African Math

Lists the numerals in Amashi, the language of the Abashi (Kivu, Congo / Zaire) and discusses grammatical aspects. H. Burssens, Arithmétique, in: Les peuplades de l’Entre Congo-Ubangi (Ngbandi, Ngbaka, Mbandja, Ngombe et Gens d’Eau), International African Institute, London, 1958, 171-172 Presents brief information on the numeration systems among the Ngbandi, Ngbaka [7=6+1; 9=5+4], Mbandja [7=6+1; 9=8+1] and Ngombe (Congo / Zaire) L. Bynon-Polak, L’expression des ordinaux dans les langues bantoues [The expression of ordinal numbers in the Bantu languages], Africana Linguistica II, Annales du Musée Royal de l’Afrique Centrale, Sciences Humaines, Tervuren (Belgium), 1967, #55, 127-160 Comparative linguistic study of the construction of the words for ordinal numbers in Bantu languages. Includes maps on the geographical distribution of the four basic methods of construction analysed by the author. Jean-Pierre Caprile, Adoum Khamis & Ndjerassem Ngabot : Pour une terminologie de l’enseignement du calcul dans les langues africaines : la structure d’expression des nombres et des techniques opératoires dans deux langues “sara” du sud du Tchad, le “ngambay” et le “mango” [Towards a terminology for the teaching of arithmetic in African languages], Bulletin de l’AELIA (Association d’études linguistiques interculturelles africaines), 1983, 6, 273-287 Discusses the expressions used for numbers and operations in two “sara” languages from Chad : “ngambay” and “mango”. Jean-Pierre Caprile : Numérations orales et enseignement des mathématiques en Afrique [Oral numeration and the teaching of mathematics in Africa], LENGAS, revue de sociolinguistique, Montpellier (France), 1987, no. 21, 143-162 Paper presented at a session organised by the African Bureau of Educational Sciences in Kisangani (Congo / Zaire) in December 1984. It gives some information on systems of numeration in Africa (Sara-ngambay in Chad; Birom in Nigeria; Banda in Central-Africa) and outside Africa. Chantal Collard, Les “noms-numéros” chez les Guidar [The “names- numbers” among the Guidar], L’Homme, revue française d’anthropologie, 1973, Vol. XIII(3), 45-59 Analyses the way the Guidar in North-Cameroon give names to their children. The first name indicates the order in which the mother gave birth (and also the sex in the case of the first four children); the second name is the name-number of the father of the child. E.g. the first of an individual called Tizi Dawaï expresses that he is a boy and the first child of his mother; his surname indicates that his father is the seventh child of his respective mother. 9 Sylvie Fainzang, Les sexes et leur nombres - Sens et fonction du 3 et du 4 dans une societé burkinabé [The sexes and their numbers. The meaning and function of 3 and 4 in a Burkinabe society], L’Homme, revue française d’anthropologie, 1985, Vol. 96, 97-109 “The author analyzes in sociological terms the widespread West-African tendency to associate the numbers 3 and 4 with man and woman respectively, practice usually attributed to certain aspects of male and female anatomy. An analysis of Bisa society (Burkina Faso) shows how the meaning and function of this symbolism are directly related to representations of the person on the one hand, and to social space as defined by residence rules on the other. The author suggests that the discourse implied by this symbolism serves to found social relations between the sexes and to legitimate male domination”. (109) Solange de Ganay, Graphie bambara des nombres [Bambara graphical representation of numbers], Journal de la société des africanistes, 1950, 20(2) : 295-305 Describes and displays graphical signs used by Bambara (Mali) to represent numbers. P. Garnier, Les noms de nombre en bambara [The number words in Bambara], Notes africaines, 1954, 62, p. 50 Short comment on the words in Bambara (Mali) for 7, 9 (related to the duration of a pregnancy), 20 (related to the word for human being), and 40 (related to the word for mat). As 7 is a secret number, the author does not know an expression for it other than the indirect ‘wuoron-fla’, that is, the ‘second six’. Carlos Gonzalez