Subject to Change. Last Revision: 24 April 2009.

Announcements

April 7: HW5 and HW6 have been modified. See Assignments to get the revised versions.

Revised End of Year Schedule:

  • Thurs. May 7: Comprehensive (midterm) class examination given in class
  • Tues. May 12: Homework 6 is due electronically; there is no exam on this day.
  • Thurs. May 14: Projects due electronically

Assignments  Syllabus  Peer Evaluation Form  Lecture Notes and Handouts Latex GeoGebra

Class Location: JR-214 (Jerome Richfield Hall)  [Campus Map]
Class Time: Tuesday/Thursday 7:00-8:15 PM
Class Number: 14974
Instructor: Bruce E Shapiro, Ph.D.
Office Hours: To be announced.

Don't drop by the office that the Math Department has listed for me: I will never be there so you will be wasting your time.

Email: bruce.e.shapiro at csun.edu
Telephone: 626-395-8161 - Don't abuse it, please! If you leave a message tell me who you are and why you are calling, being specific. I ignore phone messages like "This is Joe from your class, I wanted to ask you something."

Don't call the number the Math department lists for me. I don't use that telephone and I don't check the messages there (ever).

In any case you are more likely to reach me a lot more quickly by email.

Class Web Page: http://www.beshapiro.com/math370/
Students are responsible for checking the web page regularly for announcements and homework assignments.
 
Catalog Description

picture of CSUN catalog cover Math 370 Description. Prerequisite or Corequisite: MATH 320. Helps students write rigorous proofs of results of plane Euclidean geometry. Visualization and development of geometric intuition through the use of dynamic geometry software. Includes history, axiomatic structure, and theorems of plane Euclidean geometry, geometric transformations of the plane: rigid motions, similarities, and inversion, coordinate geometry, and an introduction to non-Euclidean geometries.

Description of Math 320 (pre/co-req): Helps students transition from a primarily computational mode of doing mathematics to a more conceptual mode of doing mathematics. Emphasis on proofs, taught in the context of elementary number theory, combinatorics, and analysis; the language of sets, relations, order, equivalence classes, functions, cardinality is introduced. Students are expected to write large numbers of proofs and clearly communicate mathematical ideas.

 
Course Objectives:

Image of Woman Teaching Geometry, from a medieval translation of Euclid's Elements. To provide a survey of the topics in and applications of geometry including:

  • Foundations of geometry
  • Methods and applications of proof in mathematics
  • Different axiomatic systems for developing geometry
  • Relationship between geometry and algebra
  • Historical development of geometry
  • Different types of geometry: Euclidean and Non-Euclidean
  • California standards for geometry education
  • Use of technology in the classroom
  • Writing mathematics documents electronically
  • Develop experience in collaborative learning
 
Student Learning Outcomes:
Upon completing this class, the student should be able to*:

  • Understand the foundations of the geometry (MSMR 2)
  • Be familiar with the California content standards for Secondary Geometry, and understand the concepts described in those standards.
  • Develop a lesson plan for a secondary geometry class.
  • Produce a mathematics document electronically.
  • Map the principals and concepts of geometry to the California content standards for for secondary geometry.
  • Work together effectively in groups to develop and present material others.
  • Know the Parallel Postulate and its implications (MSMR 2.1a)
  • Know the variants of the parallel postulate for non-Euclidean geometry. (MSMR 2.1b)
  • Prove theorems and solve problems involving similarity and congruence (MSMR 2.2a)
  • Understand, apply, and justify properties of triangles. (MSMR 2.2b)
  • Understand, apply, and justify properties of polygons and circles. (MSMR 2.2c)
  • Justify and perform the classical constructions (MSMR 2.2d)
  • Perform constructions using software
  • Use techniques in coordinate geometry to prove geometric theorems (MSMR 2.2e)
  • Understand of parallelism and perpendicularity of lines and planes in three dimensions (MSMR 2.3a)
  • Understand, apply, and justify properties of three-dimensional objects (MSMR 2.3b)
  • Understand the basic properties of isometries (MSMR 2.4a)
  • Understand the basic properties of dilations (MSMR 2.4b)

*MSMR = Mathematics Subject Matter Requirements, California Commission on Teacher Credentialing.

 
Topics Covered:

The following subjects will be covered (not necessarily in this order):

  1. Using Latex
  2. Using Geogebra
  3. Introduction to Euclid's Elements
  4. Axiomatic Systems
  5. Incidence Geometry
  6. Hilbert's Axioms
  7. Proving Theorems
  8. Plane Geometry
  9. Neutral Geometry
  10. Euclidean Geometry
  11. Pythagorean Theorem
  12. Trigonometry*
  13. Hyperbolic Geometry
  14. Spherical Geometry*
  15. Polygons and Circles
  16. Euclidean Constructions
  17. Transformations and Rotations
  18. Tesselations in the plane*
  19. Computational Geometry*
*As time permits.
 
Collaborative
Learning:

Much of this class will involve collaborative learning. In addition to lectures, you will be exptected to work together in groups of approximately 3 students on your homework and class projects.

Every student in the class will make at least one short (5 minute) presentation to the entire class, either as part of the midterm project or final project. Students who present on the midterm project will not be expected to present on the final, and vice-versa.

