Contact Information: My contact information is posted on my web page.
Course Description: A rigorous course in axiomatic geometry. Birkoff's metric approach (in which the axioms incorporate the concept of real numbers) is used. Throughout the course, various models will be introduced to illustrate the axioms, definitions and theorems. These models include the familiar Cartesian Plane and Spherical Geometry models, but also less familiar models such as the Klein disk and the Poincaré disk. Substantial introduction to the method of proof will be provided, including discussion of conditional statements and quantified conditional statements and their negations, and discussion of proof structure for direct proofs, proving the contrapositive, and proof by contradiction.
Prerequisites Shown in Online Course Description: (MATH 3050 Discrete Math or CS 3000 Introduction to Discrete Structures) and (MATH 3200 Applied Linear Algebra or MATH 3210 Linear Algebra)
Sufficient Prerequisite: Concurrent registration in (MATH 3050 Discrete Math or CS 3000 Introduction to Discrete Structures or MATH 3200 Applied Linear Algebra or MATH 3210 Linear Algebra). If you satisfy any of these Sufficient Prerequisites and would like to take MATH 3110/5110, contact Mark Barsamian to request permission to register.
Cross-Listing: Note that this is a cross-listed course: Undergraduate students register for MATH 3110; Graduate students, for MATH 5110.
Special Needs: If you have physical, psychiatric, or learning disabilities that require accommodations, please let me know as soon as possible so that your needs may be appropriately met.
Class Meetings: Mon, Wed, Fri 9:40am – 10:35am in Morton 326
Final Exam: Fri May 2, 1:00pm – 3:00pm in Morton 326
Attendance Policy:
Attendance is required for all class meetings, and your attendance (or absence) will be recorded, but attendance is not used in the calculation of your course grade.
Missing Class: If you miss a class for any reason, it is your responsibility to learn the stuff that you missed. You can do this by studying a classmate's notes and by reading the textbook. Prof. Barsamian will not use office hours to teach topics discussed in class meetings to students who were absent.
Missing a Quiz or Exam Because of Illness: If you are too sick to take a quiz or exam, then you must do these three things:
Send Prof. Barsamian an e-mail before the quiz/exam, telling him that you are going to miss it because of illness. He will arrange for a date and time for a Make-Up quiz/exam. (Generally, the Make-up for a Friday quiz/exam needs to take place on the following Monday or Tuesday. Therefore, it is important to communicate with him right away.)
Go to the Hudson Student Health Center (or some other Medical Professional) to get examined.
Later, you will need to bring Prof. Barsamian your documentation from the Hudson Student Health Center (or a Medical Professional) showing that you were treated there.
Without those three things, you will not be given a make-up.
(Observe that self-diagnosis of an illness is not a valid documentation of an illness. In other words, you can't just tell Prof. Barsamian that you did not come to a Quiz or Exam because you were not feeling well, and expect to get a Make-Up Quiz or Exam. If you are too sick to come to a Quiz or Exam, then you should be sick enough to go to a medical professional to get diagnosed and treated.)
Missing Quizzes or Exams Because of University Activity: If you have a University Activity that conflicts with one of our quizzes or exams, you must contact Prof. Barsamian well before the quiz or exam to discuss arrangements for a make-up. They will need to see documentation of your activity. If you miss a quiz or an exam because of a University Activity without notifying Prof. Barsamian in advance, you will not be given a make-up.
Missing Quizzes or Exams Because of Religious Observation: The Ohio University Faculty Handbook states the following:
Students may be absent for up to three days each academic semester to take time off for reasons of faith or religious or spiritual belief system or participate in organized activities conducted under the auspices of a religious denomination, church, or other religious or spiritual organization. Faculty shall not impose an academic penalty because of a student being absent nor shall faculty question the sincerity of a student's religious or spiritual belief systems. Students are expected to notify faculty in writing of specific dates requested for alternative accommodations no later than fourteen days after the first day of instruction.
For MATH 3110/5110, this means that if you will be missing any Spring 2025 Quizzes or Exams for religious reasons, and if you want to have a Make-Up Quiz/Exam, you will need to notify Mark Barsamian no later than Wed Jan 29. You and Prof. Barsamian will work out the dates/times of your Make-Up Quiz/Exam. (In general, if you are going to miss a Friday Quiz/Exam, Prof. Barsamian will schedule you for a Make-Up on the following Monday or Tuesday.)
