COLLEGE GEOMETRY, S2015, MATH 50036-306 / 50036- 506
Instructors: Lectures: MW 16:00-17:15 SMLC-120, Dimiter Vassilev, Associate Professor; Office: SMLC, Office 326; Email: vassilev@unm.edu
Office Hours: Monday, Wednesday 2pm-3pm, Friday 10am-11am. Feel free to stop-by anytime if you have a quick question.
Textbook: Lee J. M., Axiomatic Geometry.
Catalog Description: An axiomatic approach to fundamentals of geometry, both Euclidean and non-Euclidean. Emphasis on historical development of geometry
Prerequisite: C (not C-) or better in 162 or 215..
Please note the following guidelines for the course:
GRADING: Your total course grade is based on your ranking and percentile in the class computed using the in-class exams, online homework, weekly quizzes and the final exam scaled as follows:
Two in-class exams: 100 points each (200 total)
Homework (lowest two will be dropped): 200 points
Quizzes (lowest two will be dropped): 100 points
Final Exam: 200 points
Total: 700 points
To get full credit on exams and quizzes you need to show your work, neatly, in clear and correct mathematical notation, annotated by English sentences where appropriate. You will be graded based on the work shown, not on the answer.
Note on Ws: If you withdraw after the 3rd week of class, you will receive a W. If you do not withdraw, you will receive a letter grade of A,B,C,D or F (and not a W).
CALCULATORS: We will not use any (graphing or non-graphing) calculators on the exams or quizzes.
EXAMS: The exam dates are given in the syllabus. No makeup exams will be given unless you contact your instructor ahead of time with a documented “university authorized absence” (illness, family emergency, active participation in scholarly or athletic events).
ATTENDANCE: Attendance at UNM and homework is mandatory. If you have missed more than 4 attendance+homework+quizzes in the first 3 weeks you will be dropped from the course. Similarly, students with absences and lack of work during the rest of the semester may be dropped. Tardiness or early departure may be regarded as absence. Please note that it is the students responsibility to drop the course if he/she stops attending. A failing grade of F may be assigned if the student stops attending and does not drop.
STUDENT BEHAVIOUR: Be courteous and respectful towards the class: be on time for lectures, turn off cell-phones and refrain from talking in class, leaving the classroom in the middle of a lecture or doing any other activity that could be disruptive to the class. Cheating will not be tolerated.
ACCESSIBILITY STATEMENT: We will accommodate students with documented disabilities. During the first two weeks of the semester, those students should inform the instructor of their particular needs.
HOMEWORK: Homework related material including solutions of some problems will be posted on UNMLearn. The general rule is that homework assigned in one week is due the first class of the following week.
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Day |
Class Date |
Home Work |
Due Date |
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M |
1/12 |
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Wednesday, 1/21 at the beginning of
class
HW1 |
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W |
1/14 |
Appendix G/ GD; Read Chapter I |
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1/19 |
MLK - no class |
Monday, 1/26 at the beginning of
class
HW2 |
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W |
1/21 |
1) 2A, 2) 2H, 3) 2I (go to UNMLearn for text) |
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M |
1/26 |
1)2C, 2) 2E |
Monday, 2/02 at the beginning of
class
HW3 |
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W |
1/28 |
3) 2D, 4) 2T |
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M |
2/2 |
1) Let A be an affine I.G. We say that two lines l and l' are equivalent if they coincide or they are parallel. Show that if l is equivalent to l', and l' is equivalent to l", then l is equivalent to l". This completes the proof of the claim made in class that we have an equivalence relation. |
Monday, 2/9 at the beginning of
class
HW4 |
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W |
2/4 |
2) Let A be an incidence geometry in which every line has at least three distinct points. a) What are the least number of points and lines that A can have? b) Answer part a) assuming in addition that A satisfies the Euclidean parallel postulate. |
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2/9 |
1) Let A be an incidence geometry in which every line has at least three distinct points and A satisfies the Euclidean parallel postulate. Show that there is a model of A with 9 points and 12 lines. 2) 3F |
Monday, 2/16 at the beginning of
class
HW5 |
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W |
2/11 |
3) 3D, 4) 3G |
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M |
2/16 |
1) 3H, 2) 3L |
Monday, 2/23 at the beginning of
class
HW6 |
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W |
2/18 |
3) 3L 4) Let A , B and C be three noncollinear points. Show that if P is a point on the segment AB then the segment CP does not intersect the segments AC and BC. Note: In particular, this fixes the gap in the example of a "faulty proof" showing that the two base angles of an isosceles triangle are equal. |
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2/23 |
2) Prove Theorem 3.50. |
Monday, 3/2 at the beginning of
class
HW7 |
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W |
2/25 |
3) 4A 4) 4E |
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M |
3/2 |
Homework posted on ILEARN |
Monday, 3/16 at the beginning of
class HW8 (see ILEARN for solutions) |
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W |
3/4 |
Midterm 1 |
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M |
3/9 |
Spring Break |
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W |
3/11 |
Spring Break |
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M |
3/16 |
1) 5D 2) 5G with the following correction: Show that given two triangles ∆ABC and ∆A'B'C' such that angle ABC =angle A'B'C', AC=A’C’ and CB=C’B’, then either angle ABC =angle A'B'C' or they are non-equal supplementary angles. This is almost a proof of Theorem 5.24, Exercise 5G, except for the fact that as stated Theorem 5.24 is formally not correct. Hint: Compare the lengths of the segments AB and A'B'. |
Monday, 3/23 at the beginning of
class HW9 (see ILEARN for selected solutions) |
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W |
3/18 |
3) 6D 4)6F 5) read Chapter 6 (have questions ready for Monday) |
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3/23 |
1) 4I 2) 5I |
Monday, 3/30 at the beginning of
class
HW10 |
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W |
3/25 |
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M |
3/30 |
1) 7G 2) 7K 3) 10A |
Monday, 4/6 at the beginning of
class
HW11 |
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W |
4/1 |
4) 10D 5) 10G |
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M |
4/6 |
1) 9D |
Monday, 4/13 at the beginning of
class HW12 (see ILEARN for selected solutions) |
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W |
4/8 |
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4/13 |
1) 12A 2) 12C |
Monday, 4/20 at the beginning of
class HW13
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W |
4/15 |
3) 12D 4) Let ∆ABC be a right triangle and H be the foot of the altitude from C to the hypotenuse AB. a) Show ∆AHC and ∆CHB are similar triangles. b) Show that BC2=BH ·BA and CH2=HA ·HB. |
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4/20 |
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Monday, 4/27 at the beginning of
class HW14 (see ILEARN for solutions) |
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W |
4/22 |
Midterm 2 |
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M |
4/27 |
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W |
4/29 |
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F |
5/4 |
Final Exam Monday, May 4, 5:30pm–7:30pm |
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