MARC 主機 00000cam  2200457Ki 4500 
001    898086761 
003    OCoLC 
005    20151030025011.0 
008    141212s2015    sz       b    000 0 eng d 
020    331914426X 
020    9783319144269 
035    (OCoLC)898086761|z(OCoLC)911263411 
050    QA241|b.M54 2015 
082 04 512.7/4|223 
100 1  Millman, Richard S.,|d1945-|eauthor 
245 10 Problems and proofs in numbers and algebra /|cRichard S. 
       Millman, Peter J. Shiue, Eric Brendan Kahn 
264  1 Cham :|bSpringer,|c[2015] 
264  4 |c©2015 
300    x, 223 pages ;|c24 cm 
336    text|btxt|2rdacontent 
337    unmediated|bn|2rdamedia 
338    volume|2rdacarrier 
504    Includes bibliographic references 
520    Designed to facilitate the transition from undergraduate 
       calculus and differential equations to learning about 
       proofs, this book helps students develop the rigorous 
       mathematical reasoning needed for advanced courses in 
       analysis, abstract algebra, and more. Students will focus 
       on both how to prove theorems and solve problem sets in-
       depth; that is, where multiple steps are needed to prove 
       or solve. This proof technique is developed by examining 
       two specific content themes and their applications in-
       depth: number theory and algebra. This choice of content 
       themes enables students to develop an understanding of 
       proof technique in the context of topics with which they 
       are already familiar, as well as reinforcing natural and 
       conceptual understandings of mathematical methods and 
       styles. The key to the text is its interesting and 
       intriguing problems, exercises, theorems, and proofs, 
       showing how students will transition from the usual, more 
       routine calculus to abstraction while also learning how to
       prove or solve complex problems. This method of 
       instruction is augmented by examining applications of 
       number theory in systems such as RSA cryptography, 
       Universal Product Code (UPC), and International Standard 
       Book Number (ISBN). The numerous problems and examples 
       included in each section reward curiosity and 
       insightfulness over more simplistic approaches. Each 
       problem set begins with a few easy problems, progressing 
       to problems or proofs with multi-step solutions. Exercises
       in the text stay close to the examples of the section, 
       allowing students the immediate opportunity to practice 
       developing techniques 
650  0 Number theory 
650  0 Proof theory 
650  0 Algebra 
650  7 Algebra.|2fast|0(OCoLC)fst00804885 
650  7 Number theory.|2fast|0(OCoLC)fst01041214 
650  7 Proof theory.|2fast|0(OCoLC)fst01078942 
700 1  Shiue, Peter Jau-Shyong,|d1941-|eauthor 
700 1  Kahn, Eric Brendan,|eauthor 
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA241 .M54 2015    在架上    30340200544173