TO:
Beth Dobkin, Provost
FROM:
Keith Ogawa, Chair
Academic Senate
DATE:
January 9, 2014
RE:
Senate Action S-13/14-23CA
New Course Proposal
Math 131: Topology
At the December 12, 2013 meeting of the Academic Senate, the attached New Course Proposal for Math 131, Topology was
approved on the Consent Agenda.
The item was approved by the Undergraduate Educational Policies Committee by a vote of 8-0 and forwarded to the Senate's
Consent Agenda. This action was assigned Senate Action #S-13/14-23CA.
Attachment
Cc: President James Donahue
Vice Provost Richard Carp
Dean Roy Wensley
November 6, 2013
Prof. Anna Novakov, Chair
UEPC
Dear Prof. Novakov and Members of the UEPC,
Attached you will find a proposal for a “new” course in the Department of Mathematics and
Computer Science (DOMACS). In actuality the course is not entirely new; we have run a course on
Topology in spring 2010 semester as a special topics course and we are again planning to offer one
again in spring 2014. The course was well received by mathematics majors and a few other science
majors. We would like to title this new course MATH 131 Topology.
As we look to modernize our major we plan to offer different tracks for our majors depending on
their future interests. One of the tracks is a “pure mathematics” track for students planning to
attend graduate school in mathematics or teach secondary mathematics. Looking into various
graduate schools’ programs we have observed that Topology is often a required but advanced
course. We believe a grounding in basic point-set topology would prepare our students to succeed in
a graduate program and help future teachers understand basic mathematical notions of distance,
continuity, connectedness, and compactness, all which have some importance in almost every other
area of mathematics. The proposed course, MATH 131, has been approved by the DOMACS faculty,
has been circulated to the chairs and program directors of the School of Science, and approved by
the Dean of the School of Science. Please find attached the New Course Proposal Form for your
consideration as well as the Library Review and course syllabus.
Sincerely,
Kathy Porter
Department of Mathematics and Computer Science
St. Mary’s College of California
NEW COURSE PROPOSAL FORM
1. School of Science, Department of Mathematics and Computer Science,
Math 131:Topology, Upper division
2. Justification for the course
1) Objectives of MATH 131
1. Students will be able to express topological concepts orally and in writing. Students
will also be able to prove statements and solve topological problems in a variety of
situations. Clear communication of ideas is expected and will be demonstrated in group
peer-work settings, in class at the blackboard, in presentations, on quizzes and exams,
and in homework. Other students in the course should be able to understand the
explanations as well as the reasons for validity.
2. Students will extend their ability to reason mathematically and understand logical
arguments. During class, statements, precise meanings, and validity of theorems will
be discussed; proofs of theorems will be presented. Students will demonstrate their
understanding of mathematical reasoning and the validity of logical arguments during
class discussions, group work, homework, and exams.
3. Students will learn a specific group of mathematical facts that they can use in future
mathematics courses. It is expected that students will spend considerable time outside
of class on this goal. Students will demonstrate their capability in this area on
homework, group work, board work, presentations, quizzes, and exams.
2) Relation to College Goals
Studying topology will strengthen students’ mathematical understanding of many mathematical
concepts such as distance, nearness, and continuity, essential concepts in almost all mathematical
fields. Topology has important connections and utility in other areas such as chaos theory,
continuum mechanics, mathematical economics and finance, mathematics of communication, and
computer graphics. Introducing students to topology will open connections to numerous fields of
study for these students. This course will shape students into better mathematicians, scientists, and
teachers by making the student think deeper about mathematics and its relationships with the world.
3) Student Assessment and Pass/Fail Grading
Assessment of student performance in Math 131 will typically be based on written examinations,
homework assignments, classroom quizzes, presentations, and a comprehensive final exam. The
pass/fail option may be exercised in the case that students are taking the course as an elective; in this
case the course will not satisfy major/minor requirements.
3. Student Population
Some mathematics majors will choose to take MATH 131. In particular students planning to go to
graduate school in mathematics or to teach secondary school mathematics will be guided towards this
course and will benefit from the knowledge. In addition, the course may be attractive to other science
majors as there are connections to topology in computer science, economics, engineering, and
physics. It will also be an interesting class for mathematics minors to take as one of their 3 upper
division classes. We estimate that 12 students will take the course each semester it is offered (we
hope more!).
4. Relationship to present College curriculum
Math 131 will replace the current Math 130 Abstract Geometry. Students arrive at Saint Mary’s
College with a background in geometry from their high school studies. Topology will extend the
students’ knowledge from geometry to a study of a subject where the concepts of nearness and
continuity are more important than the geometric property of shape.
5. Extraordinary implementation costs
None.
6. Library resources
The instructor has consulted with the librarian subject selector for mathematics, and some additional
materials will be purchased or returned to the Library collection from storage in support of this class.
