Info
| |
An exploration of the ideas behind computer
programming, including function calls,
object oriented programming, data structures,
and lots of other cool stuff.
The Mathematica language is quite versatile,
allowing for a variety of programming styles -
and its easy to draw lots of pretty pictures.
This course (or any of the similar ones
offered each fall in languages like Java,
Perl, or C++) serves as a foundation for
further work in computer science or any related field.
The parenthesis so common in both computer science
and mathematics should perhaps be inserted into the title
of this course so reads "An Intro to Programming (with Mathematica)"
rather than "An Intro to (Programming with Mathematica)".
In other words, my intention is to have the focus of
the course on programming - what it is,
how it works, why one might want to do it, and so on - rather
than Mathematica itself. However, programming
isn't a subject that is easily studied in the abstract;
instead, you need to climb in and get your hands dirty
by actually doing it - which is exactly what we're going to do.
Depending on your level of math comfort, I expect
that many of you will find the textbook intimidating;
the author uses calculus and other higher math freely,
and is writing prose generally aimed at a mathematically
literate audience. It is my intention, however, to
extract out the parts related to the goals of this course,
without requiring the calculus bits.
So you shouldn't need an extensive math background.
However, you will need to be able read and explore mathematical
ideas, including being able to learn new notations
and syntax - but then, all programming languages
require that, really.
Grading will be based on weekly assignments,
a final project, and two take home tests
along the way, as well as a class participation grade.
I plan to drop the lowest of those five scores
and average the other four for your final grade.
This webpage will continue to change throughout the semester
as assignments and resources are added.
|
|
Tentative Syllabus
date week topic
---------------------------------------------------------------------------
Sep 3 0
7, 9 1 intro
14, 16 2 functions, ...
21, 23 3 variables, operators, ...
28, 30 4 control flow
Oct 5, 7 5 mid-term grades I/O
12, 14 6 practice
21, 7 Hendrick's days sorting
26, 28 8 computability
Nov 2, 4 9 databases
9, 11 10 object oriented programming
16, 18 11 lists and recursion
23 Thanksgiving functional programmin
29, 2 12
Dec 7 13
== details ================================================================
week topic textbook
---------------------------------------------------------------------------
I) intro
1 a) general "how-to" for using the mathematica system chap 1
b) general intro to programming and my notes
II) programming notions
*2 functions, programs, subroutines, comments (API), debug chap 2
3 atoms, operators, boolean expressions, variables, lists and my notes
4 conditionals and loops .
5 I/O Import, Export .
6 practice; packages .
III) classic CS ideas
7 sorting chap 6
8 computability chap 12
9 databases chap 13
IV) styles of programming
10 object oriented programm (Java, C++) chap 14
11 lists and recursion (Lisp) chap 9
12 functional programming (Haskell) chap 11
13 we'll see
|
Assignments
- for Tues September 7
- Send me (mahoney@marlboro.edu)
an email telling me you're registering for this class.
- Try out Mathematica on one of the lab machines.
In particular, browse through the online Help system, and
- read the "Tour",
- look at "Getting Started", especially "Working with Notebooks",
- start working through "A Practical Introduction..." in "The Mathematica Book".
Be ready to bring any questions up in class.
- If you have access to the text,
browse the first chapter in the text; I'll talk more about
the computer science background in class.
- for Tues September 14
- Read chapter 1 in "Feynman Lectures on Computation", in Sci 217
- Read (and explore any topics that catch your attention)
the "Computer" entry in the wikipedia at en.wikipedia.org/wiki/Computer.
- Read the "Tutorial" (23 screens) in Mathematica's Help menu.
- Read James Kelly's "Getting Started" Mathematica notebook.
Skip the parts that feel too mathematical, but do look at
and work through at least the
"Using a notebook interface", "Help!", "Input conventions",
and "Using functions" sections.
- Do the following exercises in Mathematica; most
are from the Getting Started notebook.
- Express the number of seconds in a year in hexadecimal form. [Hint: use Help to find functions which manipulate bases and note that hexadecimal form describes a number represented in base 16.]
- Display the first 20 powers of 2, i.e. {2, 4, 8, ...}.
- Revelation 13.18: "Let him that hath understanding count the number of the beast, for it is the number of a man and his number is 666." Show that the sum of the squares of the first seven primes is the beast number.
(Hint: see the Prime and Total functions.)
- Create a notebook which presents a simple problem in your field of interest, or perhaps reproduces some recent lecture you heard, or some section of a textbook. Your notebook should have title, author information, sections, text presenting the problem and some background information, and references if appropriate. If you already possess enough Mathematica tools, include the solution also.
- Explain in English what this Mathematica expression says.
!(a && b) == (!a || !b) /. {a -> True, b -> False}
- for Tues September 21
This is a practice programming week: time to dive in.
- Do the exercises
in the
hiddenTurtle.nb notebook.
- Write, document, and test an isEven[] function that returns True for
an even number, and False for and odd one.
-
I'm not quite sure where your skills are at this point,
so I'm going to suggest several posssible programming projects.
Pick at least one (preferably two) to try out.
Whichever ones you look at,
organize your thinking by answering these questions first.
- How can I break this problem into smaller pieces?
- What kinds of data (number, strings, lists, ...) do
I need to pass around for these pieces?
- Does Mathematica have any built in functions
that might help?
- How do I want to display the answer?
- What do I need to ask the user?
So here are some possible problems. If something else similar
is bubbling in the back of your head that you'd rather try,
or these seem beyond you, talk to me about doing something else instead.
The point is to pick some kind of numeric search or puzzle or game
that can be done as a text input/ouput thing, or as a drawing thing
in the Turtle world.
