Revision for MATH

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Revision for MATH 348 Proposal Reference : 13118 Number PRN Alias : 17-18#597 Version No : 2 Submitted By : Ms Angela White Edited By : Prof Johanna Neslehova Display Printable PDF

Summary of Changes Course Title, Course Description, Restrictions

Current Data New Data Program Affected? Y Program Change N (Simple Change) - MATH 348 Topics in Form Submitted? Geometry must be removed and replace by MATH 348 Euclidean Geometry 1) B.Sc. Math Major (54 credits) under Complementary Courses 15-21 credits selected from the following at least 5 credits must be at the 400 or 500 level.; remove MATH 348 Topics in Geometry and add MATH 348 Euclidean Geometry 2) B.A Major Concentration Mathematics (36 credits) under Complementary Courses remaining credits from remove MATH 348 Topics in Geometry and add MATH 348 Euclidean Geometry 3) B.A. Minor Concentration Mathematics (18 credits)under Complementary Course List remove MATH 348 Topics in Geometry and add MATH 348 Euclidean Geometry 4) B.A Supplementary Minor Concentration in Mathematics (18 credits) under Complementary Courses remove MATH 348 Topics in Geometry and add MATH 348 Euclidean Geometry 5) B.A & Sc. Major Concentration Mathematics (36 credits) under Complementary Courses remaining credits from remove MATH 348 Topics in Geometry and add MATH 348 Euclidean Geometry 6) B.A.B,Sc. Minor Concentration Mathematics (18 credits)under Complementary Course List remove MATH 348 Topics in Geometry and add MATH 348 Euclidean Geometry Subject/Course/Term MATH 348

one term

Credit Weight or 3 credits. CEU's Course Activities A - Lecture

Course Title Course Title on Topics in Course Title on Euclidean Transcript Geometry Transcript Geometry

Course Title on Topics in Course Title on Euclidean Calendar Geometry. Calendar Geometry

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Rationale We revised the course title and content of MATH 348 to make it more suitable for students in our programs. Responsible Instructor Course Description Selected topics - the particular selection Points and lines in a triangle. may vary from year to year. Topics Quadrilaterals. Angles in a circle. include: isometries in the plane, symmetry Circumscribed and inscribed circles. groups of frieze and ornamental patterns, Congruent and similar triangles. Area. equidecomposibility, non-Euclidean Power of a point with respect to a geometry and problems in discrete circle. Ceva’s theorem. Isometries. geometry. Homothety. Inversion. Teaching Dept. 0290 : Mathematics and Statistics Administering SC : Faculty of Science Faculty/Unit Prerequisites Prerequisite: MATH 133 or equivalent or permission of instructor. Corequisites Restrictions Not open to students who have taken MATH 398 Honours Euclidean Geometry. Supplementary Calendar Info Additional Course Charges Campus Projected Enrollment Requires Resources Not Currently Available Explanation for Required Resources Consultation Reports Attached? Effective Term of 201809 Implementation File Attachments No attachments have been saved yet. To be completed by the Faculty For Continuing Studies Use

Approvals Summary

Show all comments Version Departmental Departmental Departmental Other Curric/Academic Faculty SCTP Version No. Curriculum Meeting Chair Faculty Committee Status Committee

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2 Approved by Department Meeting Edited by: Johanna Neslehova on: Jan 15 2018 1 Approved Approved Johanna by Neslehova Department Meeting Date: Meeting Dec 04 2017 Created on: Approval Date: Jan 11 2018 Jan 11 2018 View Comments

3 of 3 24/01/2018 11:15 AM Course Outline MATH 348/398: Euclidean Geometry/Honours Euclidean Geometry

Short Course Description: Points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion.

Textbook: Oﬃcial course notes are available on https://dylanmathblog.wordpress.com/topics-in-geometry/ For additional reading, see Roger A. Johnson’s Advanced Euclidean Geom- etry.

Syllabus: Reflection, bisector of a segment, circumscribed circle of a triangle, rotation, congruent triangles. Inscribed and central angles in a circle, quadrilateral inscribed in a circle. Angle bisector, “strongest theorem of geometry”, inscribed circle of a triangle, quadrilaterals with inscribed circles. Escribed circles, altitudes, orthocentre. Area, Thales’ theorem, nine-point circle, Newton’s theorem. Similarity, similar triangles, Pythagorean theorem, Napoleon’s theorem, Ptolemy’s theorem. Angle bisector theorem, circle of Apollonius. Power of a point with respect to a circle, radical axis, Bri- anchon’s theorem. Ceva’s theorem, special points in a triangle: centroid, Gergonne point, Nagel point, Lemoine point. Menelaus’ theorem, Simson line. Groups of transformations, isometry, translation, glide reflection, clas- sification of isometries. Homothety, Euler line. Inversion with respect to a circle, Apollonius problem. Hyperbolic geometry, cross-ration.

Prerequisites: MATH 133 or equivalent or permission of instructor.

Differences in the Courses: MATH 398 is intended for students in Hon- ours programs. The courses share the same lectures, but the assignments, midterm and final exam for MATH 398 will be at a higher level of difficulty and depth.

Grading Scheme for MATH 348/398: The maximum of: • 25% Assignments + 25% Midterm + 50% Final

• 25% Assignments + 75% Final

1 Statements:

• McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagia- rism and other academic oﬀences under the Code of Student Conduct and Disciplinary Procedures (see http://www.mcgill.ca/integrity for more information).

• In accord with McGill Universitys Charter of Students Rights, students in this course have the right to submit in English or in French any written work that is to be graded. This right applies to all written work that is to be graded, from one-word answers to dissertations.

• In the event of extraordinary circumstances beyond the Universitys control, the content and/or evaluation scheme in this course is subject to change.