| 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 |
|
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: |
|
 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):
- Using Latex
- Using Geogebra
- Introduction to Euclid's
Elements
- Axiomatic Systems
- Incidence Geometry
- Hilbert's Axioms
- Proving Theorems
- Plane Geometry
- Neutral Geometry
- Euclidean Geometry
- Pythagorean Theorem
- Trigonometry*
- Hyperbolic Geometry
- Spherical Geometry*
- Polygons and Circles
- Euclidean Constructions
- Transformations and Rotations
- Tesselations in the plane*
- 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:
|
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.
|
 Greenberg,
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).
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
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
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
 Reynolds,
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:
|
 - Pi:
History of Pi from MacTutor
- Egyptian:
Wikipedia |
MacTutor
- Babylonian:
Wikipedia |
Mac Tutor
- Indian:
Wikipedia |
MacTutor
- Chinese:
Wikipedia |
MacTutor
- Arabic:
MacTutor
- Mayan:
Mac Tutor | Mayan
Geometry (Morales) |
Mayan Calendar
- Greek:
MacTutor
- Pythagoras and the Pythagoreans (c.
580 BC). Original sources have all been
lost. There are some more ancient
compilations by Diogenes (c. 200),
Porphyry (c. 270), Iamblichus (c. 300),
Apuleius (c. 150), and Hierocles of
Alexandria (430), all of which were
written 3-10 centuries later. There is
modern website The
Complete Pythagoras that contains
compilations of this material. Most of
the material is philosophical quite
unrelated to geometry. But the school of
Pythagoras is responsible for the
Pythagorean Theorem and proving that
the
Square Root of 2 is irrational.
- Euclid: Euclid's Elements
(complete in PDF)
- Hilbert: The
Foundations of Geometry (1899) (complete
text in pdf)
- Birkhoff: A
Set of Postulates for Plane Geometry, Based
on Scale and Protractor, from The Annals
of Mathematics, 33(2):329-345 (1932).
- Moise: Metric
Postulates for Plane Geometry, American
Mathematical Monthly, 66(7):533-555
(1959).
- Anderson: Intuitive Geometry,
School Mathematics Studey Group
- Venema: Exploring
Advanced Geometry with Geometer's
Sketchpad
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Resources:
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Cookies:
|
 I
encourage students to bring snacks to share with
me and the rest of the class. |
|
