National Library of Australia


University of Melbourne collection assessment
Mathematics

1995

  1. Aims
  2. Methodologies
  3. Nature of the Discipline
  4. School of Mathematical Sciences
  5. Mathematical Sciences Branch Library
  6. Special Collections
  7. List Checking
  8. Shelf Scanning
  9. Evaluation by Experts
  10. Assessment of the Collections
  11. Areas of Research Strength
  12. Areas Needing to be Enriched
  13. Acknowledgements

1. Aims

2. Methodologies

The collections were assessed using criteria laid down in the Australian Conspectus Manual:

3. Nature of the Discipline

Mathematics is the oldest of the exact sciences, and among the oldest of all intellectual disciplines. It has long been valued as the training ground for systematic, logical and analytical thought. A knowledge of mathematics is invaluable for professional life in the pure and applied sciences, as well as in commerce, industry and technology, and an understanding of mathematics is invaluable in making sense of a rapidly changing and increasingly technologically complex world.

As well as being a discipline in its own right, mathematics, unlike other sciences, is not so much interdisciplinary as sub-disciplinary (in the sense of standing beneath other disciplines, supporting them). No branch of mathematics has failed to become applicable to some phase of technology or science. Physicists, chemists, biologists, economists and sociologists, for example, look to the mathematician for ever-increasing precision in formulating their theories or models. Mathematicians have contributed extensively to the solution of difficult problems in theoretical physics, astronomy and chemistry. Statistics has also become an important tool in the work of many academic disciplines, such as medicine, psychology, education, sociology, engineering and physics.

The increasing use of mathematics by other disciplines is evidenced by literature dealing with the biological and behavioural sciences, in addition to the traditional applications in the physical sciences. The literature dealing with applications of mathematics is widely dispersed, often in publications in the field of application, rather than in purely mathematical publications.

The strongest collection is in B, with the other significant collections held (unsurprisingly) in the Mathematical Sciences Branch Library, the Baillieu and the ERC. Further items are located in Physics and Engineering, and even as far afield as Architecture and Zoology. This is particularly the case with applied mathematics and statistics materials, which are not uncommonly located with the subject to which they refer and are, in consequence, scattered across campus.

This has led to vexation on the part of users, who stress that fragmentation of the collections, both books and journals, has hindered effective use. This difficulty has been noted especially by visiting scholars, who are even more severely handicapped by the lack of "user-friendly" guides to the collections and services of the University Library.

A number of possible solutions have been offered by the Department, one of which is the relocation of a number of monographs, currently located in Baillieu, which are beyond the scope of undergraduate students in mathematics. They would be more suitably located in the Maths Library, where they would be more readily accessible to researchers. The continued location of the most substantial and important journals in the Baillieu is of major concern to members of the Department and to its visitors.

Mathematics, like other sciences, relies far more heavily on serial than on monographic literature. Mathematicians do, however, make significant use of monographs, particularly those in series. There is a requirement for a wide chronological coverage, particularly of classics, which see sustained use by academic staff and postgraduate students.

Since the close of World War 2, English has become the lingua franca of the sciences. German journals in particular have increasingly encouraged articles written in English. Evidence for this trend is seen in the percentage of English articles in German mathematics journals, which doubled from 1960 to 1978. Local evidence is that the only collection containing foreign language materials is that in B, the research collection, holding much pre World War 2 material. The American Mathematical Society has an active translation programme, notably in the area of mathematics from the former Soviet bloc. Most such journals are now available in cover-to-cover translation. There is, therefore, no longer the necessity for mathematicians be able to read in other languages.

While the publishing of most other sci-tech journal literature has become monopolised by the major national professional societies and well-known commercial houses in mathematics, these sources share roughly equal status with individual university presses (eg. Oxford, Duke), regional associations (eg Rocky Mountain Mathematics Consortium, London Mathematical Society), and less familiar commercial houses (eg Birkhauser, Sithoff).

