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This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics.
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This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: CRC Press
- Seitenzahl: 538
- Erscheinungstermin: 26. August 2024
- Englisch
- Abmessung: 234mm x 156mm x 28mm
- Gewicht: 762g
- ISBN-13: 9781032261003
- ISBN-10: 1032261005
- Artikelnr.: 71237840
- Verlag: CRC Press
- Seitenzahl: 538
- Erscheinungstermin: 26. August 2024
- Englisch
- Abmessung: 234mm x 156mm x 28mm
- Gewicht: 762g
- ISBN-13: 9781032261003
- ISBN-10: 1032261005
- Artikelnr.: 71237840
Danilo R. Diedrichs is an Associate Professor of Mathematics at Wheaton College in Illinois. Raised and educated in Switzerland, he holds a PhD in applied mathematical and computational sciences from the University of Iowa, as well as a master's degree in civil engineering from the Ecole Polytechnique Fédérale in Lausanne, Switzerland. His research interests are in dynamical systems modeling applied to biology, ecology, and epidemiology. Stephen Lovett is a Professor of Mathematics at Wheaton College in Illinois. He holds a PhD in representation theory from Northeastern University. His other books include Abstract Algebra: Structures and Applications (2015), Differential Geometry of Curves and Surfaces, with Tom Banchoff (2016), and Differential Geometry of Manifolds (2019).
Part I - Introduction to Proofs. 1. Logic and Sets. 1.1. Logic and
Propositions. 1.2. Sets. 1.3. Logical Equivalences. 1.4. Operations on
Sets. 1.5. Predicates and Quantifiers. 2. Arguments and Proofs. 2.1.
Constructing Valid Arguments. 2.2. First Proof Strategies. 2.3. Proof
Strategies. 3. Functions. 3.1. Functions. 3.2. Properties of Functions.
3.3. Choice Functions and the Axiom of Choice. 4. Properties of the
Integers. 4.1. A Definition of the Integers. 4.2. Divisibility. 4.3.
Greatest Common Divisor; Least Common Multiple. 4.4. Prime Numbers. 4.5.
Induction. 4.6. Modular Arithmetic. 5. Counting and Combinatorial
Arguments. 5.1. Counting Techniques. 5.2. Concept of a Combinatorial Proof.
5.3. Pigeonhole Principle. 5.4. Countability and Cardinality. 6. Relations.
6.1. Relations. 6.2. Partial Orders. 6.3. Equivalence Relations. 6.4.
Quotient Sets. Part II - Culture, History, Reading, and Writing. 7.
Mathematical Culture, Vocation, and Careers. 7.1. 21st Century Mathematics.
7.2. Collaboration, Associations, Conferences. 7.3. Studying Upper-Level
Mathematics. 7.4. Mathematical Vocations. 8. History and Philosophy of
Mathematics. 8.1. History of Mathematics before the Scientific Revolution.
8.2. Mathematics and Science. 8.3. The Axiomatic Method. 8.4. History of
Modern Mathematics. 8.5. Philosophical Issues in Mathematics. 9. Reading
and Researching Mathematics. 9.1. Journals. 9.2. Original Research
Articles. 9.3. Reading and Expositing Original Research Articles. 9.4.
Researching Primary and Secondary Sources. 10. Writing and Presenting
Mathematics. 10.1. Mathematical Writing. 10.2. Project Reports. 10.3.
Mathematical Typesetting. 10.4. Advanced Typesetting. 10.5. Oral
Presentations. Appendix A. Rubric for Assessing Proofs. A.1. Logic. A.2.
Understanding / Terminology. A.3. Creativity. A.4. Communication. Appendix
B. Index of Theorems and Definitions from Calculus and Linear Algebra.
B.1. Calculus. B.2. Linear Algebra. Bibliography. Index.
Propositions. 1.2. Sets. 1.3. Logical Equivalences. 1.4. Operations on
Sets. 1.5. Predicates and Quantifiers. 2. Arguments and Proofs. 2.1.
Constructing Valid Arguments. 2.2. First Proof Strategies. 2.3. Proof
Strategies. 3. Functions. 3.1. Functions. 3.2. Properties of Functions.
3.3. Choice Functions and the Axiom of Choice. 4. Properties of the
Integers. 4.1. A Definition of the Integers. 4.2. Divisibility. 4.3.
Greatest Common Divisor; Least Common Multiple. 4.4. Prime Numbers. 4.5.
Induction. 4.6. Modular Arithmetic. 5. Counting and Combinatorial
Arguments. 5.1. Counting Techniques. 5.2. Concept of a Combinatorial Proof.
5.3. Pigeonhole Principle. 5.4. Countability and Cardinality. 6. Relations.
6.1. Relations. 6.2. Partial Orders. 6.3. Equivalence Relations. 6.4.
Quotient Sets. Part II - Culture, History, Reading, and Writing. 7.
Mathematical Culture, Vocation, and Careers. 7.1. 21st Century Mathematics.
7.2. Collaboration, Associations, Conferences. 7.3. Studying Upper-Level
Mathematics. 7.4. Mathematical Vocations. 8. History and Philosophy of
Mathematics. 8.1. History of Mathematics before the Scientific Revolution.
8.2. Mathematics and Science. 8.3. The Axiomatic Method. 8.4. History of
Modern Mathematics. 8.5. Philosophical Issues in Mathematics. 9. Reading
and Researching Mathematics. 9.1. Journals. 9.2. Original Research
Articles. 9.3. Reading and Expositing Original Research Articles. 9.4.
