Thesis

The division algorithm and the Hilbert scheme

Dave Bayer, The division algorithm and the Hilbert scheme, Ph.D. Thesis, Harvard University, June 1982. 168 pages.
Available from http://www.math.columbia.edu/~bayer/thesis/thesis.html

Grayscale Files for Viewing:

The following Acrobat PDF documents are best suited for viewing. Each file has an Acrobat "Bookmarks" table of contents. Each file is preprocessed for a particular viewing magnification, at which it looks best. The images have been slightly enlarged (e.g. 100 dpi masquerading as 90 dpi) and then cropped to 7.5" by 11".

PDF document, 108 dpi (6.1 Mb) for viewing at 150%.

PDF document, 90 dpi (5.1 Mb) for viewing at 125%.

PDF document, 72 dpi (3.9 Mb) for viewing at 100%.

Bitmap Files for Printing:

The following Acrobat PDF documents are best suited for printing. The file dpi_samples.pdf (158 Kb) consists of a sample page at each resolution, which can be used to help choose the file best suited for a particular printer.

PDF document, 600 dpi (7.9 Mb)

PDF document, 300 dpi (3.8 Mb)

PDF document, 200 dpi (2.5 Mb)

Production notes:

The original typed manuscript was scanned as 600 dpi bitmaps on a Macintosh G3, using an Epson Perfection 1200U scanner with an automatic document feeder.

The following is a fictionalized account of how I should have processed these files; I learned on the job. The files for printing were in fact run through Adobe Acrobat Distiller as (huge) EPS files combined into one document by a Postscript "wrapper" file. The files for viewing were processed more or less as desribed here.

Use Adobe Photoshop to scan 30 or so pages at a time, in groups of 10-15, using an automatic document feeder.
Save each window as compressed TIFF, using an "Action" consisting of 30 or more Save commands interleaved with Close commands. ("Automate Batch..." doesn't seem to work yet with scanning.)
Rename "Untitled-1.tif" as "a01.tif", and so forth. Use two digits for all numbers, and start the next batch with "b01.tif", etc., so the entire folder of images alphabetizes in correct page order.
Back in Photoshop, create an "Action" translating a raw image into a desired output format. Using "Automate Batch...", apply this action to the folder of raw images, saving in a new folder for this output format.
Organize each output folder into subfolders of 50 or fewer images each, maintaining global page order. (Reshape the folder window so each column is 50 items or fewer, and select columns.)
In Adobe Acrobat Exchange, "Import Image..." in sets of 50 or fewer images, and save optimized as a single PDF document.

For example, the Photoshop "Action" to create the 72 dpi viewing document consisted of

Convert mode to grayscale mode, ratio 3.
Image size, resolution 200 per inch.
Image size, resolution 400 per inch, bicubic interpolation.
Image size, resolution 80 per inch, bicubic interpolation.
Image size, resolution 72 per inch.
Posterize, 8 levels.
Canvas size, width 8 inches centered by height 12 inches centered.
Canvas size, width 7.5 inches right.
Canvas size, height 11.75 inches bottom.
Canvas size, height 11 inches top.
Save as compressed TIFF.
Close

Note that the 2/5 interpolation is carried out as 2 x 1/5, for greater accuracy.

Finally, create Acrobat bookmarks in one document, and use Acrobat Exchange "Replace Pages..." to create documents at different resolutions with these bookmarks. Avoid fancy page numbering schemes, which will confuse this command. Bookmarks record the viewing magnification, so use a text editor to modify the viewing magnifications, e.g. replace all occurrences of "1.25 ]" by "1.00 ]".