The Library Review is here:
Review of Library Resources and Information Literacy
For Math 131: Point-Set Topology
Prepared by: Mathematics Subject Selector Linda Wobbe October, 2013
Students in Math 131 Point-Set Topology, while not required to undertake any Library research, are expected to master
course concepts and facts, and spend considerable time outside of class doing so. It is expected that students will take
advantage of available books and reference handbooks on the following topics, and this review is based on that
expectation:
Point-set topology
Topological spaces
Metric spaces
Continuous maps
Separation axioms
Connectedness
Compactness
I. Circulating Books. There is a limited number of books on the specific topics being explored in this class. In addition,
many of the available books are older books in storage. The faculty member will be consulted to determine whether
older books will be returned to the collection or additional titles will be purchased.
Topic
Topology
Topological
Point-set
topology
# Books
194
62
6
Several in
off-site
storage; will
Topological
spaces
15
Metric spaces
12
Continuous
maps
1
Separation
axioms
1
consult with
faculty
Many in offsite storage
Some off-site
Connectedness 0
Compactness
6
Examples of titles:
A guide to topology / Steven G. Krantz. [Washington, D.C.] : Mathematical Association of America, c2009.
Introduction to topology : pure and applied / Colin Adams, Robert Franzosa.. Harlow : Prentice Hall, 2008.
Open problems in topology. II / [electronic resource] / edited by Elliott Pearl. Amsterdam ; Oxford : Elsevier, 2007
Topological library [electronic resource] : Part 2, Characteristic classes and smooth structures on manifolds / editors,
S.P. Novikov, I.A. Taimanov ; translated by V.O. Manturov. Hackensack, N.J. : World Scientific, c2010
Topological methods for set-valued nonlinear analysis [electronic resource] / Enayet U. Tarafdar & Mohammad S.R.
Chowdhury. Singapore ; Hackensack, NJ : World Scientific, c2008
Topological vector spaces / N. Bourbaki ; translated by H.G. Eggleston and S. Madan. Berlin ; New York : SpringerVerlag, c1987
II. Handbooks and Encyclopedias. The Reference collection appears adequate for this course. Reference works are
used for brief explanations and biographical information on the theorists who have developed the concepts being studied.
The Library’s Mathematics Subject Guide offers a variety of reputable alternatives to Wikipedia. Examples:
Gale Virtual Reference Library: Mathematics Encyclopedia, Science and Its Times, Complete Dictionary of Scientific
Biography – all contain historically significant topological discoveries and cogent explanations.
Princeton Companion to Mathematics. Chapters on many of the topics explored in this class.
III. Information Literacy. It is not expected that students will be required to use Library resources for this class. Students
could be directed to explore books and handbooks in the Library’s collection and to share additional information about
course concepts or the mathematicians who excelled in these areas. If that is incorporated in the class, a Library
workshop could be scheduled to help students explore the available Library resources.
IV. Recommendations.
Dr. Porter and Linda Wobbe consult regarding whether to recall specific key works in storage or to purchase new books in
course topics.
If students are required to use outside Library resources to explore course topics, Linda Wobbe will work with Dr. Porter
to develop a hands-on Library workshop to guide students to these resources.
7. Course credit and grading options
Math 131 will meet either three times for 65 minutes or two times for 100 minutes depending on how
it is scheduled. It will be worth 1.0 credit for students.
The projected average out-of-class time per
week is 8-9 hours. The format of the course is lecture/discussion.
8. Prerequisites
The prerequisite for this course is any proof based upper division course.* Eventually we plan for the
prerequisite to be Math 103 Proofs and Mathematics. This course has experimental status and will be
offered in fall 2014
9. Course description wording for College catalog
MATH 131 Topology
This course covers the fundamentals of point-set topology including topological spaces, metric
spaces, continuous maps, separation axioms, connectedness, and compactness.
The prerequisite for the course is Math 103 with a C- or better. Offered every other year.
10. Course content
Syllabus and tentative schedule (set in spring 2014) are on the next pages.
MATH 131
Point-Set Topology
PROFESSOR:
OFFICE:
TELEPHONE: EMAIL:
OFFICE HOURS:
TEXTBOOK: Topology, 2nd Edition by James Munkres
PREREQUISITES: Math 103 Proofs and Mathematics (currently an experimental class) (or
any proof-based upper division mathematics class)
COURSE OVERVIEW: In this semester we will study the basics of point set topology including the
concepts of topological spaces, continuous functions, metric spaces, connectedness, compactness, and
separation axioms. Assessments will include written homework assignments, quizzes, two one- hourlong exams, and a comprehensive two hour final exam. Assignments and quizzes will emphasize the
mastery of basic topological concepts and introductory proof writing. Exams will also cover mastery of
basic topological concepts and proof writing as well as good communication of mathematics. There is a
Moodle (Gaelearn) website for this course where assignments and all course related information will be
posted; this site should be checked often by everyone. Regular class attendance and participation is
essential for this course and is expected of all students.
