000 03874cam a22005291i 4500
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
020 _a9781000227383
_q(ePub ebook)
020 _a1000227383
_q(ePub ebook)
020 _a9781000227345
_q(PDF ebook)
020 _a1000227340
_q(PDF ebook)
020 _a9781000227369
_q(Mobipocket ebook)
020 _a1000227367
_q(Mobipocket ebook)
020 _a9781003082927
_q(ebook)
020 _a1003082920
_q(ebook)
020 _z9780367536930 (hbk.)
020 _z9780367536817 (pbk.)
024 7 _a10.1201/9781003082927
_2doi
035 _a(OCoLC)1222798167
_z(OCoLC)1222799698
035 _a(OCoLC-P)1222798167
050 4 _aQA9.54
072 7 _aMAT
_x028000
_2bisacsh
072 7 _aMAT
_x018000
_2bisacsh
072 7 _aPB
_2bicssc
082 0 4 _a511.36
_223
100 1 _aKirtland, Joseph
_c(Mathematics professor),
_eauthor.
245 1 0 _aProofs 101 :
_ban introduction to formal mathematics /
_cJoseph Kirtland.
250 _a1st.
264 1 _aBoca Raton :
_bChapman & Hall/CRC,
_c2021.
300 _a1 online resource :
_billustrations (black and white)
336 _atext
_2rdacontent
336 _astill image
_2rdacontent
337 _acomputer
_2rdamedia
338 _aonline resource
_2rdacarrier
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
650 7 _aMATHEMATICS / Logic
_2bisacsh
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