Mathematics for Social Sciences and Arts: Algebraic Modeling

本書探討了當代數學尤其是代數與社會科學和藝術應用之間的相互關聯。它提倡知識不能僅停留在學科的範疇中，而是屬於所有人，並致力於數學應用的各種聯想關係，從社會學到語言學，包括人類學、符號學、教育和認知科學。本書的貢獻闡明了代數在社會科學和人文學科中的發展、學習、理解、傳播和應用的一些方式。

本書的內容源於2021年5月24日至26日由塞爾維亞尼什大學機械工程學院主辦的虛擬會議「社會科學和藝術的數學-代數建模」。該會議匯集了來自不同學科和地理區域的學者，重點關注代數與社會科學應用的並置。會議組織者是來自四個不同大陸的高等教育機構，他們邀請了社會科學和代數領域的領先科學家為本書做出貢獻。

本書的第一部分探討了代數和數學思維，特別是從認知科學的角度學習和實踐數學，以及對教育和符號學等與人類關切相關的應用。第二部分則聚焦於代數半群及其一些延伸。本書及其所衍生的會議提供了一個成功合作的例子，其中來自不同國家和大陸的作者們帶來了代數結構、建模、社會科學和藝術方面的專業知識和深度，並以和諧的方式融合在一起。這些論述是一個豐富的資源，對數學家和非數學家都具有興趣。

Mahouton Norbert Hounkonnou is a Full Professor at the University of Abomey-Calavi, Benin. His works deal with noncommutative and nonlinear mathematics, mathematical physics and complexity. He was a member of UNESCO Scientific Council for International Basic Sciences Programme and member of the InterAcademy Partnership (IAP) working group on Harnessing Science, Engineering and Medicine to Address Africa's Challenges. He is also a member of several academies, including the Academy of Science of South Africa, Hassan II Academy of Science and Technology, Morocco, African Academy of Sciences, The World Academy of Sciences. He is the co- chair of the Network of African, European and Mediterranean Academies for Science Education, President of the Network of African Science Academies and former President of Benin National Academy of Sciences, Arts and Letters. He is member of the IAP Science Education Global Council, and representative for Africa of the International Mathematical Union (IMU) Commission for Developing Countries (CDC). He was awarded several international prestigious Prizes, the last being the American Institute of Physics 2023 Tate Medal for his efforts to build and maintain an enduring transnational African mathematical physics research and education community.

Dr. Dragana Martinovic is Professor Emerita at Faculty of Education, University of Windsor. She is a Fellow of the Fields Institute for Research in Mathematical Sciences and a Co-Director of the Fields Centre for Mathematics Education. She is a founding and current Co-Editor of the Springer book series, Mathematics Education in the Digital Era. Dragana serves on the Editorial Boards for Brill'sStudies in Mathematics in the Arts and Humanities book series, Springer's Mathematics in Mind book series, and journals such as Participatory Educational Research (PER) and Semiotica. Dragana is also the Chair of the GeoGebra Institute of Canada/Institut de GeoGebra du Canada (GIC-IGC). Dragana has co-chaired various national and international conferences. In her research, Dragana explores knowledge for teaching mathematics, ways in which technology can assist in teaching and learning of mathematics, and epistemologies of Science, Mathematics, Engineering, and Mathematics (STEM) in relation to teacher and K-12 education. Dragana's research is funded by SSHRC, KNAER, the Fields Institute, and various Canadian government organizations. She has published edited books and books of conference proceedings and multiple book chapters, refereed journal papers, and research and technical reports.

Melanija Mitrovic is a Full Professor at the University of Nis, Serbia, having received her PhD degree at the same university. She works in the field of classical and constructive algebra. Her innovating work within the theory of constructive binary structures with apartness positions her among the pioneers of constructive mathematics in Serbia. She develops interdisciplinary research investigating applications of algebraic structures to problems in engineering space, social sciences and humanities. She is, also, the Head of the Center of Applied Mathematics of the Faculty of Mechanical Engineering Nis, CAM- FMEN (since 2019), a member of the Editorial Board of Mathematics in Mind, Springer; a member of the Fields Cognitive Science Network. She holds the status of Permanent Full Professor at the International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, Benin Republic. She has held visiting professor positions at Linköping University and Malardaren University, Sweden; Bar-Ilan University, Israel; TU Wien, Austria; UTAD and University of Minho, Portugal; and Politecnico di Milano, Italy. She is member of the Grant Selection Committee (GSC) of the International Mathematical Union (IMU) Commission for Developing Countries (CDC).