The literature of mathematics comprises mainly journals, encyclopaedias, textbooks, monographs in series, proceedings of conferences and symposia, translation series, handbooks, tables, and indexing and abstracting journals.

Primary publications constitute original sources, ie publications containing new material or new presentations and discussions of known material. This category includes the research journals, the monograph series, proceedings of symposia and translation series. The principal medium for the dissemination of mathematical information is the journal, followed by the book series, including series of monographs, proceedings of symposia and translation series. Preprints are a significant form of pre-publishing professional communication. Much work of this nature is now being distributed electronically. The American Mathematical Society has been particularly active in the field of electronic publishing, maintaining an interdiscplinary team of mathematicians, librarians and information technologists to mount a number of electronic information sources. Among other activities, they make preprints available electronically, and generate the MathSci Index. The Bulletin of the Society was one of the first journals on the Internet to display mathematical formulae.

Conference material is useful as a compact source for obtaining a picture of what is going on in a particular field and who is working in it, but the published proceedings may already give an out-of-date picture.

The least common form of publication is the nonserial book. This category includes dictionaries and encyclopaedias, handbooks, mathematical tables, directories, histories, collected papers of individual mathematicians, and Festschriften. The forms that books take most often are the treatise, the monograph and the textbook. As with journals, mathematics books are published by societies, universities and academies and commercial publishers.

Secondary publications also include abstracting and reviewing journals, and indexes, which provide access to the primary publications.

4. School of Mathematical Sciences

The School forms part of the Faculty of Science. The School comprises the Department of Mathematics, the Department of Statistics and the Department of Computer Science. (The Department of Computer Science is located in the Faculty of Engineering.)

Research Areas for the Department of Mathematics:

Research Areas for the Department of Statistics:

5. Mathematical Sciences Branch Library

Like other sciences, mathematical sciences relies far more heavily on serial than on monographic literature. This is reflected in the annual bookvote allocations. The 1995 bookvote for Mathematical Sciences is $231,400.00, of which serials account for $151,110.00, or 66%. (CD ROMs are classed as subscriptions.)

The Mathematical Sciences Branch Library has roughly 10,000 monographs and has 314 journal titles. These include many with extensive runs. It contains a collection of 12 shelves of working papers, 23 shelves of conference proceedings, 16 shelves of handbooks and tables, and 24 shelves of series, comprising the Springer series in computer science.

It acquires approximately 900 new book titles per annum, most of which are components of series such as those published by the London Mathematical Society or the American Mathematical Society. (This figure is based on the average cost of an item divided into the budget, double checked against a representative sample of new books listed in the Mathematical Sciences Branch Library's Library Bulletin.)

6. Special Collections

6.1 Statistics Departmental Collection

The Statistics Department maintains a small (fewer than 100 items) collection of materials for academic staff tutoring and teaching first and second year students.

6.2 Mathematics Departmental Collection

The Mathematics Department maintains a small (fewer than 100 items) collection of materials for academic staff tutoring and teaching first and second year students.

6.3 Historical Statistical Collection

There is a collection a couple of hundred older books held in the basement of the building. This is of "sentimental" value rather than a useful adjunct to research and/or teaching.

6.4 Microforms

The University of Melbourne Library holds one of the most important collections of primary and secondary source material in microform in Australia in many and various subject areas. Notable collections of relevance to Mathematical Sciences are:

6.5 Audio-visual collections

6.6 Theses

6.7 BX Collection

The Special Collection (BX) holds approximately 600 volumes. It includes works such as:

6.8 Neumann Collection

The Neumann Collection comprises roughly 250 items dating from last century. Most are works by Carl Neumann. Roughly half of these are reprints. It is to be incorporated in the BX collection.

6.9 AX Collection

The Special Collection (AX) contains 4 items:

6.10 Morgan Collection

The Morgan collection holds 4 items in this conspectus range:

6.11 The U Collection

The U collection holds 5 items, including Mixed Mathematics 11 (Pass): lecture notes issued with the permission of the lecturer, T.M. Cherry, Melbourne University Press, 1930.