Missing Quizzes or Exams Because of Personal Travel: This course meets on Mondays, Wednesdays and Fridays, and attendance is required. Your Personal Travel (to home for the weekend, or out of town for vacations, etc) should be scheduled to not conflict with those Monday/Wednesday/Friday meetings. If you miss a Recitation, Quiz, or Exam because of Personal Travel (not an Offical University Activity), you will not be given a make-up.
Policy on Cheating:
If cheat on a quiz or exam, you will receive a zero on that quiz or exam and Prof. Barsamian will submit a report to the Office of Community Standards and Student Responsibility (CSSR).
If you cheat on another quiz or exam, you will receive a grade of F in the course and Prof. Barsamian will again submit a report to the CSSR.
Syllabus: This web page replaces the usual paper syllabus. If you need a paper syllabus (now or in the future), unhide the next four portions of hidden content (Textbook Information, Exercises, Grading, Calendar) and then print this web page.
Textbook Information:
Title: Foundations of Geometry, 3rd Edition
Author: Gerard Venema
Publisher: Pearson (2022)
Obtaining the book: All students registered for Ohio University MATH 3110/5110 receive access to an online eText. The eText is found by clicking through the following sequence:
Canvas → Digital Course Materials → Vital Source Course Dashboard.
The eText may be read in a web browser on a computer, tablet, or phone, but the reading experience will be much more convenient (especially on tablets and phones) if you download the VitalSource App and read the eText on the app. (If you read the eText on the VitalSource App, there might be lifetime access. Prof. Barsamian is not sure about this, and is trying to find out the details.)
For those of you who prefer to read a printed book, it is possible to rent or purchase a printed copy of the text through the publisher's website. And there may be a discount for the print book for the students enrolled in this course. Prof. Barsamian is trying to determine if there is a discount. (The publisher does not provide clear information about the process for purchasing the printed book.)
ISBN Numbers (for the Printed Book):
ISBN-10: 0136845266
ISBN-13: 978-0136845263
Supplemental Reading: Our course relies heavily on logical terminology, terminology that is also widely used in other proof-based math courses. The terminology is sometimes introduced in the prerequisite courses CS 3000 and MATH 3050. You may not have learned that terminology well there, or you may have learned and forgotten it. The terminology is presented in our textbook. As with most topics that our textbook covers, the material is explained pretty well, so be sure to read the textbook! But our textbook’s presentation of the terminology is very brief – only one section of the book! You may also find useful this Supplemental Reading on Logical Terminology, Notation, and Proof Structure. It gives a concise summary of the terminology that is needed for our course. It is a condensed version of some of the material that is presented in parts of Chapters 2 and 3 of Susannah Epp’s book Discrete Mathematics with Applications that is sometimes used in CS 3000 and MATH 3050. Even though it is condensed relative to the presentation in Susannah Epp’s book, the Supplemental Reading is much more detailed than the presentation in our geometry book.
Exercises:
Exercises for Ohio University 2024 - 2025 Spring Semester MATH 3110/5110 (College Geometry) (Barsamian) (from Venema, Foundations of Geometry, 3nd Edition)
Your goal should be to write solutions to all the exercises in this list.
A Suggestion for Studying: Write down the solutions to these problems. Keep your written work organized in a loose-leaf notebook. Find another student, or a tutor, or Prof. Barsamian to look over your written work with you.
Grading:
Grading System for 2024 – 2025 Spring Semester MATH 3110/5110 (Barsamian)
During the course, you will accumulate a Points Total of up to 1000 possible points.
Written Homework: 10 Assignments @ 20 points each = 200 points possible
Quizzes: 10 Quizzes @ 20 points each = 200 points possible
Exams: 3 Exams @ 150 points each = 450 points possible
Final Exam: 150 points possible
At the end of the semester, your Points Total will be divided by \(1000\) to get a percentage, and then converted into your Course Letter Grade using the 90%, 80%, 70%, 60% Grading Scale described below.
The 90%, 80%, 70%, 60% Grading Scale is used on all graded items in this course, and is used in computing your Course Letter Grade.
A grade of A, A- means that you mastered all concepts, with no significant gaps.
If \(93\% \leq score \), then letter grade is A.
If \(90\% \leq score \lt 93\%\), then letter grade is A-.
A grade of B+, B, B- means that you mastered all essential concepts and many advanced concepts, but have some significant gap.
If \(87\% \leq score \lt 90\%\), then letter grade is B+.
