MATH 171.01 (1 credit), W, 12:00NN-12:50PM, Wickersham 226
Mathematics majors taking Calculus I.
Office: Wickersham 112, Phone: 872-3659, FAX: 871-2320
Office Hours: 9:00AM-10:30AM (M_F), 9:00AM-9:30AM (Tu_Th),
or by appointment
In place of a textbook, we will have printed handouts and assigned
readings from a variety of sources.
This seminar will introduce students to a mathematical way of thinking
through a sequence of exploratory problem assignments.
Students will experience problem solving and
mathematical inquiry in a controlled
environment using discussion, collaboration, abstraction, and technologies.
The objectives of the seminar include prodding the students to
critically analyze their use of mathematics, mathematical procedures,
and technologies with a goal of having the students pierce the
``black box'' approach to mathematics.
- Course Contents:
- The semester activities may include exposure to and exploration of
the following topics and activities.
The topics may not be covered in precisely the order in which they are
Related topics from the list below will be covered together.
Whenever possible, topics from the list below will be synchronized with
the topics in the Calculus I syllabus.
- Mathematica Basics -- kernel and front-end, syntax, commonly
- Fibonacci sequence and some of its properties.
- Game theory -- students will examine the possible moves in a simple
game and determine if there exist strategies for guaranteeing a player
- Cryptanalysis -- students will be introduced to the elementary number
theory, abstract algebra, and statistics which play a role in
enciphering and deciphering messages.
- Identification numbers -- students will be introduced to check digit
schemes used to transmit, retrieve, and store data.
- Bertrand's paradox -- students will explore the probability that a
randomly selected chord of a circle is longer than a side of an
inscribed equilateral triangle.
- Complex numbers -- students will explore representations of complex
numbers, complex number arithmetic, roots of unity, etc.
- Divisibility/indivisibility of natural numbers by 2, 3, 7, or 11 and
why the familiar tests for divisibility work.
- Taylor polynomial approximations to functions -- students will
extend the concept of linear approximations of a function to higher
order polynomial approximations.
- Elementary matrix algebra -- affine transformations of the cartesian plane,
iterated function systems.
- Buffon needle problem -- students will understand how a probability
experiment can lead to an approximation to the transcendental number .
- Quadratic forms -- students will explore some of the properties of
the level curves of expressions of the form
and is a
- Conic sections -- the circle, parabola, ellipse, and hyperbola and
their geometric properties.
- Navigation -- an activity in which students will apply some of what
they have learned so far to understanding the principles of operation
of the Long Range Navigation (LORAN) system commonly used for coastal
- Envelopes of tangent lines -- students will determine the curves
formed by envelopes of tangent lines of the forms
- Computer arithmetic -- fixed and floating point representations,
round off errors, numerical precision, numerical approximation, and
- Root finding methods -- Newton's method and the secant method.
- Optimization -- an activity in which students will optimize a
function whose critical points can only be numerically approximated.
- Binomial series -- students will explore through the notion of area
under a curve the infinite series expansion of
- Mean Value Theorem for Definite Integrals -- students will explore
the relationship between the mean of a set of numbers and the mean
value of a function on an interval.
- Probability distributions -- binomial distribution and its
approximation by the normal distribution.
If time permits other topics may be covered as well.
Students are expected to attend all class meetings.
Since an objective of the seminar is to demonstrate that mathematical
inquiry is often a collaborative activity, students must be present to
participate and benefit from the seminar.
Every absence in excess of two will result in the lowering of the
students course grade by a letter grade.
Since this is a single credit course, the workload will be
The assignments of the course will be designed so that they can be
completed in the hour of class meeting and an estimated single hour of
homework per week.
Student work will be examined for correctness, generality, and evidence of
insight into mathematical ideas.
Course grades will be based on the student's participation in the
seminar and their graded written homework.
I keep a record of students' homework scores and of their class participation.
Students should also keep an individual record of graded
The course letter grades will be calculated as follows.
- Inclement Weather Policy:
If we should miss a class day due to a school closing because of
weather, any activities planned for that missed day will take place
the next time the class meets.
For example, if a test is scheduled for a day that class is canceled
on account of snow, the test will be given the next time the class
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