- Dr. Manil Suri,
Math/Psych 419, (410) 455-2311, suri@umbc.edu,

office hours: MW 3:30-4:30 or by appointment - Lectures: MW 1:00-2:15 (MP 101)
- Text: For All Practical Purposes (8th edition)
- Prerequisites: Math 106 or Grade 3,4,5
on LRC Math placement test.

Mathematics is such a vast
subject that
figuring out what to include in a one-semester course is a challenging
task.
Our goal will be to explore a series of connected topics that give a
coherent
glimpse into contemporary mathematics, while also bringing out core
principles
essential to the mathematical way of thinking. The outline of the course
is
given below. (Chapters to be covered are roughly **18**,**21**,**22**,**19.1**,**23**,**5****-8**,**19.5
**for now.)

**1. Gentle Introduction: **We'll begin with a power point
presentation
to put you in the mood for the class. I will survey your math background
and
review some basic concepts (e.g. functions).

**2. Precision and Scale:** A key core principle of math is its *precision*. We'll start **Chapter 18** with this in mind - to
get
into the habit of making precise statements and giving precise answers.
Paradoxically, for math to be actually used in practice, one has to make
approximations, so we'll also learn when this is appropriate. The concept
of *scale* leads to some interesting
explanations of why things are as they are in the world.

**3. Growth rates:** **Section
18.6 **deals with various power functions, which we will explore, along
with
such kinds of growth as logarithmic, quadratic, and so on. One of the key
uses
of math is to quantify relations, and all these different functions can be
used
as needed to model different applications. We continue with selected
topics
from **Chapters 21-22**, which give
us
an introduction into exponential growth, and also help us practice
precision
and basic math skills in a very useful context. (This will be the most
computational part of the course.) Exponential growth also introduces us
to the
key concept of *infinity,* which,
as we
will see, is one of the most important ideas in math, and ties together
most of
the topics in this course.

**4. Population growth and golden ratio:** Problem 4 of **Chapter 19** on rabbits multiplying
will
lead us to the so-called Fibonacci numbers. We will make a brief detour
into **Section 19.1 **to explore these and
the
golden ratio. We will tie this to the exponential growth we have
investigated
before.

**5. Logistic growth, dynamical systems, and chaos:** Some of the
most
exciting discoveries in mathematics over the last decades have occurred in
dynamical systems and chaos. We will explore these through selected topics
in **Chapter 23**, as well as additional
material. Computer simulations will assist in our investigations, giving
us a
taste of how mathematicians use experiments to gain intuition.

**6. Statistics:** We will look at another type of
experimentation,
that of *sampling* and *data analysis*. For this, we will
cover
selected topics from **Chapters 5-8
**(the
last on probability). The Central Limit Theorem in **Section 8.6** once again shows how all these techniques depend
on an
understanding of infinity. A knowledge of
statistics
is quite essential in today's quantification-driven world.

**7. Fractals and nature:** While some natural phenomena (e.g. the
ones
dealing with scale we saw in Chapter 18) are *deterministic* in nature, a number involve a high degree of
randomness. We will see how these lead to *fractal*
manifestations (in particular, through some class exercises involving
probability). Fractals are covered briefly in **Section 19.5**, which we will augment with additional material.
This
topic will help us understand how mathematical processes shape the
universe.

**8. Infinity and other topics:** In the final section of the
course,
we will examine further topics in mathematics,
that
will range from the philosophical (e.g. the nature of infinity) to the
practical (e.g. further student-requested applications of contemporary
mathematics).

**Goals**

The primary goal of this course is to gain knowledge and appreciation of contemporary mathematics. More specific goals, together with topics that help attain them, are listed below.

1. Gain an understanding of how mathematical processes shape our world. (Topics 1,2,4,5,7)

2. Enhance precision, computational skills, and other core mathematical qualities. (Topics 2,3,6)

3. Acquire content- and technique-based knowledge (e.g. statistics) that can be practically applied outside this course. (Topics 3,6)

4. Appreciate the use of the computer as an experimental tool (Topics 5,6,7)

5. Learn to think mathematically. (Topics 1 to 8)

6. Learn about broader issues and open questions in mathematics. (Topics 1,8)

- HOMEWORK is an essential part of the course. A few
problems from each section will be assigned to be handed in for
grading.
These are accessible through my website and the blackboard site.

To do well in the test and final, you should make sure you can solve other similar problems from the book. Homework for sections completed in any given week (M-W) will be due the next Wednesday. ALL HW will be counted - lowest grades will NOT be dropped. Only selected problems from the HW may be graded for credit. LATE HW CANNOT BE ACCEPTED WITHOUT MEDICAL (or other similar) VALIDATION. - PROJECTS. In addition to mathematical problems,
there
will be one or more essays/projects.
- CLASSWORK/QUIZZES From time to time, work done in
class
will be collected for grading. You will need to keep up with the
material
to do well in this.
- MID-TERM The date will be
announced at least 2 weeks in advance.
- FINAL This will be
cumulative.
It will be on Wed, May 16 from 1 to 3 pm in MP 101.
- MAKE-UPS for the mid-term will only be allowed
under
special circumstances with written documentation and prior approval
if
possible. If you miss it, contact me immediately (i.e. on that day)
via
e-mail (or phone). MAKE-UPS for CLASSWORK will not be given, since
the
lowest two scores are dropped. (If your final grade at the end of the
course turns out to hinge on missed classwork,
then suitable accommodation will be made, PROVIDED you have a good
reason
for your absence.)

- Homework: 20%
- Projects: 10%
- Classwork: 15%
- Mid-term: 22%
- Final: 33%
- Cut-offs: A: 90%, B: 80%, C: 65%, D: 55%

Keeping
up with the material is going to be essential. Also, being an active
participant in class will enable you to do well grade-wise. Please be
informed
that some of the topics to be covered are not adequately presented in the
book
- another reason to make sure you attend (and stay alert in) class. Study
groups are encouraged, as is discussion of homework. However, turning in
work
copied from another student is unacceptable, and will be considered
cheating
(see "Academic Conduct" below).

Please don't be late for
class.
If you expect to be more than five minutes late, please clear this with me
beforehand. Similarly, don't leave until the class is over (unless cleared
with
me beforehand). No hand-held devices or texting. No chatting amongst
yourselves.

Wed,
Feb 8 is the last date to drop a class without a W on your transcript.
Mon, Apr
16 is the last date to drop this class with a grade of W. Please do not
hesitate to talk to me if you need some guidance on how to proceed
regarding
these dates.

By
enrolling in this course, each student assumes the responsibilities of an
active participant in UMBC's scholarly community in which everyone's
academic
work and behavior are held to the highest standards of honesty. Cheating,
fabrication, plagiarism, and helping others to commit these acts are all
forms
of academic dishonesty, and they are wrong. Academic misconduct could
result in
disciplinary action that may include, but is not limited to, suspension or
dismissal. To read the full Student Academic Conduct Policy, consult the
UMBC
Student Handbook, the Faculty Handbook, or the UMBC Policies section of
the
UMBC Directory.

If
you require accommodations for this class based on disability, please make
an
appointment to meet with me to discuss your SSS-approved accommodations.
Please
see http://my.umbc.edu/groups/sss/documents/838
for more
information.