video 50
88 hours (60%)
Online Forum Discussion 8
Assessment 30
Personal study 30
68 hours (40%)
Tasks 22
Practical Teaching 10
Preparation
Bibliographic Search 6
TOTAL 156 88 68
Required Textbook(s)
Marvin Jay Greenberg, Euclidean and Non-Euclidean Geometries.
Development and History, 3rd Edition, W. H. Freeman, 1993.
Mathematics - Tlf: (+34) 902 102 101Euclidean and Non-Euclidean Geometry I
Class Schedule
Week Lesson Content
1 Euclid’s Geometry: The Origins of Geometry
2 The axiomatic Method
1 3 Euclid's First Four Postulates
4 Logic and Incidence Geometry
5 Informal Logic
Homework 1
6 Models
7 Hilbert’s Axioms: Flaws in Euclid
2 8 Axioms of Betweenness and Congruence
9 Axioms of Continuity and Parallelism
10 Neutral Geometry
Quiz 1
11 Geometry without the Parallel Axiom
12 History of the Parallel Postulate
3 13 Midterm Test
14 The Discovery of Non-Euclidean Geometry
15 Subsequent Developments
Homework 2
16 Hyperbolic Geometry
17 Classification of Parallels
4 18 Independence of the Parallel Postulate
19 Philosophical Implications
20 Geometry of Physical Space
Quiz 2
21 Geometric Transformations
22 Applications to Geometric Problems
5 23 Future Results in Hyperbolic Geometry
24 Coordinates in the Hyperbolic Plane
25 Final Exam
Mathematics - Tlf: (+34) 902 102 101Euclidean and Non-Euclidean Geometry I
Rating System
1. Assessment
ASSESSMENT ITEM PERCENT OF FINAL GRADE
2 Homework 20% (10% for each)
2 Quizzes 20% (10% for each)
Midterm Test 25%
Final Exam 35%
2. Grading Scale
A+ 96-100 A 90-95 A- 85-89
B+ 82-84 B 78-81 B- 75-77
C+ 71-74 C 66-70 C- 62-65
D 60-61 F < 60
General Expectations
Students are expected to:
Attend all classes and be responsible for all materials covered in class and
otherwise assigned;
Complete the daily required reading and assignments before class;
Review the previous class notes before class and make notes about questions you
have about the previous class or the course reading;
Participate in class discussions and complete required written work on time;
Refrain from texting, phoning or engaging in computer activities unrelated to class
during the class period;
While class participation is welcome, even required, you are expected to refrain
from private conversations during the class period.
Mathematics - Tlf: (+34) 902 102 101Euclidean and Non-Euclidean Geometry I
Attending Policy
Regular and prompt attendance is required. Attendance will be taken at the start of the
course. Those that miss their name, during roll call, will be counted as absent.
Students can miss up to three classes (including labs) and earn 7% (out of 10%). After
the third absence, students will earn a grade of 0% (out of 10%). Arriving late and/or
leaving before the end of the class are equivalent to absences.
Policy on “Late Withdrawals”
In accordance with the policy of UCAM, appeals for late withdrawal will be approved
ONLY in case of medical emergency and similar crises.
Academic Honesty
All students are expected to respect academic honesty policy. Instructors will fail
assignments that show any evidence of plagiarism or other forms of cheating and will
also report the student's information to the University Administration Office. A
student reported to the University for cheating will be placed on the list of disciplinary
probation; a student reported twice will be suspended or expelled.
Special Needs or Assistance
Please contact the University Administrative Office immediately if you have a
learning disability, a medical issue, or any other type of problem that prevents
professors from seeing you have learned the course material.
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