I Wish They'd Taught Me That: Overlooked and Omitted Topics in Mathematics
暫譯: 我希望他們教過我：數學中被忽視和省略的主題

《我希望他們教我這些：數學中被忽視和省略的主題》關注的是每位本科數學學生「應該」知道但可能從未接觸過的主題。這些主題並不是每個課程大綱中都會佔據主導地位的內容，而是那些美麗、有用且易於接觸的壯麗秘密，但卻無法解釋地隱藏在主流課程之外。

本書的每一章都涉及一個學生幾乎肯定不熟悉的不同主題。以生動、對話的風格撰寫，讀者在每個部分結束時應該感到具備了進一步探索該領域的知識。

特色
- 涵蓋數學各個領域的主題，包括幾何、邏輯、分析、代數、數值分析和拓撲
- 許多範例、圖表和練習
- 資源集合，讓有興趣的讀者可以進一步了解每個主題
- 每章的非技術性介紹

Robin Pemantle grew up in Berkeley in the 1960's and 70's. You can probablyguess what that was like; then double that. He became interested in mathematics when he was very young. By age four, according to family lore, mathematics was his
career plan (to the chagrin of NASA and the local fire stations). Robin's PhD in probability theory got its start when Persi Diaconis, a mathematician and former magician, visited M.I.T. Robin was supposed to be working on a dissertation in combinatorics (a subject to which he later returned), but found himself working mostly on problems he heard from Persi. During a year off traveling in the South Pacific, he ended up working on probability theory in various youth hostels and on boats. Robin received his PhD in 1988, spent three years on post-doctoral fellowships in Berkeley, Ithaca and Oregon State, most of the 1990's at UW-Madison, three years at Ohio State, and has been at Penn since 2003. Robin's research focuses on two areas. Within Probability Theory, the research concerns discrete probability models, including random graph theory, processes with reinforcement, statistical models and random walks. The other research area, analytic combinatorics, is the subject of a textbook with Mark C. Wilson and Steve Melczer (2013, 2024). Robin has been interested in Mathematics Education from an early age, growing up with an insider's view of an alternative school, and teaching mathematics to grades 5-8 during his college years and before. Robin has written books and articles on mathematics education, most recently having published a book on K-12 education, with co-author Henri Picciotto, entitled, "There is No One Way to Teach Math."
(Routledge, 2024). In direct and indirect ways, Project SEED has played a big role in Robin's life as a math educator. Robin has held a Sloan Fellowship, a Presidential Faculty Fellowship, the Rollo Davidson Prize, and a Lilly Teaching Fellowship. He was a top five finisher in the Putnam Competition and is a Simons Fellow, a fellow of the American Mathematical Society and a fellow of the Institute for Mathematical Statistics. Most recently, he was inducted into the National Academy of Sciences as a member of the class of 2024.

Julian Gould grew up in the suburbs of Minneapolis, Minnesota. His father's advice was always, "Take math until you just can't take it anymore." The advice had a much larger impact on Julian's life than intended. Julian received his bachelor's and master's degrees from Johns Hopkins University, and is hopefully no longer a PhD candidate in mathematics at the University of Pennsylvania. He originally planned to study homotopy type theory, but his research took a turn toward applied algebraic topology and cellular sheaf theory. Before beginning his PhD, Julian worked as an associate quantitative analyst at T. Rowe Price in Baltimore. Julian's passion for teaching began during his freshman year at Johns Hopkins, tutoring the football team in economics. He has received multiple honors for his work in the classroom, including Penn's university-wide Dean's Award for Distinguished Teaching by Graduate Students. He serves as a Master TA in the Penn mathematics department and helps lead the annual training for first-time teaching assistants. His friendship with Robin began when he was a teaching assistant for Robin's introductory
calculus course for Wharton students. Julian has mentored seven undergraduate students through Penn's Directed Reading
Program on topics ranging from descriptive set theory and categorical computer science to financial mathematics, topological data analysis, and game-theoretic models of international relations. His experiences mentoring students helped motivate and inspire many aspects of this book. When he isn't doing math, Julian likes to write about philosophy, trade on prediction markets, and pick up heavy things.

羅賓·佩曼特（Robin Pemantle）在1960年代和70年代的伯克利長大。你大概可以猜到那是什麼樣的情況；然後再加倍。他在很小的時候就對數學產生了興趣。根據家族的傳說，四歲時數學已經是他的職業計劃（這讓NASA和當地的消防局感到不安）。羅賓的概率論博士學位始於數學家和前魔術師佩爾西·迪亞科尼斯（Persi Diaconis）訪問麻省理工學院（M.I.T.）時。羅賓原本應該在組合數學（他後來又回到這個主題）上撰寫論文，但他發現自己主要在解決佩爾西提出的問題。在南太平洋旅行的一年中，他在各種青年旅館和船上從事概率論的研究。羅賓於1988年獲得博士學位，之後在伯克利、伊薩卡和俄勒岡州的博士後研究中度過了三年，1990年代大部分時間在威斯康辛大學麥迪遜分校（UW-Madison），在俄亥俄州立大學待了三年，自2003年以來一直在賓夕法尼亞大學（Penn）。羅賓的研究集中在兩個領域。在概率論中，研究涉及離散概率模型，包括隨機圖論、增強過程、統計模型和隨機遊走。另一個研究領域，解析組合學，是他與馬克·C·威爾遜（Mark C. Wilson）和史蒂夫·梅爾策（Steve Melczer）共同編寫的教科書的主題（2013年，2024年）。羅賓從小就對數學教育感興趣，成長於一所替代學校的內部視角，並在大學期間及之前教授五到八年級的數學。羅賓撰寫了有關數學教育的書籍和文章，最近與合著者亨利·皮奇奧托（Henri Picciotto）共同出版了一本關於K-12教育的書，名為《沒有一種教數學的方法》（There is No One Way to Teach Math）（Routledge，2024年）。在直接和間接的方式上，SEED計劃在羅賓的數學教育者生涯中扮演了重要角色。羅賓曾獲得斯隆獎學金、總統教職獎學金、羅洛·戴維森獎（Rollo Davidson Prize）和莉莉教學獎學金。他在普特南競賽中名列前五，並且是西蒙斯獎學金得主、美國數學學會的會員以及數學統計學會的會員。最近，他被選為2024年國家科學院的成員。

朱利安·古爾德（Julian Gould）在明尼蘇達州的明尼阿波利斯郊區長大。他父親的建議總是：「學習數學，直到你再也無法忍受為止。」這個建議對朱利安的生活產生了比預期更大的影響。朱利安在約翰霍普金斯大學獲得了學士和碩士學位，並希望不再是賓夕法尼亞大學的數學博士候選人。他最初計劃研究同倫類型理論，但他的研究轉向了應用代數拓撲和細胞束理論。在開始攻讀博士學位之前，朱利安曾在巴爾的摩的T. Rowe Price擔任助理定量分析師。朱利安對教學的熱情始於他在約翰霍普金斯大學的第一年，當時他為足球隊輔導經濟學。他因在課堂上的工作獲得了多項榮譽，包括賓夕法尼亞大學全校範圍內的研究生傑出教學院長獎。他在賓夕法尼亞大學數學系擔任主教學助理，並協助領導首次教學助理的年度培訓。他與羅賓的友誼始於他擔任羅賓的沃頓學生入門微積分課程的教學助理。朱利安通過賓夕法尼亞大學的定向閱讀計劃指導了七名本科生，主題涵蓋描述集合論、範疇計算機科學、金融數學、拓撲數據分析和國際關係的博弈論模型。他指導學生的經驗激勵並啟發了本書的許多方面。當他不在做數學時，朱利安喜歡寫作哲學、在預測市場上交易和搬運重物。