Proofs 101 : an introduction to formal mathematics /
Proofs 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 a...
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
Chapman and Hall/CRC,
2021.
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| Edition: | 1st. |
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | Proofs 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 |
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| Item Description: | <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> |
| Physical Description: | 1 online resource : illustrations (black and white) |
| ISBN: | 9781000227383 1000227383 9781000227345 1000227340 9781000227369 1000227367 9781003082927 1003082920 |