Echegaray, Los sistemas de numeración y los numerales en los pueblos de la Guinea Española [The number systems and numerals among the peoples of Spanish Guinea (Equatorial Guinea)], Archivos del Instituto de Estudios Africanos, IV, 12, 1950, 19-29 Describes counting methods using fingers, knots, pebbles, etc., and number words (mostly decimal, some with auxiliary base five). Marcel Griaule, Numération secrète [Secret numeration], in: Jeux Dogon, Institut d’Ethnologie, Paris, 1938, p. 222 In his book on children’s games of the Dogon in Mali, Griaule presents two examples of a secret numeration (one to ten) used (and invented ?) by the children of the Pamyon and Guinna neighborhoods and often not understood by children from other neighbourhoods. Karl Laman, Arithmetic, in: The Kongo, Upsala: Studia Ethnographica Upsaliensia, Vol. IV, 1968, 8-9 Describes briefly counting and measuring among the Sundi. Accounts are kept by means of stones, palm nuts, knots, tally sticks, etc. In games the score may be kept by putting aside certain objects, by tying knots in a string, or by chanting a jingle (examples are given). 10 Lucien Lévy-Bruhl, La numération chez les Bergdama, Africa, Journal of the International Institute of African Languages and Cultures, 1929, Vol. II, No. 2, 162-173 Compares aspects of (finger) counting of the Bergdama (Berg Damara) of South Africa and Namibia with the (verbal) counting of their neighbours, the Nama. Guy Nicolas, Un système numérique symbolique : le quatre, le trois et le sept dans la cosmologie d’une société hausa (vallée de Maradi) [A symbolic numerical system : four, three and seven in the cosmology of a Hausa society (Maradi valley)], Cahiers d’études africaines, Paris, 1968, VIII(3), 566-616 The numbers four (hudu), three (uku) and seven (bakwai) play an important role in ritual, economic and social life among the Hausa in the Maradi valley (Niger). This role is described, analysed and discussed. H. Sawyer & S. K. Todd, The significance of the numbers 3 and 4 among the Mende of Sierra Leone, Sierra Leone Studies : A Journal of the Arts and Sciences, 1970, 26, 29-36 Discusses “the significance and incidence of the use of the figure three to symbolise female activity, and of the figure four to symbolise male participation among the Mende” (p. 30). Leo Stappers, Het hoofdtelwoord in de Bantoe-talen [The cardinal number in the Bantu languages], Africana Linguistica II, Annales du Musée Royal de l’Afrique Centrale, Sciences Humaines, Tervuren (Belgium), 1967, #55, 175-198 Compares the prefixes used in the Bantu languages in connection with the cardinal numbers one to five. The paper analyses also ‘abstract’ counting (i.e. without reference to the objects), and ‘distributive’ (‘two by two’, ...) and ‘multiplicative’ use of cardinals in the Bantu languages. Maps with information on the geographical distribution are included. Placidus Tempels, De tel-gebaren der Bashila [The number-gestures of the Bashila], Congo-Overzee, 1938, IV. 2, 49-53 Describes the number-gestures among the (Ba)Shila in Congo / Zaire. There are two series, one for counting from 1 to 10, and one for indicating individually numbers (cardinal numbers). Toussaint-Yaovi Tchitchi: Numérations traditionnelles et aritmétique moderne, in: Hountondji, Paulin (Ed.), Les savoirs endogènes: pistes pour une recherche, CODESRIA, Dakar (Senegal), 1994, 109-138 Discusses traditional numeration in “àjá” (Benin) and possibilities of and experimentation with a decimalisation (to be continued) 11 5. HAVE YOU READ? 5.1 On the History of Mathematics in Africa #278 Høyrup, Jens : Hero, Ps.-Hero, and Near Eastern practical geometry. An investigation of Metrica, Geometrica, and other treatises, Antike Naturwissenschaft und ihre Rezeption, Trier (Germany), Vol. 7, 1997, 67-93 [a pre-print was published by Roskilde University Centre - Section for Philosophy and Science Studies, Roskilde (Denmark) in 1996] The author intends to “firstly, that Hero’s geometry depends to a greater extent than usually assumed on Near Eastern practical geometry or its descendant traditions in the classical world, and that the conventional image [of Hero] as the transformer of theoretical into applied mathematics is only a half-truth; secondly, that much of what is shared by Hero’s Metrica and the pseudo-Heronian collections assembled by Heiberg as Geometrica are shared borrowings from the same tradition... ” (p. 67). 