7. List Checking

A number of lists were used to assess the collection strengths. The list checking took 34 hours.

7.1 Bibliography used for list checking:

7.1.2 Results of the list checking

7.1.2.1 Monographs

It was difficult to find an up to date list for monograph checking, but Current Index to Statistics and Current Mathematical Publications were useful. Checking from older books such as Dorling (1977) indicated a strong monograph collection; however, the date of publication skews the total figures, as many titles, and indeed, topics, of research relevant to departmental research groups date from after 1977, and the number of titles available continues to increase rapidly. The checking of a chapter in Mount (1989) dealing with newly developing areas produced evidence of a heartening 77.5% holdings, but note the date - already 6 years old. This must be set against a 40% hit rate from CIS and 38.7% from CMP.

These figures lend weight to the concerns of the academic staff that the collections are not meeting their needs in research, teaching or learning, as even the undergraduate collections are not as strong as they need to be.

Table I: Monographs

 
	 
Title No. checked No. held %
VIS 20 8 40
CMP 93 36 38.7
Dorling 772 593 76.8
Hurt 57 41 71.9
Malinowsky 41 29 70.7
Mount 49 38 77.5
Total 1032 745 72.2

7.1.2.2 Serials:

There was no suitable Australian list to check, but checking the core journals in the disciplines indicated strong journal collections in each area. This must be set against the perceptions of the academic staff that the journals collection is missing major titles, that backruns for newly acquired titles are necessary, and that many titles have recently been cancelled. One problem with using MR is the American bias in terminology. Americans commonly use the term "mathematics" to mean "pure mathematics", whereas the interests of the Department of Mathematics are equally divided between pure and applied mathematics. A strike rate of 50% from MR is relevant only for pure mathematics.



Table 2: Serials

 
	 
Title No. checked No. held %
CIS 100 70 70
Jagus. 50 42 84
Liang 344 214 61.3
Malinowsky 59 41 69.5
MR 1667 841 504
Stankus 27 24 88.8
Total 2247 1232 54.8

8. Shelf Scanning

A shelf scan was undertaken concurrently with list checking. This took 18 hours. Libraries on campus holding items in the relevant DDC numbers were examined. This provided a valuable overview of the monograph coverage particularly. As mentioned previously, holdings are scattered throughout a number of libraries.

9. Evaluation by Experts

Detailed and lengthy discussions were held with a number of academic staff members from the School and the Maths Librarian. These staff members assisted the Conspectus Officer to assign levels to worksheets and provided advice on areas which need to be built up to support fields of teaching and research. They reinforced the knowledge that use of the literature cannot be judged solely by borrowing statistics, and further demonstrated that inhouse use is impossible to ascertain within the discipline. The expressed fear was that lack of such statistical evidence may lead to uninformed weeding by library staff and a disregard of the need for duplicate copies to be retained. Assurances were given that weeding would not occur without the involvement and agreement of the academic staff.

10. Assessment of the Collections

10.1 Dictionaries and encyclopaedias

The collection of dictionaries and encyclopaedias is considered comprehensive, a level 4 collection. All major items are held and are up to date.(Eighty per cent of titles checked against Hurt, and 75% checked against Malinowsky.)

One concern is that these items are not always located in the Maths Library; for example, the Encyclopedia of Mathematics, subscribed to by Physics and held in the Physics Research Library.

