Course Web Page

    Course: MATH 3110/5110

    Title: College Geometry

    Campus: Ohio University, Athens Campus

    Department: Mathematics

    Academic Year: 2023 - 2024

    Term: Spring Semester

    Instructor: Mark Barsamian

    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 12:55pm – 1:50pm in Morton 218

    Final Exam: Fri May 3, 3:10pm – 5:10pm in Morton 218

    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, or reading the Lecture notes that Mark Barsamian posts online, and by reading the textbook. Your Instructors 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:

    1. Send Mark 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.)
    2. Go to the Hudson Student Health Center (or some other Medical Professional) to get examined.
    3. Later, you will need to bring your Professor 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. (When you miss a Quiz or Exam and are not given a Make-Up, the missed Quiz or Exam will be considered your one Quiz or Exam score that gets dropped.)

    (Observe that self-diagnosis of an illness is not a valid documentation of an illness. In other words, you can't just tell your Professor 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 your Professor 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 your Professor 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 2024 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 Tuesday, January 30, 2023 . You and Mark 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, Mark Barsamian will schedule you for a Make-Up on the following Monday or Tuesday.)

    Missing Presentations, 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. (When you miss a Quiz or Exam and are not given a Make-Up, the missed Quiz or Exam will be considered your one Quiz or Exam score that gets dropped.)

    Policy on Cheating:

    If cheat on a quiz or exam, you will receive a zero on that quiz or exam and your Instructor 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 your Instructor 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, 2 nd Edition

    Author: Gerard Venema

    Publisher: Pearson (2011)

    ISBN Numbers: ISBN-13: 978-0136020585 Be sure that you get the 2nd Edition.

    Remarks about the book:

    • It is an excellent book.
    • Please note that you should get the 2nd Edition. This is NOT the newest edition.
    • There is a newer, 3rd edition of the same book, but I have chosen the 2nd edition instead. The reasons are,
      • The 2nd Edition is fine. Nothing in Geometry changed since 2011.
      • You can buy used copies of the 2nd Edition on Amazon starting around $25 (including shipping). By contrast the newer 3rd edition can only be obtained as a rental book (which is a used book), and it costs about $80 to rent the book for a semester.
    • My recommendation is that you buy the book right away: The publisher is not printing any more of the 2nd Edition, of course, and so the supplies of that edition will dwindle over time. As they do, the prices will go up.

    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.

    List of Axioms, Definitions, Theorems: List of Axioms Definitions Theorems pages 1 – 42

    Exercises:

    Exercises for Ohio University 2023 - 2024 Spring Semester MATH 3110/5110 (College Geometry) (Barsamian)
    (from Venema, Foundations of Geometry, 2 nd Edition )
    Your goal should be to write solutions to all the exercises in this list.

    Printable PDF of the Calendar and Exercise List

    ( Red exercises are to be turned in and graded. See the Printable List above for the due dates.)

    • 2.4: 2 , 3, 4 , 5, 6 , 7 , 8, 10, 11 , 12, 13
    • 2.4: 2 , 3, 4 , 5, 6 , 7 , 8, 10, 11 , 12, 13
    • 2.5: 1 , 2 , 3 , 4, 5, 6, 7, 9, 10, 11 , 12 , 13 , 14, 15, 16
    • 2.6: 1, 2 , 3 , 4 , 5, 6, 7, 8
    • 3.2: 1, 5 , 7 , 9, 10, 12 , 15 , 16, 17 , 18, 21, 23
    • 3.3: 1 , 2 , 4, 5
    • 3.4: 1
    • 3.5: 1, 2 , 3, 4, 5
    • 3.6: 1, 2
    • 3.7: 1, 2
    • 4.1: 1
    • 4.2: 1 , 2, 4 , 5
    • 4.3: 1 , 2 , 3, 4, 6, 7 , 8 , 9
    • 4.4: 1, 2 , 3
    • 4.5: 1 , 2
    • 4.6: 1 , 6 , 8, 10 , 11
    • 4.7: 1 , 2, 3, 6
    • 4.8: 1, 2, 3, 4, 5, 6, 7
    • 5.1: 1, 3 , 5 , 6, 7, 8
    • 5.3: 1 , 2 , 3, 4
    • 5.4: 1 , 2, 3, 5
    • 5.5: 1 , 2, 3, 4 , 6 , 7
    • 5.6: 1 , 2, 4 , 5 , 6, 7, 12
    • 7.1: 1, 2, 3
    • 7.2: 1, 2, 3, 4, 5, 8, 9
    • 8.1: 1 , 2 , 3, 5 , 6, 7
    • 8.2: 1, 2, 3
    • 8.3: 1, 5, 6 , 7 , 8
    • 8.4: 1, 3
    • 8.5: 1, 2, 5
    • 8.6:1

    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 Mark Barsamian to look over your written work with you.

    Grading:

    Grading System for 2023 – 2024 Spring Semester MATH 3110/5110 (Barsamian)

    During the course, you will accumulate a Points Total of up to 1000 possible points .

    • Written Homework: 9 Assignments @ 20 points each = 180 points possible
    • Quizzes: Best 8 of 9 Quizzes @ 20 points each = 160 points possible
    • Exams: Best 2 of 3 Exams @ 220 points each = 440 points possible
    • Final Exam: 220 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 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

    Grade Calculation Worksheet

    Use this to calculate your Current Letter Grade throughout the semester: Grade Calculation Worksheet

    Calendar:

    Calendar for MATH 3110/5110 (Barsamian) 2023 – 2024 Spring Semester

    Printable PDF of the Calendar and Exercise List

    Items in red are graded.