5.2 Publications on the History of Mathematics, Ethnomathematics and Mathematics Education #279 Gerdes, Paulus: Geometry from Africa : Mathematical and educational explorations, The Mathematical Association of America [Classroom Resource Materials Series], Washington DC, 1999, xii + 210 pp. [Foreword by Arthur B. Powell] (ISBN 0-88385-715-4) Presents geometrical ideas from Africa south of the Sahara, with suggestions how they can be explored both mathematically and in mathematics education (secondary school, teacher education, university). The book is organised in the following parts: Preface (Geometrical and educational explorations inspired by African cultural activities); Part 1: On geometrical ideas in Africa south of the Sahara [overview, pp.2-53]; Part 2: From African designs to discovering the Pythagorean Theorem [pp.54-87]; Part 3: Geometrical ideas in crafts and possibilities for their educational exploration [Explores ideas from house building, wall decoration, mat and basket weaving, pp.88-155]; Part 4: The ‘sona’ sand drawing tradition and possibilities for its educational use [pp.156-204]. #280 Gerdes, Paulus: On some Geometrical and Architectural Ideas from African Art and Craft, in: Kim Williams (Ed.), Nexus II: Architecture and Mathematics, Editora Dell’Erba, Fucecchio (Italy), 1998, 75-86 (cf. # 272) Presents some examples of geometrical ideas in traditional African building, as well as some further suggestions for architectural shapes inspired by African art and craft. 12 #281 Houndonougbo, Victor: Processus stochastique du Fâ: une approche mathématique de la géomancie des côtes du Bénin, in: Hountondji, Paulin (Ed.), Les savoirs endogènes: pistes pour une recherche, CODESRIA, Dakar (Senegal), 1994, 139-157 Analyses Fâ divination practices in the coastal zones of Benin from a mathematical point of view (theory of probability). #282 Olivier, Alwyn & Karen Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, Cape Town (South Africa), 1998, 4 volumes. The proceedings contain the following contributions and abstracts which may interest the readers of the AMUCHMA-Newsletter : * Draisma, Jan (Mozambique): On verbal addition and subtraction in Mozambican Bantu languages, Vol. 2, 272-279; * Mosimege, Mogege David (South Africa): Culture, games and mathematics education : An exploration based on string figures, Vol. 3, 279-286; * Mogari, David (South Africa) : Some geometrical constructs and pupil’s construction of miniature wire toy cars, Vol. 4, 284; * Soares, Daniel (Mozambique) : On the geometry involved in the building of traditional houses with rectangular base in Mozambique, Vol. 4, 307; * Mucavele, João (Mozambique): The mathakuzana game as a didactical resource for the development of number sense and oral arithmetic. #283 Zaslavsky, Claudia, Africa Counts : Number and Pattern in African Cultures, Third edition, Lawrence Hill, 1999, 368 pp. [ISBN 1-55652-350-5] Reprint of Claudia Zaslavsky’s classical study, updated with an additional chapter on ethnomathematics in Africa (cf. #20, 199). 5.3 Other publications on the History of Mathematics by African mathematicians #284 Djebbar, Ahmed : La jolle histoire de l’algèbre, in: Science et Vie Junior Special Math, Paris, December 1998 - February 1999, 34-47 #285 Boudine, Jean-Pierre et Djebbar, Ahmed : Omar Khayyam, le poète des maths, in: Science et Vie Junior Special Math, Paris, December 1998 - February 1999, 42-43 Special issue of the popular journal “Science and Life - Junior” on the history of algebra. 5.4 Publications on the History of Mathematics and the African Diaspora None were reported. 