If \(83\% \leq score \lt 87\% \), then letter grade is B.
If \(80\% \leq score \lt 83\%\), then letter grade is B-.
A grade of C+, C, C- means that you mastered most essential concepts and some advanced concepts, but have many significant gaps.
If \(77\% \leq score \lt 80\%\), then letter grade is C+.
If \(73\% \leq score \lt 77\%\), then letter grade is C.
If \(70\% \leq score \lt 73\%\), then letter grade is C-.
A grade of D+, D, D- means that you mastered some essential concepts.
If \(67\% \leq score \lt 70\%\), then letter grade is D+.
If \(63\% \leq score \lt 67\% \), then letter grade is D.
If \(60\% \leq score \lt 63\%\), then letter grade is D-.
A grade of F means that you did not master essential concepts.
If \(0\% \leq score \lt 60\%\), then letter grade is F.
There are no dropped Quizzes or Exams in this course.
There is no Grade Curving in this course.
There is no Extra Credit in this course.
Attendance is recorded but is not part of your course grade
Wed Jan 15 (From Chapter 2 Axiomatic Systems and Incidence Geometry)
2.1 The structure of an axiomatic system, 2.2 An Example: Incidence geometry
Fri Jan 17:
2.3 The parallel postulates in incidence geometry; 2.4 Axiomatic systems and the real world
Mon Jan 20: MLK Holiday: No Class
Wed Jan 22:
2.5 Theorems, proofs, and logic
Fri Jan 24:
2.6 Some theorems from incidence geometry
(Last Day to Drop Without getting a W and being charged for Digital Course Materials.)
(Homework H01 due at the start of class)
(Quiz Q01 at the end of class)
Mon Jan 27:
(From Chapter 3 Axioms for Plane Geometry)
3.1 The Undefined terms and two fundamental axioms, 3.2 Distance and the Ruler Postulate
Wed Jan 29:
3.2 Distance and the Ruler Postulate
Fri Jan 31:
3.3 Plane Separation
(Homework H02 due at the start of class.)
(Quiz Q02 at the end of class)
Mon Feb 3:
3.4 Angle measure and the Protractor Postulate
Wed Feb 5:
3.5 The Crossbar Theorem and the Linear Pair Theorem
Fri Feb 7:
3.6 The Side-Angle-Side Postulate
(Homework H03 due at the start of class.)
(Quiz Q03 at the end of class)
Mon Feb 10:
3.7 The parallel postulates and models
Wed Feb 12: ExamX1Covering Chapters 2 and 3
Exam X1 Information
Information about the Exam will be posted closer to the Exam date.
Fri Feb 14: Exam
(From Chapter 4 Neutral Geometry)
4.1 The Exterior Angle Theorem and existence of perpendiculars
Mon Feb 17:
4.2 Triangle congruence conditions
Wed Feb 19:
4.3 Three inequalities for triangles
Fri Feb 21:
4.4 The Alternate Interior Angles Theorem
(Homework H04 due at the start of class.)
(Quiz Q04 at the end of class)
Mon Feb 24:
4.5 The Saccheri-Legendre Theorem
Wed Feb 26:
4.6 Quadrilaterals
Fri Feb 28:
4.7 Statements equivalent to the Euclidean Parallel Postulate
(Homework H05 due at the start of class.)
(Quiz Q05 at the end of class)
Mon Mar 3:
4.7 Statements equivalent to the Euclidean Parallel Postulate
Wed Mar 5:
4.8 Rectangles and defect
Fri Mar 7: Exam X2Covering Chapter 4
Exam X2 Information
Information about the Exam will be posted closer to the Exam date.
Mon Mar 10 – Fri Mar 14 is Spring Break: No class!
Mon Mar 17:
(From Chapter 5 Euclidean Geometry)
5.1 Basic theorems of Euclidean geometry
Wed Mar 19:
5.2 The Parallel Projection Theorem; 5.3 Similar triangles
Fri Mar 21:
5.4 The Pythagorean Theorem
(Homework H06 due at the start of class.)
(Quiz Q06 at the end of class)
Wed Mar 26
5.6 Exploring the Euclidean geometry of the triangle
Fri Mar 28:
5.6 Exploring the Euclidean geometry of the triangle
(Homework H07 due at the start of class.)
(Quiz Q07 at the end of class)
(Last Day to Drop)
Mon Mar 31:
(From Chapter 7 Area)
7.1 The Neutral Area Postulate
