A Mathematical Journey to Relativity: Deriving Special and General Relativity with Basic Mathematics
暫譯: 相對論的數學之旅：用基礎數學推導特殊與一般相對論

這本教科書的第二版包含超過100頁的新內容，包括四個新章節，以及對微分幾何概念及其應用的改進討論。這本教科書旨在提供特殊相對論和一般相對論的全面幾何描述，從基本的歐幾里得幾何開始，進而探討更高級的非歐幾里得幾何和微分幾何。讀者將學習到施瓦茨希爾德度量（Schwarzschild metric）、行星的相對論軌跡、光的偏折、黑洞，以及宇宙學解決方案，如德西特（de Sitter）、弗里德曼-勒梅特-羅伯遜-沃克（Friedman-Lemaître-Robertson-Walker）和哥德爾（Gödel）解，並探討它們對觀察到的物理世界的影響。此外，本書提供逐步解決問題和練習的解答，使其成為本科生和希望更好理解特殊相對論和一般相對論的讀者的理想入門書。在這個新版本中，報導了關於度量-仿射重力理論和一般相對論等效表述的廣泛討論。其目的是呈現一些對於從高級角度研究一般相對論的博士生和研究人員可能有用的主題。

Wladimir-Georges Boskoff graduated from the Faculty of Mathematics, University of Bucharest in 1982 and completed his Ph.D. at the same university in 1994. Since 1990 he has been a member of the Department of Mathematics at the Ovidius university, teaching courses on various subjects, including Euclidean and non-Euclidean geometry, differential geometry, calculus on manifolds, mechanics and relativity, astronomy, and other subjects. His scientific papers and books relate to the foundations of geometry, Euclidean and hyperbolic geometry, metric geometry, differential geometry, modified theories of gravity, general relativity, and the history of mathematics. He has been an invited speaker at conferences in France, Japan, the USA, Greece, Italy, and Chile. He is a recipient of the Academy of Sciences of Romania's G. Tzitzeica Prize for contributions to geometry (1996), and the Romanian Mathematical Society Medal for contributions at mathematical education (2010).

Salvatore Capozziello is Full Professor of Astronomy and Astrophysics at the Department of Physics at the Università di Napoli "Federico II" where he teaches General Relativity and Cosmology. He is visiting Professor at the Gran Sasso Science Institute (L'Aquila, Italy), Honorary Professor at the Tomsk State Pedagogical University (Tomsk, Russia), Member of the Lepage Research Institute (Presov, Slovakia) and Foreign Member of the Serbian Academy of Non-linear Sciences (Belgrade, Serbia). He is the Coordinator of the PhD in Cosmology, Space Science & Space Technology (SPACE) at the Scuola Superiore Meridionale, Napoli. He is the Managing Editor of the International Journal of Geometric Methods in Modern Physics (World Scientific). He also holds research appointments at Istituto Nazionale di Fisica Nucleare (INFN), Istituto Nazionale di Astrofisica (INAF), and Gruppo Nazionale di Fisica Matematica (GNFM-INDAM). From 2012 to 2018, he was President of the Italian Society for General Relativity and Gravitation (SIGRAV). He spent periods of his scientific career in Germany, Poland, UK, Mexico, USA, South Africa, Canada, France, and Japan. His research focuses on general relativity, cosmology, relativistic astrophysics, and physics of gravitation in their theoretical and phenomenological aspects, in particular extended theories of gravity and their cosmological and astrophysical applications. His main scientific achievements have been the introduction of the concept of the curvature quintessence to explain the cosmological dark energy and the use of Noether symmetries as selection rules for observable universes. In November 2023, he received the Yang-Hui Award by the ICMAACS, University of Shanghai, China. He is the author of more than 650 refereed papers and 9 books. He is listed as one of the Top Italian Scientists.

**Wladimir-Georges Boskoff** 於1982年畢業於布加勒斯特大學數學系，並於1994年在同一所大學完成博士學位。自1990年以來，他一直是奧維迪烏斯大學數學系的成員，教授各種課程，包括歐幾里得幾何和非歐幾里得幾何、微分幾何、流形上的微積分、力學和相對論、天文學及其他主題。他的科學論文和書籍涉及幾何的基礎、歐幾里得幾何和雙曲幾何、度量幾何、微分幾何、修正的引力理論、廣義相對論以及數學史。他曾在法國、日本、美國、希臘、義大利和智利的會議上擔任邀請演講者。他是羅馬尼亞科學院G. Tzitzeica獎的獲得者，以表彰他對幾何的貢獻（1996年），以及羅馬尼亞數學學會的獎章，以表彰他在數學教育方面的貢獻（2010年）。

**Salvatore Capozziello** 是那不勒斯「費德里科二世」大學物理系的天文學和天體物理學全職教授，教授廣義相對論和宇宙學。他是意大利拉奎拉的Gran Sasso科學研究所的訪問教授，俄羅斯托木斯克國立教育大學的榮譽教授，斯洛伐克Presov的Lepage研究所成員，以及塞爾維亞貝爾格萊德的非線性科學學院外籍成員。他是那不勒斯南方高等學校宇宙學、空間科學與空間技術（SPACE）博士課程的協調員。他是《現代物理中的幾何方法國際期刊》（World Scientific）的主編。他還在國家核物理研究所（INFN）、國家天體物理研究所（INAF）和國家數學物理小組（GNFM-INDAM）擔任研究職位。從2012年到2018年，他是意大利廣義相對論與引力學會（SIGRAV）的會長。他的科學職業生涯曾在德國、波蘭、英國、墨西哥、美國、南非、加拿大、法國和日本度過。他的研究重點是廣義相對論、宇宙學、相對論天體物理學以及引力物理的理論和現象學方面，特別是擴展的引力理論及其宇宙學和天體物理應用。他的主要科學成就包括引入曲率本質的概念以解釋宇宙學的暗能量，以及使用Noether對稱作為可觀測宇宙的選擇規則。2023年11月，他獲得了中國上海大學ICMAACS頒發的楊輝獎。他是650多篇經審核的論文和9本書的作者，並被列為頂尖意大利科學家之一。