13 6. ANNOUNCEMENTS * 5th Pan African Congress of Mathematicians (PACOM’2000) The 5th Pan African Congress of Mathematicians (PACOM’2000) will take place at the University of the Western Cape (UWC), Cape Town, South Africa, from 24 to 31 January 2000. The general theme of the congress is “Africa in the World Mathematical Year 2000 : Assessment and promotion of mathematical education and research at the dawn of the 3rd millennium”. A special effort will be made by the AMU for supporting some deserving young African mathematicians. Interested mathematicians are requested to send their CV with the title and abstract of their communication to the President of the AMU, Prof. A. Kerkour, and a copy to the secretary-general of AMU, Prof. D. Sangaré. The General Assembly of the African Mathematical Union (AMU) will be held at the same place on January 23. For more information on the programme of PACOM’2000, contact the Chairman of the Local Organising Committee : Prof. Jan Persens, Director of International Relations, University of the Western Cape, Private Bag X17, Bellville, 7535 South Africa (Tel: +27-21-959-2884/3340; Fax: +27-21-9592655; E-mail: jpersens@uwc.ac.za) Mogege Mosimege and Paulus Gerdes will coordinate the session on mathematics and culture / ethnomathematics / history of mathematics in Africa. If you like to presen a paper in this session, please contact with the coordinators. * 10th Pan African Mathematics Olympiad (PAMO) The 10th Pan African Mathematics Olympiad will take place at the University of Cape Town (UCT), Cape Town, South Africa from January 17 to 24, 2000, that is in the week preceding PACOM’2000. For more information, contact the Chairperson of the AMU Commission on Mathematical Olympiads : Prof. Nouzha El Yacoubi, Department of Mathematics and Informatics, Faculty of Science, P. O. Box 1014, Rabat, Morocco [Fax : +212 7 77 30 44; E-mail : elyac-sb@fsr.ac.ma] or the convener, Local Organising Committee : Prof. John Webb., Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, South Africa [Fax : +27 21 686 0476; E-mail : jhwebb@maths.uct.ac.za] 14 * Proceedings of the 3rd and 5th Maghrebian Colloquia on the History of Arabic Mathematics The Proceedings of the 3rd and 5th Maghrebian Colloquia on the History of Arabic Mathematics have been published. Detailed information on the contents will be given in issue 23 of the AMUCHMA-Newsletter : * Actes du 3e Colloque maghrebin sur l’histoire des mathématiques arabes, Alger, 1-3 Decembre 1990, Office des Publications Universitaires, Alger, 1998, 280 pp.; * Actes du 5e Colloque maghrebin sur l’histoire des mathématiques arabes, Hammamet, 1-3 Decembre 1994, A.T.S.M. / Impression IMPAK, Tunis, 1998, 357 pp. * XXIst International Congress of History of Science (ICHS) The XXIst International Congress of History of Science will take place in Mexico City from the 8th to the 14th of July, 2001. The general topic for this congress is “Science and Cultural Diversity”. “A limited number of grants will be available for participants from selected regions in order to assure the more possible participation of researchers from all parts of the world”. For further information, please contact: Prof. Juan José Saldaña, Chairman of the Organizing Committee of the XXIst ICHS, Apartado Postal 21-873, C.P. 04000 México, D.F., Mexico (e-mail : xxiichs@servidor.unam.mx), or visit the web-site of the International Union of History and Philosophy of Science / Division of History of Science (IUHPS/DHS): www.cilea.it/history/DHS * New international journal “Board Games Studies” “Board Games Studies is an academic journal for historical and systematic research on board games, Its object is to provide a forum for board games research from all academic disciplines in order to further the understanding of the development and distribution of board games within an interdisciplinary academic context. Articles are accepted in English, French, and German”. The journal is published by the Research School CNWS, Leiden University, Netherlands. For more information, contact the managing editor Alex de Voogt. The first issue (1998) contains a review (pp. 112-113) by Philip Townshend of the book by Elisio Silva on mancala type games from Angola (cf. AMUCHMA 18: #217). On p. 67, appear the following references to papers by Philip Townshend on board games in Africa: * Autour du jeu de Mankala, Zaire-Afrique, 105: 