Introduction to Higher Mathematics
TuTh 1:30-2:50, PSCI 218; 3 credit hours
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You are welcome to
come at other times, but in that case you might want to make
an appointment, just to make sure that I will be there then. You can
make an appointment simply by talking to me before or after class, by
calling me at my
or at home, or by sending e-mail.
You may also ask any questions directly via phone or e-mail. If I'm
not in when you call, please leave a message on the voice-mail or
answering machine with your name, number, and a good time for me to
call you back. I will try to respond to your phone or
as soon as possible.
Calculus I (Math 1411), which you may take concurrently. We will not use calculus, though we will occasionally need some topics from pre-calculus. The pre-requisite
is for mathematical maturity, and to encourage you to complete your calculus sequence.
Course Philosophy and Objectives:
This course is built on the
proposition that you learn mathematics, and how to construct
mathematical proofs, better when you formulate the questions and
discover the answers yourself.
Upon successful completion of the course, you will be able to
investigate mathematical questions, big and small, both experimentally
This is very different from courses like pre-calculus,
calculus and differential equations, which are primarily focused on
computations. Although there are computations in this course, they
are a tool for discovering, and proving, more general mathematical
Laboratories in mathematical experimentation: A Bridge to
higher mathematics, by Mount Holyoke College.
This book consists of 16 mathematical "labs". We will go through the following labs, at
the rate of two weeks per lab:
- Ch. 1: Iterations of Linear Functions
- Ch. 9: Parametric Curve Representation
- Ch. 3: The Euclidean Algorithm
- Ch. 14: Iteration of Quadratic Functions
- Ch. 5: The Coloring of Graphs
- Ch. 6: Randomized Response Surveys
You may also go through one additional lab, or another topic of your
choosing (with my approval), on your own, at the end of the semester
(more details about this option are below).
Class time will be devoted exclusively to labs. Each
lab will start with a brief explanation of the question or problem to
be explored. You will perform experiments (usually with a computer or
programmable calculator) and gather data. The data will lead you to
make your own conjectures, which you will then test and refine by
further experimentation. Finally, when you are more certain of your
conjectures, you will prove them carefully. (In practice, this
process is rarely as straightforward and linear as outlined here. You
will often revisit earlier steps as you carry out later steps.)
You may work in small groups of your choosing in class (as well as
out of class). There will also be whole-class discussions about your
experimental and theoretical discoveries.
After two weeks of work in class (and while you are starting the
next lab), you will have a week or two to write up your discoveries,
both experimental and theoretical, into a clearly-written report.
(Guidelines and suggestions for how to write and format your report
are on pp. xvii-xviii of the text; more details, and a rubric, are
on a separate handout.) Although you may work with other students
during the lab, you must write your report yourself. You may not
consult any outside resources (including the internet) without
After each report is graded and returned to you, you will have
approximately one more week to revise your report for a better grade,
if you like, up to one letter grade higher than the grade of your
initial report. Revised reports must be complete; in other words, it
should be possible to understand your revised report without reading
your original report. (But do turn in your original report with the
The final grade for each lab will be the grade on your
revised report, if you turn one in; otherwise, it will simply be the
grade of your initial report.
At the end of the semester, you will have the option of turning in
one extra revision of one lab; in this case, the grade you receive on
the extra revision will replace the grade of the original revision
(still, only up to one letter grade higher than the grade on your
initial report). Alternatively, you may investigate, on your own, an
additional lab, or another topic of your choosing (with my approval);
in this case, the grade you receive on the additional lab will replace
your lowest final grade from among the first six, if this helps your
grade. Note that you may turn in an extra revision or an
additional lab (or neither), not both.
Your grade for the course will be the average of the final grades for
each of the six labs.
The deadline for student-initiated drops with a W is Friday, October
31. After this date, you can only drop with the Dean's approval,
which is granted only under extenuating circumstances.
I hope everyone will complete the course successfully, but if you are
having doubts about your progress, I will be happy to discuss your
standing in the course to help you decide whether or not to drop.
You are only allowed three enrollments in this course, and
students enrolled after Fall 2007 are only allowed six withdrawals in their entire academic
career, so please exercise the drop option judiciously.
Academic dishonesty: It is UTEP's policy, and mine, for all suspected cases or acts of alleged scholastic dishonesty to be referred to the Dean of Students for investigation and
appropriate disposition. See Section 1.3.1 of the Handbook for Operating Procedures.
There is no particular penalty for attendance in this course, but if you miss a
class, then I expect you to work on the lab on your own time before the next class, so
you do not fall behind your classmates.
Courtesy: We all have to show courtesy to each other, and the class as a whole, during class
time. Please arrive to class on time (or let me know when you have to be late, and
why); do not engage in side conversations when one person (me, or another student)
is talking to the whole class; turn off your cell phone (or at least set it to not ring out
loud), and do not engage in phone, email, or text conversations during class.
Disabilities: If you have, or suspect you have, a disability and need an accommodation, you
should contact the Disabled Student Services Office (DSSO) at 747-5148, email@example.com,
or Union East room 106. You are responsible for presenting to me any DSS accommodation letters and instructions.
Exceptional circumstances: If you anticipate the possibility of missing large portions of class
time, due to exceptional circumstances such as military service and/or training, or
childbirth, please let me know as soon as possible.