    Mon Jan 15: Holiday: No Class

    Wed Jan 17: (From Chapter 2 Axiomatic Systems and Incidence Geometry)
    2.1 The structure of an axiomatic system, 2.2 An Example: Incidence geometry

    Fri Jan 19: 2.3 The parallel postulates in incidence geometry; 2.4 Axiomatic systems and the real world( Lecture Notes )

    Mon Jan 22: 2.5 Theorems, proofs, and logic

    Wed Jan 24: 2.6 Some theorems from incidence geometry

    Fri Jan 26: (From Chapter 3 Axioms for Plane Geometry)
    3.1 The Undefined terms and two fundamental axioms, 3.2 Distance and the Ruler Postulate(Last Day to Drop Without a W) (Homework H1 due at the start of class) (Quiz Q1 at the end of class)

    Mon Jan 29: 3.2 Distance and the Ruler Postulate

    Wed Jan 31: 3.2 Distance and the Ruler Postulate; 3.3 Plane Separation

    Fri Feb 2: 3.3 Plane Separation(Homework H2 due at the start of class.) (Quiz Q2 at the end of class)

    Mon Feb 5: 3.4 Angle measure and the Protractor Postulate

    Wed Feb 7: 3.5 The Crossbar Theorem and the Linear Pair Theorem

    Fri Feb 9: 3.6 The Side-Angle-Side Postulate (Homework H3 due at the start of class.) (Quiz Q3 at the end of class)

    Mon Feb 12: 3.7 The parallel postulates and models

    Wed Feb 14: 3.7 The parallel postulates and models

    Fri Feb 16: Exam X1 Covering Chapters 2 and 3

    Mon Feb 19: (From Chapter 4 Neutral Geometry)
    4.1 The Exterior Angle Theorem and existence of perpendiculars

    Wed Feb 21: 4.2 Triangle congruence conditions

    Fri Feb 23: 4.3 Three inequalities for triangles(Homework H4 due at the start of class.) (Quiz Q4 at the end of class)

    Mon Feb 26: 4.3 Three inequalities for triangles

    Wed Feb 28: 4.4 The Alternate Interior Angles Theorem

    Fri Mar 1: 4.5 The Saccheri-Legendre Theorem(Homework H5 due at the start of class.) (Quiz Q5 at the end of class)

    Mon Mar 4: 4.6 Quadrilaterals

    Wed Mar 6: 4.7 Statements equivalent to the Euclidean Parallel Postulate

    Fri Mar 8: 4.7 Statements equivalent to the Euclidean Parallel Postulate(Homework H6 due at the start of class.) (Quiz Q6 at the end of class)

    Mon Mar 11 – Fri Mar 15 is Spring Break: No class!

    Mon Mar 18: 4.8 Rectangles and defect

    Wed Mar 20: Exam X2 Covering Chapter 4

    Exam X2 Information

    • Problem about Congruent Objects (Concepts from Sections 4.2, 4.3)
    • Problem about Larger and Smaller Objects, or about inequalities, or about Parallel Lines (Concepts from Sections 4.1, 4.3, 4.4, 4.5)
    • Problem about Quadrilaterals (Concepts from Section 4.6)
    • Problem about Statements Equivalent to the Euclidean Parallel Postulate (Concepts from Section 4.7)
    • Problem related to Rectangles and Defect (Concepts from Section 4.8)

    Fri Mar 22: (From Chapter 5 Euclidean Geometry)
    5.1 Basic theorems of Euclidean geometry

    Mon Mar 25: 5.2 The Parallel Projection Theorem; 5.3 Similar triangles

    Wed Mar 27 5.4 The Pythagorean Theorem

    Fri Mar 29: 5.5 Trigonometry ( Group Work: Solving Triangles )(Last Day to Drop) (Homework H7 due at the start of class.) (Quiz Q7 at the end of class)

    Mon Apr 1: 5.6 Exploring the Euclidean geometry of the triangle

    Wed Apr 3: 5.6 Exploring the Euclidean geometry of the triangle

    Fri Apr 5: 5.6 Exploring the Euclidean geometry of the triangle(Homework H8 due at the start of class.) (Quiz Q8 at the end of class)

    Mon Apr 8: (From Chapter 7 Area)
    7.1 The Neutral Area Postulate( Lecture Notes )

    Wed Apr 10: 7.2 Area in Euclidean geometry

    Fri Apr 12: Exam X3 Covering Chapter 5 and Sections 7.1, 7.2

    Exam X3 Information

    • Problem about Basic theorems of Euclidean Geometry (Concepts from Section 5.1)
    • Problem about Parallel Projection and/or Similar Triangles (Concepts from Sections 5.2, 5.3)
    • Problem about the Pythagorean Theorem and/or Trigonometry (Concepts from Sections 5.4, 5.5)
    • Problem about the Euclidean geometry of the triangle (Concepts from Section 5.6)
    • Problem about Area (Concepts from Sections 7.1, 7.2)

    Mon Apr 15: (From Chapter 8 Circles)
    8.1 Circles and lines in neutral geometry

    Wed Apr 17: 8.2 Circles and triangles in neutral geometry

    Fri Apr 19: 8.3 Circles in Euclidean geometry

    Mon Apr 22: 8.4 Circular continuity; 8.5 Circumference and area of Euclidean circles (Homework H9 due at the start of class.) (Quiz Q9 at the end of class)

    Wed Apr 24: 8.6 Exploring Euclidean circles

    Fri Apr 26: 8.6 Exploring Euclidean circles

    Fri May 3: Final Exam FX from 3:10pm – 5:10pm

    page maintained by Mark Barsamian , last updated Sun Apr 21, 2024

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