10.2 Monographs

The total collection of monographs in the division is approximately 30,000. In newly developing areas, such as chaos theory and fractals, the study presented in Mount (1989) indicates that the collection is maintaining at least a level 3b standard; however, this research area falls outside the Conspectus Dewey numbers for Mathematical Sciences. Considerable dissatisfaction was expressed by the academic staff concerning the poor quality of the collection in most areas, including areas where the Department undertakes research. While most publishers have named series for their mathematics publications, not all these series have standing orders placed for them. There remains a considerable number of titles purchased individually. By default, therefore, a considerable number of titles are not purchased. Visitors to the Department comment on "holes" they perceive in the collections. These span the years 1920-1990 and are the result of financial constraints. The introduction by Springer and Wiley of classics reprint series will ameliorate this problem if sufficient funds are provided and care is taken to identify and acquire missing titles. SIAM classics in applied mathematics, and reprints published by Dover and Chelsea should also be considered for standing orders.

The overall level of the collection is 3aE.

10.3 Serials

The serials collection includes most major works, eg. 67 out of 100 titles of core journals in CIS, and 24 out of 27 titles used in a study by Stankus of multispeciality mathematics journals. A number of these titles, however, are recently placed subscriptions. Cancellation of journals has been necessitated by lack of funds. One example is Zentralblatt, one of the two major review journals. Cancellation of journals previously subscribed to, which have now been renewed, has left gaps in the runs which should be filled. Subscriptions for recently established journal titles do not always start from volume 1; funds need to be provided to supply backruns of these titles.

10.4 Indexing and abstracting services

The University of Melbourne Library holds or provides access to the major indexes and abstracts in the discipline in print and/or electronic format. The electronic formats are available as CD-ROMs and/or online, through commercial vendors or through AARNet/Internet.

  • These include
  • The February/March 1995 issue of Database reports a study comparing coverage of mathematics in current awareness databases, which included Current Contents and UnCover. The results concluded that UnCover provided more comprehensive and current coverage of titles than any of the others. This being the case, there appears to be a sound argument for concentrating upon the provision of, and training in use of, CARL's UnCover as a current awareness and indexing tool.

    10.5 World Wide Web Sites

    Many academics and graduate students make use of the information available through the world wide web. The following sites are examples of the diverse sources available for research:

    These sites and the information they contain cannot yet be seen as substitutes for the more traditional print, microform and electronic sources, but as supplementing them. Concerns are regularly expressed by academic staff about the need for careful monitoring of technological changes in information dissemination.

    10.6 Electronic Journals

    The following are examples of refereed electronic journals available in the areas of mathematics and statistics:

    10.7 Mathematical Sciences E-Prints

    11. Areas of Research Strength

    11.1 History of Mathematics

    11.2 Chaos and Fractals

    Note: Chaos and Fractals falls outside of the Mathematical Sciences Conspectus numbers.

    11.3 Group Theory

    11.4 Graph Theory

    11.5 Statistical Mechanics

    Note: Statistical Mechanics falls outside of the Mathematical Sciences Conspectus numbers.

    12. Areas Needing to be Enriched

    The collections are not adequate to meet the research needs of the Department. They need strengthening in most research areas with an increased volume of monographs and many new titles of journals, including backruns to 1970s.

    The following areas are given as examples of research areas needing strengthening.

    12.1 Operations Research

    Many titles are held only in the McLennan Library of the Melbourne Business School and are inaccessible to undergraduate students. These titles need to be held on campus, preferably in the Mathematical Sciences Branch Library.

    Note:Operations Research falls outside of the Mathematical Sciences Conspectus numbers.

    12.2 Topology

    This is a level 3b collection, but requires further strengthening.

    12.3 Simulated Annealing

    This is a newly developing research area, where there are as yet no specialist journals. Articles of interest in this area are found in journals such as those on Operations Research and Algorithms.

    Acknowledgments

    Thanks are gratefully offered to the many people who gave freely of their time and advice. The academic staff generously gave much thought and time to assist me to build a picture of the current collections and the needs that they are required to meet. Their support has been invaluable. I thank particularly Alan Burns, Juliet Flesch, Elisabeth Garran, Graeme Murphy, Judith Purser and Merete Smith from the Library, for their support and assistance.

    Last modified: August 18 2004.