287-297, 1976; * Les jeux de Makala du Zaire, du Rwanda et du Burundi, Cahiers du CEDAF, Brussels, 3: 1-76, 1977; * Mankala Games, Bulletin of the International Committee on Urgent Anthropological and Ethnological Research, 19: 47-54, 1977; 15 * The South West African game of Illhus in the wider context of African Mankala, Journal of the South West African Scientific Society, 31: 85-98, 1977; * Mankala in Eastern and Southern Africa: a Distributional Analysis, Azania, 14: 108-138, 1979; * Bao (Mankala): The Swahili Ethic in African Idiom, Paideuma, 28: 175-191, 1982; * Games in Culture: A Contextual Analysis of the Swahili Board Game and its relevance to Variation in African Mankala, Ph.D. thesis, University of Cambridge, 1986. The following references to publications by Richard Pankhurst are presented on page 67: * Gabata and related Board-games of Ethiopia and the Horn of Africa, Ethiopia Observer, 14(3): 154-206, 1971; * Gabata and other Board-Games of Ethiopia and the Horn of Africa, Azania, 17: 27-41, 1982. The managing editor, Alex de Voogt, published two books on mancala board games : * Limits of the mind : towards a characterisation of Bao mastership, Research School CNWS, Leiden (Netherlands), 1995, 169 p. Ph. D. thesis in which the Bao game as played on the island Zanzibar (Tanzania) is analysed (cf. # 276); * Mancala board games, British Museum Press, London, 1997, 80 p. The book looks briefly at the social and cultural context of the game, but focuses mainly on the boards themselves. It also contains a catalogue of the 105 boards (many from Africa) in the British Museum’s collection. 7. ADDRESSES OF SCHOLARS, INSTITUTIONS AND PUBLISHERS MENTIONED IN THIS NEWSLETTER * Blyden, Eluemuno R. : President, Genetic Designs, Maine, USA [E-mail: eblyden@khepera.com] * CODESRIA (Council for the Development of Social Science Research in Africa) : B.P. 3304, Dakar, Senegal (Fax : +221-241289; E-mail : codesria@sonatel.senet.net) * Draisma, Jan : Departamento de Matemática, Universidade Pedagógica, C.P.2025, Beira, Mozambique (E-mail : draisma@upb.uem.mz, draisma@zebra.uem.mz) * Editora Dell’Erba : piazza Garibaldi 3, 50054 Fucecchio FI, Italy (Fax : +571-242093, E-mail : EdErba@leonet.it) * Folkerts, Menso : Institut für Geschichte der Naturwissenschaften der Univertsität München, Postfach, D-80306 München, Germany * Gnanvo, Cyprien : Département de Mathématiques, Faculté des Sciences et techniques, Université Nationale du Bénin, 04 BP 0440, Cotonou, Benin 16 * Houndonougbo, Victor: Directeur de l’Ecole normale intégrée de Parakou, Parakou, Benin * Hountondji, Paulin : Directeur, Centre Africain des Hautes Etudes, BP 1268, Cotonou, Benin (E-mail : hountond@syfed.bj.refer.org) * Høyrup, Jens : Institute of Communication Research, Educational Research and Theory of Science, Roskilde University, P.O.Box 260, DK-4000 Roskilde, Denmark (E-mail : jensh@frode.ruc.dk) * Kerkour, Ahmed : President of the AMU, Zankat Ait Rkha, Dar Yamina - Bir Kacem - Rabat, Morocco (E-mail : akerkour@mis.net.ma) * Mathematical Association of America, P.O.Box 91112, Washington, D.C. 20090-1112, USA (Tel: 1-800-331-1622, +301-617-7800; Fax: +301-206- 9789; Webpage: www.maa.org/books) * Mogari, David : Department of Mathematics and Science Education, University of Venda, Private Bag X5050, 0950 Thohoyandou, South Africa (E-mail : dmogari@caddy.univen.ac.za) * Mosimege, David Mogege: Manager Indigenous Technologies CSIR, Building 41, P.O.Box 395, Pretoria 0001, South Africa (E-mail: mmosimeg@csir.co.za) * Mucavele, João : Departamento de Matemática, Universidade Pedagógica, C.P.2025, Beira, Mozambique (E-mail : ....) * Persens, Jan: Director of International Relations, University of the Western Cape, Private Bag X17, Bellville, 7535 South Africa (Tel: +27-21-959- 2884/3340; Fax: +27-21-9592655; E-mail: jpersens@uwc.ac.za) * Powell, Arthur: Academic Foundations Department, Rutgers University, 175 University Avenue, Newark, New Jersey 07102, USA (Fax: 201- 648 5700; E-mail: abpowell@andromeda.rutgers.edu) * Samso, Julio : Dep. Arabe, Facultad Filologia, Universidad Barcelona, Gran Via 585, 08007 Barcelona, Spain * Sangare, Daouda : Secretary-General AMU, 1409 Quartier de la Grande delle, F-14200 Hérouville Saint Clair, France (Tel/Fax : +33 2 31 53 71 88; E-mail : daouda@math.unicaen.fr) * Seepe, Sipho : Department of Mathematics and Science Education, University of Venda, Private bag X5050, Thohoyandou 0950, South Africa * Soares, Daniel : Departamento de Matemática, Universidade Pedagógica, C.P.2025, Beira, Mozambique (E-mail : upbeira@lemep.uem.mz) * Souissi, Mohamed : 7 Rue de Teheran, 2000 Le Bardo, Tunis, Tunisia * Tchitchi, Toussaint-Yaovi : Centre national de linguistique appliquée (CENALA), Université Nationale du Bénin, Cotonou, Benin * Voogt, Alex de: Board Games Studies, Onderzoekinstituut CNWS, Rijksuniversiteit leiden, Postbus 9515, NL-2300 RA Leiden (Fax: +31 3554 30697; E-mail: boardgames@iname.com) * Webb., John : Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, South Africa [Fax : +27 21 686 0476; E-mail : jhwebb@maths.uct.ac.za]17 * Yacoubi, Nouzha El : Department of Mathematics and Informatics, Faculty of Science, P. O. Box 1014, Rabat, Morocco [Fax : +212 7 77 30 44; E- mail : elyac-sb@fsr.ac.ma] * Zaslavsky, Claudia : 45 Fairview Av. #13-1, New York, NY 10040, USA 8. SUGGESTIONS What are your suggestions for improving the AMUCHMA Newsletter? What are your suggestions for other activities of AMUCHMA? Send your suggestions, comments, information, questions and any other contributions to the chairman or secretary of AMUCHMA. Send articles, books and manuscripts for the AMUCHMA Documentation Centre to the Chairman or Secretary. 9. DO YOU WANT TO RECEIVE THE NEXT AMUCHMA- NEWSLETTER? The AMUCHMA Newsletter, published in Arabic, English and French, is available free of charge upon request. Send requests to the Chairman Paulus Gerdes: Universidade Pedagógica, C.P. 915, Maputo, Mozambique (Fax: 258-1-422113; E-mail: pgerdes@virconn.com) for the English version; or to the Secretary Ahmed Djebbar: Département de Mathématiques, Bâtiment 425, Université de Paris-Sud, 91405 Orsay Cedex, France (Fax: 33-1- 47015917; E-mail: Ahmed.Djebbar@wanadoo.fr) for the French and Arabic versions. Readers who would like to receive the AMUCHMA Journal in Portuguese should contact the chairman, C.P. 915, Maputo, Mozambique. 10. AMUCHMA-NEWSLETTER website Thanks to Scott Williams, the English language edition of all issues of the AMUCHMA Newsletter is also accessible on the following website: http://www.math.buffalo.edu/mad/amuchma_online.html The English version of AMUCHMA 22 is reproduced and distributed 17 * Yacoubi, Nouzha El : Department of Mathematics and Informatics, Faculty of Science, P. O. Box 1014, Rabat, Morocco [Fax : +212 7 77 30 44; E- mail : elyac-sb@fsr.ac.ma] * Zaslavsky, Claudia : 45 Fairview Av. #13-1, New York, NY 10040, USA 8. SUGGESTIONS What are your suggestions for improving the AMUCHMA Newsletter? What are your suggestions for other activities of AMUCHMA? Send your suggestions, comments, information, questions and any other contributions to the chairman or secretary of AMUCHMA. Send articles, books and manuscripts for the AMUCHMA Documentation Centre to the Chairman or Secretary. 9. DO YOU WANT TO RECEIVE THE NEXT AMUCHMA- NEWSLETTER? The AMUCHMA Newsletter, published in Arabic, English and French, is available free of charge upon request. Send requests to the Chairman Paulus Gerdes: Universidade Pedagógica, C.P. 915, Maputo, Mozambique (Fax: 258-1-422113; E-mail: pgerdes@virconn.com) for the English version; or to the Secretary Ahmed Djebbar: Département de Mathématiques, Bâtiment 425, Université de Paris-Sud, 91405 Orsay Cedex, France (Fax: 33-1- 47015917; E-mail: Ahmed.Djebbar@wanadoo.fr) for the French and Arabic versions. Readers who would like to receive the AMUCHMA Journal in Portuguese should contact the chairman, C.P. 915, Maputo, Mozambique. 10. AMUCHMA-NEWSLETTER website Thanks to Scott Williams, the English language edition of all issues of the AMUCHMA Newsletter is also accessible on the following website: http://www.math.buffalo.edu/mad/amuchma_online.html The English version of AMUCHMA 22 is reproduced and distributed with financial support from SIDA-SAREC (Sweden)