Overview
The purpose of Cajori Two is to allow a glimpse of the evolution of American undergraduate mathematics curricula in the twentieth century. For 20 campuses, we present abbreviated snapshots of curricula of their mathematics department(s)1 in 1905, 1915, 1925, . . ., 20052. In addition, there will be dozens of tables providing summaries and comparisons of various sorts, most of them in the form of time series.
[In this project, “mathematics” should be interpreted broadly. For example, when we write “Mathematics Department”, we might also mean a department whose title is “Department of Mathematical Science” or perhaps “Department of Mathematics and Computer Science” or “Department of Applied Mathematics” – indeed, any department with “Mathematics” or “Mathematical” in its name, as long as it is not a department of mathematics education3.]
In some cases, a campus will have multiple departments qualifying as mathematics departments. For example, at Stanford there was, for a time a pure mathematics department alongside an applied mathematics department. Later there was a merger of the two. When departments merge, we consider the result a third department, since its mission is now altered. For Stanford there are, first of all, three separate data sets: for the pure department, for the applied department, and for the merged department. Thus, our 20 campuses comprise 25 different departments. But in addition, for the users convenience, we also provide, for each campus with multiple mathematics departments, data for the combination of all departments (a “combo”) – what one might call campus-wide data showing all the available undergraduate mathematics. Thus the number of departments and combos is 28.
Cajori Two was based on photocopies, or sometimes scans, from the catalogs of the schools in question. We owe a debt of gratitude to the archivists of the various schools for providing us with this data.
The following results of this project will be available online:
1. Scans of the catalog photocopies just mentioned.
2. Downloadable Excel workbooks. One type of workbook is the Abbreviated Catalog Data workbook. Such a workbook contains abbreviated textual information about courses, which the project staff has extracted from the catalogs. The abbreviation of a course would be entered in a cell of the Excel workbook something like this:
| [201]; 3cr; pre: none listed; ac: recommended for all freshmen. |
3. There is another type of workbook containing numerical summaries and tabulations derived from the Abbreviated Catalog Data. The user creates these, tailored to his or her particular needs, with the software provided in the download (see below4.) We refer to the use of these resources as the Download-for-Excel approach, since downloading is the first step.
4. An on-line database (using MySQL) containing numerical data that can be searched in various ways by the remote user. Information about this is contained below. This is an alternative to the Download-for-Excel approach.
Online Analysis
This can currently be carried out at http://matcmp.ncc.edu/taormij/cajori_two (but this location will probably change.) Help and documentation for this material is found within the website and is described only briefly here. A great variety of ways of viewing the data are possible because there is an underlying use of the database program MySQL powering the website. The user need have no knowledge of MySQL. To a considerable extent, this online approach to the data yields the same opportunities as the Download-for-Excel approach, but there are a few differences described below. But online analysis is probably simpler for the first time user who only wants to browse data without making a record of the results.
The Download-for-Excel Approach to the Analysis
These are of four kinds of files you will receive:
1. Abbreviated Catalog Data in Excel workbooks;
2. VBA code in other Excel workbooks;
3. Word files explaining our methods, explaining the use of the Excel-based Data Analysis Software, giving advice to the browser of tables, and giving standardized descriptions of courses we looked for in catalogs;
4. Excel files with tabular data documenting the VBA code.
5. Sample output obtained by running the VBA code.
All of this is in the folder CajoriTwo_4.0.zip which you can download.
Comparing the Download-for-Excel approach and Online Approaches to Data Analysis.
Briefly, the Online approach is better for a first look. The Download-for-Excel approach requires an investment to lean a few things, an investment that will be repaid as more work with Cajori Two is undertaken. A discussion of this topic can be found at the start of the essay you reach by clicking the website button Online Tool: Perspective And Examples. The same discussion is also found in the downloadable folder CajoriTwo_4.0 which you can get by first clicking the button Download for Excel Analysis. After the folder has been downloaded, go to
CajoriTwo_4.0\DataAnalysis\AnalysisAfterDownloadPerspectiveAndExamples
within the downloaded folder.
What to Read Next
Click the button Three Ways to Access the Data (a quick read).
Next, if you want a quick jump into the online analysis, click the button Online Data Analysis Tool and then jump. But, for doing an intelligent job of online analysis you should also read what is available through the button Online Tool Perspective And Examples.
If you want to skip online analysis, which might be a good plan if you want to do a lot of work with this data and want to record your analyses in the most graceful way, click the button Download for Excel Analysis. Then download the CajoriTwo_4.0 folder found there. Within this folder you will be able to see the Abbreviated Catalog Data workbooks, or just read a brief overview of them. In the DataAnalysis folder you should start by examining
AnalysisAfterDownloadPerspectiveAndExamples.docx
Request and Acknowledgments
Request for Feedback
This version is as complete and error-free as we have been able to manage. But if you find errors, bugs or other improvements, we would like to hear from you. Write to Walter Meyer or Larry D'Antonio.
But please note that what seems like a bug in the display with one browser may work just find with another. So try different browsers if you run into anything clunky.
Acknowledgements
We gratefully acknowledge the material assistance of the Mathematical Association of America, Adelphi University, Farmingdale State University, Nassau Community College, Ramapo State University and York College of CUNY. In addition, the following students pitched in to help: Synthia Gratia, Chun Him Yam (Tim), and Andrew Robinson, Yuan Guan (Annie), and Dan Summers. Finally, we acknowledge our project muse Rochelle Wilson Meyer.
Last but not least we gratefully acknowledge the time and effort expended by the archivists at the institutions we studied. Those institutions and their websites are:
Bowdoin College | |
Bryn Mawr College | |
City College of New York | |
Colorado College | |
Georgetown U. | |
Johns Hopkins U. | |
Massachusetts Institute of Technology | |
Morgan State U. | |
Reed College | |
Samford U. | |
San Jose State U. | |
Stanford U. | |
Tuskegee U. | |
U. California at Berkeley | |
U. S. Military Academy at WestPoint | |
U. Texas at Austin | |
U. Wisconsin at Madison | |
Vassar College | |
Williams College | |
Yale U. |
1Note that at some campuses there may be multiple mathematics departments, for example a pure department and an applied department and perhaps later the merger of the two. In such cases, each will have its own workbook. In addition we present a “combination” workbook showing all courses in all departments at that campus.
2For some departments we do not have the entire series of years. In some cases older catalogs could not be found. At least one of the institutions did not exist in 1905, etc.
3Departments of mathematics education have a distinctly different mission from the departments we are interested in and their curricula are often not really comparable to those of the departments we really wanted to study.
4Excel needs to be installed for this software to work.