Problems and proofs in numbers and algebra:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Springer
2015
|
| Schlagworte: | |
| Online-Zugang: | DE-634 DE-861 DE-91 DE-19 DE-703 DE-20 DE-739 Volltext Abstract |
| Beschreibung: | 1 Online-Ressource (X, 223 S.) 9 illus |
| ISBN: | 9783319144276 |
| DOI: | 10.1007/978-3-319-14427-6 |
Internformat
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Datensatz im Suchindex
| _version_ | 1825547757994115072 |
|---|---|
| adam_text |
PROBLEMS AND PROOFS IN NUMBERS AND ALGEBRA
/ MILLMAN, RICHARD S.
: 2015
ABSTRACT / INHALTSTEXT
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. BEYOND THE UNDERGRADUATE MATHEMATICS STUDENT
AUDIENCE, THE TEXT CAN ALSO OFFER A RIGOROUS TREATMENT OF MATHEMATICS
CONTENT (NUMBERS AND ALGEBRA) FOR HIGH ACHIEVING HIGH SCHOOL STUDENTS.
FURTHERMORE, PROSPECTIVE TEACHERS WILL ADD TO THE BREADTH OF THE
AUDIENCE AS MATH EDUCATION MAJORS, WILL UNDERSTAND MORE THOROUGHLY
METHODS OF PROOF, AND WILL ADD TO THE DEPTH OF THEIR MATHEMATICAL
KNOWLEDGE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. |
| any_adam_object | 1 |
| author | Millman, Richard S. 1945- Shiue, Peter J. Kahn, Eric Brendan 1982- |
| author_GND | (DE-588)172259630 (DE-588)1069677337 |
| author_facet | Millman, Richard S. 1945- Shiue, Peter J. Kahn, Eric Brendan 1982- |
| author_role | aut aut aut |
| author_sort | Millman, Richard S. 1945- |
| author_variant | r s m rs rsm p j s pj pjs e b k eb ebk |
| building | Verbundindex |
| bvnumber | BV042387153 |
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| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-14427-6 |
| format | Electronic eBook |
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| indexdate | 2025-03-03T05:00:09Z |
| institution | BVB |
| isbn | 9783319144276 |
| language | English |
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| physical | 1 Online-Ressource (X, 223 S.) 9 illus |
| psigel | ZDB-2-SMA UBY_PDA_SMA ZDB-2-SMA_2015 |
| publishDate | 2015 |
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| publisher | Springer |
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| spelling | Millman, Richard S. 1945- Verfasser (DE-588)172259630 aut Problems and proofs in numbers and algebra Richard S. Millman ; Peter J. Shiue ; Eric Brendan Kahn Cham [u.a.] Springer 2015 1 Online-Ressource (X, 223 S.) 9 illus txt rdacontent c rdamedia cr rdacarrier Mathematics Algebra Logic, Symbolic and mathematical Number theory General Algebraic Systems Number Theory Mathematical Logic and Foundations Mathematik Shiue, Peter J. Verfasser aut Kahn, Eric Brendan 1982- Verfasser (DE-588)1069677337 aut Erscheint auch als Druckausgabe 978-3-319-14426-9 https://doi.org/10.1007/978-3-319-14427-6 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027823113&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Millman, Richard S. 1945- Shiue, Peter J. Kahn, Eric Brendan 1982- Problems and proofs in numbers and algebra Mathematics Algebra Logic, Symbolic and mathematical Number theory General Algebraic Systems Number Theory Mathematical Logic and Foundations Mathematik |
| title | Problems and proofs in numbers and algebra |
| title_auth | Problems and proofs in numbers and algebra |
| title_exact_search | Problems and proofs in numbers and algebra |
| title_full | Problems and proofs in numbers and algebra Richard S. Millman ; Peter J. Shiue ; Eric Brendan Kahn |
| title_fullStr | Problems and proofs in numbers and algebra Richard S. Millman ; Peter J. Shiue ; Eric Brendan Kahn |
| title_full_unstemmed | Problems and proofs in numbers and algebra Richard S. Millman ; Peter J. Shiue ; Eric Brendan Kahn |
| title_short | Problems and proofs in numbers and algebra |
| title_sort | problems and proofs in numbers and algebra |
| topic | Mathematics Algebra Logic, Symbolic and mathematical Number theory General Algebraic Systems Number Theory Mathematical Logic and Foundations Mathematik |
| topic_facet | Mathematics Algebra Logic, Symbolic and mathematical Number theory General Algebraic Systems Number Theory Mathematical Logic and Foundations Mathematik |
| url | https://doi.org/10.1007/978-3-319-14427-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027823113&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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