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Math across the UH system


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System-wide Math Course Coordination Meeting

Lower Division Math Courses

Calculus Courses

Syllabi for UH Manoa Calculus Courses

Lower Division Math Courses


Equivalencies Across the University of Hawaii System, Chaminade and HPU for Lower Level Mathematics Courses

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Syllabi for UH Manoa Calculus Courses

215 syllabus

241 syllabus

242 syllabus

243 syllabus

244 syllabus

251A syllabus

252A syllabus

253A syllabus

System-wide Math Course Coordination Meeting

Representatives of the various Math Departments in the UH System met at
Kapiolani CC to discuss the coordination of our programs. There were

  • 7 faculty members from UH Manoa
  • 2 from the UH office of the Vice Chancellor for Academic Affairs,
  • 1 from UH Hilo,
  • 1 from UH West Oahu,
  • 5 from Kapiolani CC,
  • 0 from Honolulu CC,
  • 4 from Leeward CC,
  • 2 from Windward CC,
  • 1 from Kauai CC,
  • 1 from Maui CC,
  • 1 from Hawaii CC,
  • for a total of 25.

This report is an informal summary of the discussion.

I. Calculus

Overall we are in fairly good
shape with respect to calculus. The course syllabi are similar at the
different campuses, and articulate smoothly. We will obtain the course
descriptions/syllabi and make them available for comparison. These should
be sent to J. B. Nation (email address listed at the bottom).

UH Manoa has revised its numbering scheme for calculus (241-242-243-244),
while the other campuses have kept the traditional scheme (205-206-231-232).
The system would like us to eventually adopt a uniform scheme.

The use of computers was discussed. Most campuses use computers in
calculus, and most instructors feel that it is an effective tool for
illustrating calculus concepts. The way in which the computer is used
varies some with the instructor, but this was not thought to be a major
issue. A few campuses still do not have adequate facilities to do this
effectively.

There are two minor differences in the curriculum. Following requests
from the Engineering College, Manoa now has vectors in Calculus I and
an introduction to differential equations in Calculus II. Both of these
seem to fit rather well, and we would like to suggest that other schools
consider it.

The importance of completing the syllabus in all calculus courses
was noted.

Standards in calculus has not been a major problem, with the exception
of the usual anecdotal reports. (None of us wants to be held responsible
for our worst C student.) It is important that we keep it this way.

The applied calculus course, Math 215 at Manoa, was discussed as a
viable alternative for calculus I. Currently, roughly 40% of the first
semester calculus students at Manoa are in 215. While the course is
slightly more applied and less theoretical than 205/241, it is intended
to be a substantial calculus course. While having two (or more) options
might be difficult for the smaller schools, other campuses have a large
enough calculus enrollment to justify the option. Smaller campuses could
consider alternating the courses.

Business calculus, Math 203 at UHM, is a less substantial alternative.
It remains true, however, that we can offer a better business calculus
course than business or agriculture departments. If there is enough
demand, offering a “better business calculus” would be a service to
our students.

II. Math 100

There was a major discussion
about the spirit and topics of Math 100. There was general agreement with
the principle that Math 100 should introduce students to the beauty and
precision of mathematics, including mathematical reasoning as well as
counting and algebra. The argument as to which topics best serve that
purpose was more vocal. One side argued that financial math and probability/statistics
did not serve this purpose well. The response was that these topics have
meaning for the students because of their applicability, and that they
illustrate the use of important ideas such as geometric series. It was
emphasized that, the memo of 15 years ago notwithstanding, no one should
dictate the topics for Math 100. Rather, we should insist that a variety
of topics and approaches be covered, and that these be done in a non-cookbook
fashion.

It was noted that teaching Math 100 in a reasonably-sized class can
be much more effective than a large class, but this is a matter over
which we have little control.

With respect to the problem of the Manoa Gen Ed requirements, see
below.

III. Articulation

According to Executive policy
E5.209 the AA degree at any UH community college satisfies the Manoa Gen
Ed requirements, and any 100 level non-technical course transfers to any
other UH institution. The say of the “receiving institution” in this situation
is somewhat cloudy, but it is clear that the administration would prefer
that they say “yes.” However, the various colleges may (and do) have additional
core requirements in addition to the Manoa Gen Ed requirements, and the
transferred credits may not apply to these additional requirements.

Problems with non-Fast Track approval were due to the fact that we
were to approve equivalencies only, and did not have the authority to
approve courses per se.

The Manoa Symbolic Reasoning requirement (FS) is not a math requirement.
It was not written by or for math people, nor specifically approved
by them. The broadly written hallmarks are hard to satisfy with the
broad class of our elementary courses. Nonetheless, that is the objective.
In particular, Math 100 is no longer a quantitative reasoning course,
it is a logic course (!).

A more minor problem: Math 103 – “College Algebra” – is designed for
students transfering to HPU, Chaminade and UNLV (etc). Nonetheless,
it transfers to UHM for credit, though the same course at other schools
probably does not.

IV. Elementary Education

History: Manoa’s old Math
111 failed because we didn’t give high enough grades. This left us in
the undesirable position of having no role in the education of primary
teachers, while those students took Math 100, an inappropriate substitute.