Philippa (Pip) Pattison is an Emeritus Professor at the University of Melbourne and University of Sydney, having retired in 2021 as Deputy Vice-Chancellor Education at the University of Sydney. Pip's research is focussed primarily on the development of mathematical and statistical models for social networks and network processes. Following early work on algebraic models for social networks, she developed in collaboration with others a hierarchy of statistical models for social networks that recognise the potential endogeneity of network processes and can reproduce a wide variety of their observed characteristics. She and her colleagues have extended these models to a variety of data structures and forms and have developed methods for estimating models from partial network data resulting from snowball sampling designs. These developments are now being widely applied across a number of social and behavioural science domains. Pip's work has attracted a number of awards, including the University of Melbourne Special Thesis Award in 1983, the Australian Psychological Society Early Career Award in 1988, and the Simmel Award of the International Network for Social Network Analysis in 2002. Pip was elected a Fellow of the Academy of Social Sciences in Australia in 1995 and became an Officer of the Order of Australia in 2015.

Mahouton Norbert Hounkonnou是貝南阿博梅-卡拉維大學的教授。他的研究涉及非交換和非線性數學、數學物理和複雜性。他曾是聯合國教科文組織國際基礎科學計劃科學委員會的成員，也是國際學術合作組織(IAP)解決非洲挑戰的科學、工程和醫學工作組的成員。他還是多個學術機構的成員，包括南非科學院、摩洛哥哈桑二世科學和技術學院、非洲科學院和世界科學院。他是非洲、歐洲和地中海學術院科學教育網絡的聯合主席，非洲科學院網絡主席，以及貝南國家科學、藝術和文學學院的前主席。他是IAP科學教育全球委員會的成員，也是國際數學聯盟(IMU)發展中國家委員會(CDC)在非洲的代表。他曾獲得多個國際知名獎項，最近一次是2023年美國物理學會頒發的泰特獎，以表彰他在建立和維護持久的跨國非洲數學物理研究和教育社群方面的努力。

Dragana Martinovic博士是溫莎大學教育學院的名譽教授。她是數學科學研究領域Fields研究所的研究員，也是Fields數學教育中心的聯合主任。她是Springer書籍系列《數學教育在數字時代》的創始人和現任共同編輯。Dragana還擔任Brill的《數學與藝術人文研究》書籍系列、Springer的《心智中的數學》書籍系列以及《參與式教育研究》和《符號學》等期刊的編輯委員會成員。Dragana還是加拿大GeoGebra學院的主席。她曾共同主持過多個國家和國際會議。在她的研究中，Dragana探討數學教學的知識，技術在數學教學和學習中的應用，以及科學、數學、工程和數學(STEM)的知識論與教師和K-12教育的關係。Dragana的研究由SSHRC、KNAER、Fields研究所和加拿大各個政府組織資助。她出版了編輯的書籍、會議論文集和多篇書籍章節、審查過的期刊論文以及研究和技術報告。

Melanija Mitrovic是塞爾維亞尼斯大學的教授，並在同一所大學獲得了博士學位。她從事古典和建構性代數領域的研究。她在建構性二元結構理論方面的創新工作使她成為塞爾維亞建構性數學的先驅之一。她開展了跨學科研究，探索代數結構在工程空間、社會科學和人文學科中的應用問題。她還是尼斯機械工程學院應用數學中心的負責人，也是Springer的《心智中的數學》編輯委員會成員，以及Fields認知科學網絡的成員。她在聯合國教科文組織數學物理和應用數學國際講座(ICMPA-UNESCO Chair)擁有永久全職教授的地位。她曾在瑞典林雪平大學、瑞典馬拉達倫大學、以色列巴伊蘭大學、奧地利維也納工業大學、葡萄牙UTAD和米尼奧大學以及意大利米蘭理工大學擔任訪問教授。她是國際數學聯盟(IMU)發展中國家委員會(CDC)的資助選擇委員會(GSC)成員。

Philippa (Pip) Pattison是溫莎大學的名譽教授。