- Perfect numbers ... we did this in class.
- A "magic square" is a rectangular grid of numbers whose
rows, columns, and diagonals add up to the same number.
Can you write a program to find one? More than one?
How big are they?
- Rearrange 1..9 to find fractions such that 1/23 + 4/56 + 7/89 = 1
- Write a program that simulates one of the state lottery games
(you'll have to look up some rules online), letting the user pick
a number, generating a winning number, and looking for a win with payoffs.
- Write a program that simulates a dice game like
craps (find rules online, e.g. here) or Cosmic Wimpout (http://www.cosmicwimpout.com/cwrules.htm), or a simplified
version of one of these.
- Play the classic "Mine sweep" game.
- Play hangman. (You'll have to pick a random word from
a list of possible words, and count letters - look for
string manipulation functions.
- for Tues September 28
- More practice - pick another of the many projects from last week,
and try again.
- Read (if you havne't already) chapters 1 and 2 in the text.
- We'll be moving into chapter 6 - searching - next week.
- for Tues October 5
- Read chapter 6 in the text, on searching and sorting.
The author's style is fairly technical, but don't let
that scare you away - most of what's in there is pretty
cool once you see how it works.
- Browse through
Sort algorithms on the Wikipedia to see the range of what's out there.
- Pick any two of the sorting algorithms listed
on the wikipedia site, above. Describe in words
how the algorithm proceeds, and work out (by hand)
what each would do on a short list like {6,4,1,7,1}.
(I call your attention to the "Stupid sort" for a particularly simple one,
and the "bogosort" for a particluarly amusing one.")
- See my version of Mathematica code to do this stuff
in code/search_and_sort
- Of those two, pick one to implement in Mathematica.
(Get help, if need be, or start with implementations in the wikipedia.)
Test your routine on various kinds of initial scrambled lists
(at least random and reverse order) and see how they work as
the size of the list gets big. While it may be hard to distinguish
Mathematica's behavior from the algorithm's behavior, it'd be
great if you could measure the O(n) behavior as n gets larger.
- Pick any one of the exercises on pg 138 and following to do.
- for Tues October 12
- An extra week to finish last week's assingnment.
- Check out my example of a binary tree
dictionary, complete with random words :
code/dictionary.
- for Thurs October 21 (Tues is Hendrick's days)
This is a practice with file input/output and data manipulation week.
- Read the Mathematica documentation on
the commands Directory[], SetDirectory[],
Import[], and Export[], BarChart[] (in the Graphics`Graphics` Add-on Package)
and ListPlot[].
- A .csv file with survey data from a statistics course last
year is here. Download it, import it into mathematica, and create a histogram
of the women's heights as a bar chart. That is, for each of a number
of ranges of heights (5 ft, 5 ft 1 in, 5 ft 2 in, ...) count how many
women fall in that range.
- With the same data, make plots that shows each woman's height
as a function of (a) her mother's height, (b) her father's height,
and (c) the average of her parent's height. Does your intuition
lead you to any conclusions?
- Again with that data, create a new file that has the ages and heights of
the black haired men.
- Here is a link to the text of
Moby Dick.
Read it in one line at a time, and make a list of the 50 most frequently
used words. Do you think these numbers are representative of the English
language, or of this author? (You can find other public texts at
the Gutenberg project, http://promo.net/pg/.)
- for Tues October 26
- Finish up at least the .csv stuff from last time.
- Read online about Conway's Game of Life; there are many good online sources.
- Submit a preliminary proposal for your final project. This is your only
written assignment for this week - so put some thought in. I want more than
one sentence here - tell me some thought on how you're going to go about the
project, what readings (if any) you've found on the topic, and how you think
it might work in Mathematica.
- for Tues November 2
- Read about computer graphics and how they work in Mathematica :
- Check out the blurbs on
raster graphics
and "vector graphics" in the wikipedia. There are links there to human vision, as well, that make interesting reading.
- Explore my mathmatica notebooks in code/graphics/ and code/oct_28/
- Read the parts of the online Mathematica documentation
that discuss the Graphics object, the Graphics3D object,
as well as some of the more general discussions of graphics :
"Tour/Visualization" and especially the section
"The Mathematica Book / Principles of Mathematica / The Structure of Graphics and Sound". (You can read this in the big hardcopy version of the book on the shelf in 217.)
- Look over the code/TurtleGraphics.nb notebook we did earlier this semester,
and see how I did the graphics stuff in it.
- Please do more thinking about your project, and report what you've done,
either some research, or create an initial specification for your project
code : what Mathematica functions do you want, and what should they do?
- Play around with some kind of graphics in Mathematica.
What exactly is up to you. You're welcome to start with some
of my code, but I would like to see evidence that you've
looked at the documentation and added some new features.
Draw a pattern, or animate some random shapes,
or rotate a raster image, or create (or even solve) a random maze...
- for Tues November 9
- Read about buttons and mathematica notebooks,
both (a) in the help file, and (b) looking at
the examples in the buttons/
directory, including the "LightsOut" game I showed
in class.
- Continue work on your term projects, including
brief a progress report as to what you got
done this week.
- Create a mathematica notebook that has three buttons,
which change what is displayed below them.
The idea is something like this, where the picture
depends on which button is pushed.
button1 | button2 | button3
---------------------------
| picture |
---------------------------
- for Thurs Nov 11 and Tues Nov 16
- Be ready to discuss and look at in class your project.
- for Tues Nov 30 - optional
- Last weekly assignment.
- Read the beginning of chapter 14 in the text
- Write a short mathematica program in an object oriented style.
See object_oriented.
Either convert one of the programs you've written earlier
this semester, or follow the assignment in the objects.nb file.
|