Some folks in the College of Education were concerned about this situation,
and joined us in attempting to revive a math course for elementary education
majors. UHM has added Math 111 and 112, and the Big Island schools have
107-108.

Supposedly at least the first course will be required starting in
2006 (!). It is good for the state and education for us to be involved
in this, if it flies.

The problem solving (constructivist approach) is crucial, but too
limiting to be used exclusively. More experience should help find a
balance. Standards can be a problem, but again experience will help
us adjust this.


MATH 100 satisfies the general education requirement for quantitative reasoning.

For details, see Topics
in Mathematics (Math 100)

MATH 100 should include:

Proofs. The student should be able to follow and present some basic
proofs. The goal is to develop critical thinking skills.

Topics which illustrate the beauty and power of mathematics. Topics
should include at least a few topics from advanced math courses and
their applications such as topology, group theory, network theory, etc.
The goal should be an appreciation of what mathematicians do.

Algorithms should not be used without developing their derivations.
The goal should be to develop the logic behind formulae.

Topics may include the history of number systems to illustrate the
universality of mathematics, as well as the cultural differences. The
goal should be to illustrate the advantage of and encourage the appreciation
of different perspectives.

Topics may involve the mathematics behind popular “logic” puzzles.
The goal is to illustrate what “common sense” is expected by society.

Participants



To foil email harvesters, addresses in the above binary image can
not be cut and pasted.

Calculus Courses

  UHM UHH HCC KCC LCC WCC Hawaii Kauai Maui
Computer Lab 241 205 206 206   206     205 thru 232
  242 206              
ODE’s 242 206 232 232 205 206     232
    232     232        
Polar 244 231 231 231 231 231     231
Vectors 241 231 231 231 231 231     231
  243                
Series 242 206 206 206 206 206 206 206 206

Putnam exam

Putnam

Past winners of this national competition include physicist and Nobel Prize Laureates Richard Feynman and Kenneth Wilson. Amongst mathematicians, the list of Putnam Fellows includes a huge number of famous mathematicians including Fields Medalist John Milnor and former UH Manoa Mathematics Professor William Hanf.

Each year, the examination will be constructed to test originality as well as technical competence. It is expected that the contestant will be familiar with the formal theories embodied in undergraduate mathematics.

It is assumed that such training, designed for mathematics and physical science majors, will include somewhat more sophisticated mathematical concepts than is the case in minimal courses. Thus the differential equations course is presumed to include some references to qualitative existence theorems and subtleties beyond the routine solution devices.

Questions will be included that cut across the bounds of various disciplines, and self-contained questions that do not fit into any of the usual categories may be included. It will be assumed that the contestant has acquired a familiarity with the body of mathematical lore commonly discussed in mathematics clubs or in courses with such titles as Survey of the Foundations of Mathematics.

It is also expected that the self-contained questions involving elementary concepts from group theory, set theory, graph theory, lattice theory, number theory, and cardinal arithmetic will not be entirely foreign to the contestant's experience.

For more information concerning the Putnam competition; which is given each year in December, contact Prof Pavel Guerzhoy.

December already past? Participate in the Hanf competition.

Resources

Past Putnam exams

1980 1990 2000
1981 1991 2001
1982 1992 2002
1983 1993 2003
1984 1994 2004
1985 1995 2005
1986 1996
1987 1997 2007
1988 1998 2008
1989 1999 2009

Program goals

Recipients of an undergraduate degree in mathematics study:

  • real analysis in one and several variables,
  • linear algebra and the theory of vector spaces,
  • several mathematical topics at the junior and senior level,
  • in
    depth at least one advanced topic of mathematics, an approved two-course
    sequence.

In addition, students acquire the ability and skills to:

  • develop and write direct proofs, proofs by
    contradiction, and proofs by induction,
  • formulate definitions and give examples and
    counterexamples,
  • read mathematics without supervision,
  • follow and explain algorithms,
  • apply mathematics to other fields.

Finally, recipients of an undergraduate degree in mathematics learn about research in mathematics.

LaTeX

LaTeX samples
Click here and scroll down to Presentation schedule
It's time to learn to use LaTeX!
  1. First you need to install it on your machine.
    • For Mac OS X users, I suggest MacTeX. Click on the "MacTeX.mpkg.zip" link, download the file to your machine and run it. (You will need to unzip it first.)
    • For Windows users, I suggest proTeXt. This is a superset of MiKTeX but easier to install.
    • For Linux users, most Linux distributions come with TeX; otherwise I recommend TeX Live.
  2. The Not so short introduction to LaTeX is a very handy reference. It's worth reading Chapters 1.1-1.4 and then reading the first couple of pages of Chapter 2. All of the math symbols we'll need are in Chapter 3.Once you have LaTeX installed on your machine, open up TeXShop (Mac), TeXWorks (Windows), or your favorite Linux text editor. Download the following sample tex file and try to compile it: Sample File. (In TeXShop and TeXworks, look under the menu option "Typeset" and click on LaTeX.)