000 | 03874cam a22005291i 4500 | ||
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001 | 9781003082927 | ||
003 | FlBoTFG | ||
005 | 20220509192927.0 | ||
006 | m d | ||
007 | cr ||||||||||| | ||
008 | 200907s2021 flua ob 001 0 eng d | ||
040 |
_aOCoLC-P _beng _erda _epn _cOCoLC-P |
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020 |
_a9781000227383 _q(ePub ebook) |
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020 |
_a1000227383 _q(ePub ebook) |
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020 |
_a9781000227345 _q(PDF ebook) |
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020 |
_a1000227340 _q(PDF ebook) |
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_a9781000227369 _q(Mobipocket ebook) |
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_a1000227367 _q(Mobipocket ebook) |
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020 |
_a9781003082927 _q(ebook) |
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020 |
_a1003082920 _q(ebook) |
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020 | _z9780367536930 (hbk.) | ||
020 | _z9780367536817 (pbk.) | ||
024 | 7 |
_a10.1201/9781003082927 _2doi |
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035 |
_a(OCoLC)1222798167 _z(OCoLC)1222799698 |
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035 | _a(OCoLC-P)1222798167 | ||
050 | 4 | _aQA9.54 | |
072 | 7 |
_aMAT _x028000 _2bisacsh |
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072 | 7 |
_aMAT _x018000 _2bisacsh |
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072 | 7 |
_aPB _2bicssc |
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082 | 0 | 4 |
_a511.36 _223 |
100 | 1 |
_aKirtland, Joseph _c(Mathematics professor), _eauthor. |
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245 | 1 | 0 |
_aProofs 101 : _ban introduction to formal mathematics / _cJoseph Kirtland. |
250 | _a1st. | ||
264 | 1 |
_aBoca Raton : _bChapman & Hall/CRC, _c2021. |
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300 |
_a1 online resource : _billustrations (black and white) |
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336 |
_atext _2rdacontent |
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336 |
_astill image _2rdacontent |
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337 |
_acomputer _2rdamedia |
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338 |
_aonline resource _2rdacarrier |
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500 | _a<P><STRONG>1. Logic.</STRONG> 1.1 Introduction. 1.2. Statements and Logical Connectives. 1.3 Logical Equivalence. 1.4. Predicates and Quantifiers. 1.5. Negation. <STRONG>2. Proof Techniques</STRONG>. 2.1. Introduction. 2.2. The Axiomatic and Rigorous Nature of Mathematics. 2.3. Foundations. 2.4. Direct Proof. 2.5. Proof by Contrapositive. 2.5. Proof by Cases. 2.6. Proof by Contradiction. <STRONG>3. Sets.</STRONG> 3.1. The Concept of a Set. 3.2. Subset of Set Equality. 3.3. Operations on Sets. 3.4. Indexed Sets. 3.5. Russel's Paradox. <STRONG>4. Proof by Mathematical Induction.</STRONG> 4.1. Introduction. 4.2. The Principle of Mathematical Induction. 4.3. Proof by strong Induction. <STRONG>5. Relations.</STRONG> 5.1. Introduction. 5.2. Properties of Relations. 5.3. Equivalence Relations.<STRONG> 6. Introduction.</STRONG> 6.1. Definition of a Function. 6.2. One-To-One and Onto Functions. 6.3. Composition of Functions. 6.4. Inverse of a Function.<STRONG> 7. Cardinality of Sets.</STRONG> 7.1. Introduction. 7.2. Sets with the same Cardinality. 7.3. Finite and Infinite Sets. 7.4. Countably Infinite Sets. 7.5. Uncountable Sets. 7.6 Comparing Cardinalities. </P> | ||
520 | _aProofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra. The book prepares students for the proofs they will need to analyze and write the axiomatic nature of mathematics and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry with them throughout their future studies. Features Designed to be teachable across a single semester Suitable as an undergraduate textbook for Introduction to Proofs or Transition to Advanced Mathematics courses Offers a balanced variety of easy, moderate, and difficult exercises | ||
588 | _aOCLC-licensed vendor bibliographic record. | ||
650 | 0 | _aProof theory. | |
650 | 7 |
_aMATHEMATICS / Set Theory _2bisacsh |
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650 | 7 |
_aMATHEMATICS / Logic _2bisacsh |
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856 | 4 | 0 |
_3Taylor & Francis _uhttps://www.taylorfrancis.com/books/9781003082927 |
856 | 4 | 2 |
_3OCLC metadata license agreement _uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf |
999 |
_c126686 _d126686 |