From: Hugh.Montgomery@MATH.LSA.UMICH.EDU (Hugh Montgomery)
Newsgroups: sci.math.numberthy
Subject: CLINT second edition
Date: 9 Sep 94 14:26:05 GMT


                                   ANNOUNCING

                              THE SECOND EDITION OF

                   COMPUTATIONAL LABORATORIES IN NUMBER THEORY
                                    (CLINT)
                          with assoicated software for
                         IBM-compatible PCs running DOS

I have been experimenting with a number theory laboratory class that students
take concurrently with their first (undergraduate) course in number theory.
The lecture course meets 3 hrs/week, the laboratory 1 hr/week.  Thus far the
laboratory course is optional, but my thesis is that students who participate
in the labs will perform better in the lecture course.
     The 123 page CLINT manual, written in plain TeX, contains 17 labs and
documentation for the software.  The labs are linked to the text ``An
Introduction to the Theory of Numbers'', Fifth Edition, by Ivan Niven, Herbert
S. Zuckerman, and Hugh L. Montgomery, John Wiley & Sons, New York, 1991.  The
software consists of 70 programs written in Turbo Pascal (Version 57.0).  Both
source code and compiled code are provided.  The programs are of three main
types:
     1) Quick calculations (e.g. gcd(a, b), phi(n))
     2) Tables (e.g. powers (mod m), indices (mod p), Farey fractions)
     3) Demonstrations of algorithms (e.g. Euclidean, powering, Pollard rho)
Instructors using the NZM text may find these programs useful for in-class
demonstrations, even in the absence of any laboratory.
     The CLINT students are not expected to have any knowledge of Pascal, nor
are they exprected to do any programming.  However, students with interests in
programming will find opportunities to write some programs of their own.  A
library of 28 basic number-theoretic routines is provided, to aid such efforts.
     I want my students to understand what the computer is calculating, rather
than view the computer as some sort of magical black box.  Consequently, the
algorithms employed in these programs are restricted---with a few minor
exceptions---to those discussed in NZM.  This has some disadvantages,
particularly in factoring (no quadratic sieve), primality proving (no
Atkin-Morain or Adleman-Rumely), and in finding roots of polynomials modulo p
(no Cantor-Zassenhaus).
     I want my source code to be as simple as possible, so that students
can comprehend it.  Hence I use no multiple-precision arithmetic.  (A multiple-
precision arithmetic package would require that students master a host of
specialized data types, functions and procedures before the code would make
sense.)  Consequently, integers are restricted to have size < 10^{18}.  This is
a disadvantage in some contexts, such as factoring, Pell's equation, and
continued fractions.  For such topics I would turn to UBASIC, which
accommodates integers up to 10^{2600}.

     The TeXfiles that create the CLINT manual, and the software are available
by anonymous ftp at the address ftp.math.lsa.umich.edu, in the directory
/pub/clint.  There you will find the following files available:
       readme         General instrucitons
       clint0.tex     title page of lab manual
       clint1.tex     forematter (pages ii--x) of lab manual
       clint2.tex     the labs (pages 1--68)
       clint3.tex     program documentation (pages 69--106)
       clint4.tex     programs for the HP-28S, Further Resources
     error5-1.tex     Known errors in NZM, Fifth Edition, First Printing
     tpprgms2.exe     Turbo Pascal programs (archived)
This last file is a self-extracting archive file; it MUST be transferred in
binary. (Issue the command "type binary" before the command "get tpprgms.exe".)
The other files can be transferred in the (default) ASCII mode.  This material
may be freely copied and distributed to students using the NZM text.  (Think
"coursepack.")  If ftp is unavailable to you, you can obtain a printed copy
of the manual, and a disk containing the programs, by writing to John Wiley.
Direct your inquiry to
                       Mathematics Editor
                       John Wiley & Sons, Inc.
                       605 Third Avenue
                       New York, NY 10158-0012 USA

     John Rickert has composed an Instructor's Manual for NZM that gives
solutions to the starred problems.  This is not available by anonymous ftp,
lest it fall into students' hands.  However, John Wiley will send it to you
on request, or I can send it to you by email.

     I welcome your comments and suggestions.

                                               Hugh L. Montgomery
                                               hlm@math.lsa.umich.edu