Department
of Mathematics
Math 31H. Honors Topics in
Calculus II
Fall 2018
Course Outline
Time
and Place: MWF
10:00 am - 10:50 am Millikan 2099
Instructor:
Dr. Adolfo J. Rumbos
Office: Andrew 2287
Phone / e-mail: ext. 18713
/
Office Hours:
TuTh 9:00 am - 10:15 am, or by
appointment
Text: Approximately Calculus
by Shahriar Shahriari
American
Mathematical Society, 2006
Prerequisite: Calculus
I or equivalent course (e.g., AP Calculus AB).
Course
Description.[1]
Math 31H is a second semester calculus class that tries to teach you
about the concepts and techniques of Calculus in a novel context. The hope is
that, in addition to calculus, you will have a chance to explore some other
areas of mathematics. Calculus is a powerful theoretical and practical tool
because it allows us to approximate. The purpose of this course is to get an
appreciation for the beauty, fun, and nature of mathematics by focusing on the
basic ideas of calculus and their relation to other areas of mathematics. The
theme for this class is approximations.
We will see a number of unusual topics—such as using calculus to approximate
the number of primes—and we will cover major topics (series of transcendental
functions, Differential equations, Taylor series) of second semester Calculus. Whereas
in a traditional calculus course much time is spent on developing and
perfecting certain specific skills (integrating, applying various convergence
tests for series, solving special types of Differential Equations, etc.), in
this course we will concentrate on a deeper understanding of concepts. The topics of the course will be covered
according to the attached schedule of topics and examinations (go to the class Sakai site under “Resources”
to access this schedule and other course materials).
Structure of the Course.[2]
This course is structured somewhat differently from a traditional mathematics
course. You are expected to take an active part in developing the mathematics.
A good portion of the material that we cover will be first introduced in
homework problems before they are discussed in class. For this reason,
collaboration with your peers will be an important (and enjoyable) part of the
learning process. In addition, your questions, insights, and class
participation will be an invaluable component of the course, affecting both the
content and the attraction of the material we cover.
Assigned
Readings and Problems.[3]
There will be 3 homework assignments a week and each will consist of 5
problems. Some of the problems will be quite challenging but there will be
ample resources to support you. Homework solutions will be collected at the
start of each class; we will then proceed to discuss questions students have on
the homework problems. All the
assignments are listed in the attached schedule of readings and assignments (available
in Sakai under “Resources”).
Mentor Sessions and Collaborative
Learning. There
will be three mentor sessions scheduled for the class in the following days and
times:
Tuesdays 8:00 pm to 10 pm
Thursdays 6:00 pm to 8:00 pm
Sundays 6:00 pm to 8:00 pm
The
meetings will take place in Millikan in a room to be announced soon. The mentor
for the class is Rafa Martinez-Avial Palazuelos.
The mentor
sessions provide excellent opportunities for you to work with other students in
the class. Collaborative learning is
strongly encouraged for in this class.
You will find that working with others and discussing problems students
is the most effective way to learn the material in the class; it is also very
enjoyable. Rafa will be there to facilitate discussion and to encourage collaborative
learning.
Writing Mathematics in Paragraph
Style.[4] On
each homework a number of the problems will not be computational. These
problems generally ask for a proof or an explanation. In these cases, the
solution needs to be written in paragraph style and with complete sentences.
Please read sections 1.2 and 2.2 of the text for an explanation of \Writing
Mathematics in Paragraph Style."
Writing Clearly vs Showing your
Work.[5] In
this class, you are not obligated to \show your work"
but you
are asked to clearly write up your solutions. A \clear write up" is one
that someone can pick up and read without knowing the problem or its solution.
The purpose of this write up is so that the thinking and the reasoning becomes
clear to you. In addition, a month later, you should be able to read your
solutions and understand what you did. So, I am not interested in you \showing
your work" so that I know that you actually did it yourself. I trust you.
However, I want you to write problems clearly (and often using complete English
sentences) so that you become a clear thinker. In computational problems, all
is required is to write the crucial steps clearly. In problems that involve
reasoning and proof, you need to write in paragraph style.
Grading
Policy. Grades will be based on the homework, two
50-minute examinations, plus a comprehensive final examination. The grades will be computed as follows:
homework
20%
Two 50-minute
exams 50%
final examination 30%
Final
Examination.
Time: Wednesday,
December 19, 2018 9:00 am
Place: Millikan
2099