LEARNING OUTCOMES/OBJECTIVES:
By the end of the semester, successful students will be able to:
1. express topological concepts orally and in writing. Students will also be able to prove statements
and solve various topological problems. Clear communication of ideas is expected and will be
demonstrated in group peer-work settings, in class at the blackboard, in presentations, on quizzes
and exams, and in homework. Other students in the course should be able to understand the
explanations as well as the reasons for validity.
2. demonstrate their ability to reason mathematically and understand logical arguments. During
class, statements, precise meanings, and validity of theorems will be discussed; proofs of theorems
will be presented. Students will demonstrate their understanding of mathematical reasoning and the
validity of logical arguments during class discussions, group work, presentations, quizzes,
homework, and exams.
3. explain a specific group of mathematical facts; these ideas can be used in future mathematics
courses. It is expected that students will spend considerable time outside of class on this goal.
Students will demonstrate their capability in this area on homework, group work, board work,
presentations, quizzes, and exams.
ACADEMIC HONOR CODE
Saint Mary’s College expects every member of its community to abide by the Academic Honor Code
According to the Code, “Academic dishonesty is a serious violation of College policy because, among
other things, it undermines the bonds of trust and honesty between members of the community.”
Violations of the Code include but are not limited to acts plagiarism. For more information, please
consult the Student Handbook at www.stmarys-ca.edu/your-safety-resources/student-handbook.
STUDENT DISABILITY STATEMENT
Reasonable and appropriate accommodations, that take into account the context of the course and its
essential elements, for individuals with qualifying disabilities, are extended through the office of
Student Disability Services. Students with disabilities are encouraged to contact the Student Disability
Services Coordinator at (925) 631-4358 to set up a confidential appointment to discuss
accommodation guidelines and available services. Additional information regarding the services
available may be found at the following address on the website: www.stmarys-ca.edu/sds
DETERMINATION OF COURSE GRADES:
1. Quizzes, homework, classwork and presentations will be 30% of the course grade.
2. There will be two midterm exams. Each exam is worth 20% of the course grade.
3. There will be a COMPREHENSIVE final exam worth 30% of the course grade.
A FEW COMMENTS:
All quizzes and exams must be done without assistance from any source or person, unless you are
told otherwise. However, I do expect you to work on practice problems and to discuss the concepts with
other people in the class
.
You should expect that much of your learning will take place outside of the classroom and that
you will take responsibility for your education. This means that you must seek assistance when you
need it, prepare for each class by completing all reading and writing assignments prior to coming to
class, and realize that it is normal for you to leave the class period with questions and
concepts that you will need to explore before your understanding is complete.
The honor code and the Saint Mary's policies regarding academic honesty detailed in the student
handbook apply to this course. I encourage you to work with other students on coursework and to
consult solutions manuals as needed, but your write-ups should be in your own voice, and consist
largely of your own work. Where your argument depends heavily on another's work, say so.
Classroom etiquette: Cell phones must be turned off and not used for any purpose during class. Be
respectful of others.
Work hard, come to my office to talk topology, and have fun!!
MATH 131 Point-Set Topology
Schedule
Tentative Class
TEXT: Topology by J. Munkres (2nd Edition)
MONDAY
2/10
Welcome & Information
Review of Set Theory
Functions/Relations/
Real numbers
2/17
Topological Spaces
2/24
The Order Topology
3/3
Closed Sets and Limit
Points
3/10
More on Continuous
Functions
3/17
The Metric Topology
3/24
Student boardwork &
group work
3/31
Compact Spaces
4/7
Exam II
4/14
Easter Break
4/21
Easter Break
4/28
Student boardwork &
group work
5/5
The Urysom Lemma
WEDNESDAY
2/12
Review of Set Theory
Cartesian Products/ Finite
sets
2/19
Basis for a Topology
2/26
The Product Topology on
XxY
3/5
Student boardwork & group
work
3/12
Exam I
3/19
More on metric spaces
3/26
Connectedness
4/2
Compact Subspaces of the
Real Line
FRIDAY
2/14
Review of Set Theory
Countable and uncountable
sets
2/21
Student boardwork & group
work
2/28
The Subspace Topology
3/7
Continuous Functions
3/14
The Product Topology
3/21
The Quotient Topology
3/28
Connected Subspaces of
the Real Line
4/4
Student boardwork & group
work
4/9
Limit point Compactness
4/16
Easter Break
4/23
Countability Axioms
4/30
Normal Spaces
4/11
Local compactness
4/18
Easter Break
4/25
Separation Axioms
5/2
Normal Spaces
5/7
The Ur. Metrization Theorem
5/9
Complete Metric Spaces
5/12
Complete Metric Spaces
5/14
Compactness in Metric
Spaces
5/16
Student boardwork & group
work
DATE and TIME OF COMPREHENSIVE FINAL EXAM: