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出版商:
Springer
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出版日期:
2026-06-28
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售價:
$1,900
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貴賓價:
9.5 折
$1,805
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語言:
英文
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頁數:
160
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裝訂:
Hardcover - also called cloth, retail trade, or trade
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ISBN:
3032227119
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ISBN-13:
9783032227119
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相關分類:
線性代數 Linear-algebra
商品描述
This book is intended as a bridge between high school and college mathematics. The contents have been chosen to demonstrate the relationships among topics from the high school curriculum, including topics that may be part of a fourth year non-calculus mathematics course and first and second year college courses. As the title indicates, the common thread of this work is the linear function. The two parts of the book are devoted, in turn, to: the linear function of a real variable and the linear function of a 2-dimensional vector variable. A second common thread is the visualization of these functions as transformations of 1- or 2-dimensional Euclidean space. The topics, examples, and problems have all been chosen to encourage the integration of the major topics from the high school curriculum. Another feature of this book is that it includes proofs. Specifically, not the formal "two column proofs" often included in the study of geometry in high school, but the more informal, but nevertheless rigorous, step-by-step explanations of why what we believe to be true is indeed true. One of the common complaints of the colleges is that a large majority of incoming freshmen do not have algebra as a usable tool. In this book, algebra is seen to be an essential tool for the further study of mathematics. Algebraic skills are strengthened by constantly using algebra and by seeing the application of algebra in a variety of settings.
商品描述(中文翻譯)
本書旨在作為高中數學與大學數學之間的橋樑。內容的選擇旨在展示高中課程中各主題之間的關係，包括可能屬於第四年非微積分數學課程以及大學一年級和二年級課程的主題。正如書名所示，本書的共同主題是線性函數。書的兩個部分分別專注於：實變數的線性函數和二維向量變數的線性函數。第二個共同主題是將這些函數視覺化為一維或二維歐幾里得空間的變換。所有主題、範例和問題的選擇都旨在鼓勵整合高中課程中的主要主題。本書的另一個特點是包含證明。具體來說，並不是高中幾何學中常見的正式「兩欄證明」，而是更為非正式但仍然嚴謹的逐步解釋，說明我們所相信的真理為何確實成立。大學常見的一個抱怨是，大多數新生並沒有將代數作為可用的工具。在本書中，代數被視為進一步學習數學的基本工具。通過不斷使用代數以及在各種情境中看到代數的應用，代數技能得以加強。
作者簡介
Jennifer Edmond, Ph.D., received her Ph.D. from Syracuse University in 2018. Her research interests include combinatorics and graph theory, with a particular focus on carbon nanostructures. As a graduate fellow, she was one of the leaders of an NSF program for undergraduates at Syracuse University and the Massachusetts College of Liberal Arts, where she led many of the program's work sessions. Since completing her Ph.D., Dr. Edmond has built a successful tutoring program while raising her family. Jack E. Graver, Ph.D., is a Professor in the Department of Mathematics at Syracuse University. He received his Ph.D. from Indiana University in1964, had a two a year Post Doc at Dartmouth College, and joined the faculty at Syracuse University in 1966. His early research areas were in set theory, mathematical programming, and graph theory. Dr. Graver's research interests include chemical graph theory, specifically in the structure of carbon molecules called fullerenes. Starting as a graduate student, Dr. Graver taught NSF summer workshops for high school teachers at Indiana University. He continued teaching summer and year-long teacher workshops at Syracuse University, the College of the Virgin Islands, and at the Shell Center in England.
作者簡介(中文翻譯)
珍妮佛·艾德蒙（Jennifer Edmond），博士，於2018年獲得雪城大學（Syracuse University）的博士學位。她的研究興趣包括組合數學和圖論，特別專注於碳納米結構。作為研究生獎學金獲得者，她是雪城大學和麻薩諸塞州文理學院（Massachusetts College of Liberal Arts）一個針對本科生的國家科學基金（NSF）計畫的領導者之一，並主導了該計畫的多個工作會議。自從完成博士學位以來，艾德蒙博士在撫養家庭的同時建立了一個成功的輔導計畫。
傑克·E·格雷佛（Jack E. Graver），博士，是雪城大學數學系的教授。他於1964年獲得印第安納大學（Indiana University）的博士學位，並在達特茅斯學院（Dartmouth College）完成了兩年的博士後研究，於1966年加入雪城大學的教職。早期的研究領域包括集合論、數學規劃和圖論。格雷佛博士的研究興趣包括化學圖論，特別是碳分子結構的富勒烯（fullerenes）。作為研究生，格雷佛博士在印第安納大學教授針對高中教師的NSF夏季工作坊。他繼續在雪城大學、美屬維爾京群島學院（College of the Virgin Islands）以及英國的殼牌中心（Shell Center）教授夏季和全年教師工作坊。