How it works: Every student should attempt the homework as individuals. You will prepare copies of each assignment: one to turn in and one for each group member. Then as a group you will discuss and comment each student's homework; if there are things you don't understand, the individual should explain their arguments to the group. Based on these comments, each student will turn in a revised homework set, which may or may not agree with the group consensus. The revised set will be due one week after the initial homework set.

Each group should arrange a regular time and location to meet and discuss their homeworks and other group activities. You will be evaluated by each of your peers to determine the level of participation in the group.

Since teamwork is an important part of this course you will be penalized up to one full letter grade if you do not work well with your team. If you are having difficulty with your team or need to change teams it is your responsibility to contact me.

 

Grading Policy:

The final grade will be calculated as follows (subject to change):

Note also comments on teamwork (collaborative learning) and attendance that can reduce your grade.

 

Attendance:

Is required and your grade will be penalized if you miss too many classes.
Remember to sign in during every class. The usual penalty is 1/3 of a letter grade for each 3 days absent without valid excuse, after the first 3 freebies. Miss 0-3 days, no penalty; miss 4-6 days, 1/3 letter grade; miss 7-9 days, 2/3 letter grad; etc.

 

Textbook:

Cover Image of Venema's Book Venema, Gerard A. The Foundations of Geometry, Pearson/Prentice Hall, 2006, ISBN 0131437003. Find a copy to buy | Publisher's Web Site. MSRP: $69.33. Not cheap, but better than most of the other books on the market.

 

High School Geometry Book (optional):

This course is supposed to provide the content material required to teach a course in high school geometry. So get yourself a high school geometry book! (Optional, not required)

A list of books approved by the Los Angeles Unified School District is provided here or can be downloaded from the school district here.

By all means, if you chose to buy the book, buy a used copy of an earlier edition to save money.

Here is one example that I particularly like that you should be able to find for under $10 on the internet:

Ron Larson, Laurie Boswel, Lee Stiff, Geometry: Concepts and Skills, McDougal Littel (2003) ISBN 0618087583
Find a copy to buy | Publisher's web site.

 

Textbooks I might have chosen but didn't (and why)

They all have something good to offer.

Take a look at them if you are serious about studying geometry.

Cover Image of Geenberg's BookGreenberg, Marvin Jay. Euclidean and Non-Euclidean Geometries: Development and History, 4th Edition, Freeman, 2008, ISBN 9780716799480. Very readable, excellent historical development, clear description of axiomatic geometry. If you are serious about geometry I recommend reading this book. However, it does not cover very many of the topics needed for California standards. I was also offended by the distinction betwen "students of average ability" and "better than average students" - shouldn't the distinction be between the background and experience rather than the ability?
Find a copy to buy | Publisher's web site. MSRP: $109.95 (too expensive).

Cover Image of Noronha's book Noronha, M. Helena, Euclidean and Non-Euclidean Geometries, Prentice Hall, 2002. ISBN 9780130337177. The original Math 370 textbook. Concise and clearly written axiomatic development. Good coverage of the course topics. Because it is fairly concise it might be a bit difficult for students who are new to the field to follow, but it is very well organized. It lacks any details about the historical developmetn of geometry. Unfortunately, its out of print, though you can find a reasonably priced version online if you look hard enough, and is probably worth the money.
Find a copy to buy

Cover image of Smart's textbook, 5th edition Smart, James R. Modern Geometries, Brooks/Cole, 1998, ISBN 9780534351885. Nice coverage of many special topics. This is a good supporting book. It has the advantage that the chapters are relatively independent of one another. But it is soooo outrageously overpriced that I did not seriously consider using this book.
Find a copy to buy | Publisher's web site. MSRP: $200.95

Cover image of Isaac's textbook Isaacs, I Martin. Geometry for College Students. This is another good reference, and has been used in the past as a 370 textbook, but I did not choose it for two reasons: (1) it is outrageously overpriced, and (2) it appears to be out of print.
Search for a copy to buy MSRP: $157.95

Reynold's and Fenton cover imageReynolds, Barbara, and Fenton, William E.. College Geometry Using the Geometer's Sketchpad. This book has been used in the past for 370 as well. The main problem is that you have to buy the software for another $130. There is a student edition for less but it has some restrictions and CSUN does not have a site license.
Find a copy to buy | Publisher's web site. MSRP: $87.95

 

Supporting Documents, Classical References, and other useful links:

 

Resources:

Cover picture of the California Math Standards
 

Cookies:

I encourage students to bring snacks to share with me and the rest of the class.
 

Student Conduct

Students are expected to conduct themselves in accord with university policies on Student Conduct and Academic Dishonesty. Violation of this code could be punishable by a failing grade in the class or removal from the university, as determined by Dean of Students.

I require students to sign an affirmation that they will abide by the student conduct code (and not cheat in this class) and to reaffirm this contract at each exam. If you are uncomfortable signing this affirmation you should not enroll in this class.

The student conduct code is posted at: http://www.csun.edu/a&r/soc/studentconduct.html and is in the University Catalog, Appendix C.

View the Student Conduct Code


Download the University Catalog, Appendix C, Student Conduct Code, in pdf format..

 
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