# Math

Classes I taught, past and
present.

### Basic Algebra with Applications

*Basic Algebra with Applications* is a college-level
textbook intended for an introductory course in algebra. It
covers the most basic algebraic concepts, including axiomatic
approach, linear equations, graphing, linear systems, polynomial
equations, rational expressions, radicals, and the quadratic
formula.

Download PDF options:

- Hyper-linked,
optimized for viewing on a computer or a tablet screen.
- Printable
in color, optimized by decoloring hyper-links.
- Printable
in monochrome, optimized for black-and-white laser
printers by additionally decoloring most graphs. There are
still plenty of colors in this PDF, intended to print as
shades of gray.

Additional teaching aids are also available (ZIP with PDFs). More
than 40 short *quizzes* are intended to be given out during
class for group work and/or discussion. They follow the text very
closely, alsmost section by section. They are also class-agnostic,
and can be used as either true quizzes or as worksheets.

Instructor materials

Contributions of all kinds are welcome. Developers are invited to
browse the source code repository (git) and contact the maintainer
with comments and/or requests. The contact info can be found
within the text.

https://git.albertleadata.org/melikamp/basic-algebra

### Articles

2010-05-12 - Prime Crawler update is
due in a few days or weeks. The math part includes a treatment of
the distribution of strings of arbitrary finite length in the
period (spoiler: they will tend to be equidistributed under
certain conditions). The code will include a new data structure
for so called sparse lines, which will
allow for periods as large as the product of the first million
primes.

2009-10-09 - Prime Crawler is a
pseudo-random number generator I made up. Here is a description
and some
math [PDF] that
goes with it.

As for the code (designed to be very vanilla c++, known to build
in Slackware and Ubuntu), you
can git it:

git clone
git://buma16.bu.edu/pub/git/prime-crawler

or get this
tarball [tar.bz2]

2009-01-18 - Birthday problem: In a
group of people whose birth dates are distributed randomly,
independently and uniformly, what is the probability of the event
that at least 2 people will have the same birth
date? PDF,
LaTeX

2008-06-23 -
Staistical Haiku written by
students in MA 115 class, taught in Spring 2008 (I was a teaching
assistant then).