Researching Primary and Secondary Sources. 10. Writing and Presenting
Mathematics. 10.1. Mathematical Writing. 10.2. Project Reports. 10.3.
Mathematical Typesetting. 10.4. Advanced Typesetting. 10.5. Oral
Presentations. Appendix A. Rubric for Assessing Proofs. A.1. Logic. A.2.
Understanding / Terminology. A.3. Creativity. A.4. Communication. Appendix
B. Index of Theorems and Definitions from Calculus and Linear Algebra.
B.1. Calculus. B.2. Linear Algebra. Bibliography. Index.
Part I - Introduction to Proofs. 1. Logic and Sets. 1.1. Logic and
Propositions. 1.2. Sets. 1.3. Logical Equivalences. 1.4. Operations on
Sets. 1.5. Predicates and Quantifiers. 2. Arguments and Proofs. 2.1.
Constructing Valid Arguments. 2.2. First Proof Strategies. 2.3. Proof
Strategies. 3. Functions. 3.1. Functions. 3.2. Properties of Functions.
3.3. Choice Functions and the Axiom of Choice. 4. Properties of the
Integers. 4.1. A Definition of the Integers. 4.2. Divisibility. 4.3.
Greatest Common Divisor; Least Common Multiple. 4.4. Prime Numbers. 4.5.
Induction. 4.6. Modular Arithmetic. 5. Counting and Combinatorial
Arguments. 5.1. Counting Techniques. 5.2. Concept of a Combinatorial Proof.
5.3. Pigeonhole Principle. 5.4. Countability and Cardinality. 6. Relations.
6.1. Relations. 6.2. Partial Orders. 6.3. Equivalence Relations. 6.4.
Quotient Sets. Part II - Culture, History, Reading, and Writing. 7.
Mathematical Culture, Vocation, and Careers. 7.1. 21st Century Mathematics.
7.2. Collaboration, Associations, Conferences. 7.3. Studying Upper-Level
Mathematics. 7.4. Mathematical Vocations. 8. History and Philosophy of
Mathematics. 8.1. History of Mathematics before the Scientific Revolution.
8.2. Mathematics and Science. 8.3. The Axiomatic Method. 8.4. History of
Modern Mathematics. 8.5. Philosophical Issues in Mathematics. 9. Reading
and Researching Mathematics. 9.1. Journals. 9.2. Original Research
Articles. 9.3. Reading and Expositing Original Research Articles. 9.4.
Researching Primary and Secondary Sources. 10. Writing and Presenting
Mathematics. 10.1. Mathematical Writing. 10.2. Project Reports. 10.3.
Mathematical Typesetting. 10.4. Advanced Typesetting. 10.5. Oral
Presentations. Appendix A. Rubric for Assessing Proofs. A.1. Logic. A.2.
Understanding / Terminology. A.3. Creativity. A.4. Communication. Appendix
B. Index of Theorems and Definitions from Calculus and Linear Algebra.
B.1. Calculus. B.2. Linear Algebra. Bibliography. Index.
Propositions. 1.2. Sets. 1.3. Logical Equivalences. 1.4. Operations on
Sets. 1.5. Predicates and Quantifiers. 2. Arguments and Proofs. 2.1.
Constructing Valid Arguments. 2.2. First Proof Strategies. 2.3. Proof
Strategies. 3. Functions. 3.1. Functions. 3.2. Properties of Functions.
3.3. Choice Functions and the Axiom of Choice. 4. Properties of the
Integers. 4.1. A Definition of the Integers. 4.2. Divisibility. 4.3.
Greatest Common Divisor; Least Common Multiple. 4.4. Prime Numbers. 4.5.
Induction. 4.6. Modular Arithmetic. 5. Counting and Combinatorial
Arguments. 5.1. Counting Techniques. 5.2. Concept of a Combinatorial Proof.
5.3. Pigeonhole Principle. 5.4. Countability and Cardinality. 6. Relations.
6.1. Relations. 6.2. Partial Orders. 6.3. Equivalence Relations. 6.4.
Quotient Sets. Part II - Culture, History, Reading, and Writing. 7.
Mathematical Culture, Vocation, and Careers. 7.1. 21st Century Mathematics.
7.2. Collaboration, Associations, Conferences. 7.3. Studying Upper-Level
Mathematics. 7.4. Mathematical Vocations. 8. History and Philosophy of
Mathematics. 8.1. History of Mathematics before the Scientific Revolution.
8.2. Mathematics and Science. 8.3. The Axiomatic Method. 8.4. History of
Modern Mathematics. 8.5. Philosophical Issues in Mathematics. 9. Reading
and Researching Mathematics. 9.1. Journals. 9.2. Original Research
Articles. 9.3. Reading and Expositing Original Research Articles. 9.4.
Researching Primary and Secondary Sources. 10. Writing and Presenting
Mathematics. 10.1. Mathematical Writing. 10.2. Project Reports. 10.3.
Mathematical Typesetting. 10.4. Advanced Typesetting. 10.5. Oral
Presentations. Appendix A. Rubric for Assessing Proofs. A.1. Logic. A.2.
Understanding / Terminology. A.3. Creativity. A.4. Communication. Appendix
B. Index of Theorems and Definitions from Calculus and Linear Algebra.
B.1. Calculus. B.2. Linear Algebra. Bibliography. Index.