Transition to Advanced Mathematics
portes grátis
Transition to Advanced Mathematics
Diedrichs, Danilo R.; Lovett, Stephen
Taylor & Francis Ltd
05/2022
552
Dura
Inglês
9780367494445
15 a 20 dias
848
Descrição não disponível.
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.
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Transition;Advanced Mathematics;proofs;introduction to proofs;algebra;analysis;set theory;logic;topology;typeset in LaTeX;modern mathematics;philosophical issues in mathematics;21st century mathematics;mathematical culture;Hasse Diagram;Mathematical writing;Research Articles;probability;Axiomatic Method;Reduced Row Echelon Form;Quotient Set;Original Research Articles;Choice Function;Mathematical Expressions;Pigeonhole Principle;Greatest Lower Bound;In-text Citation;Combinatorial Proof;LaTeX Code;Vocational Discernment;Partial Order;Ancient Greece;Vocational Pathway;Backward Learning;Mathematical Associations;Peer Reviewed Journal Articles;Equivalence Relation;Binary Operation;National Libraries;Axiomatic System
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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Transition;Advanced Mathematics;proofs;introduction to proofs;algebra;analysis;set theory;logic;topology;typeset in LaTeX;modern mathematics;philosophical issues in mathematics;21st century mathematics;mathematical culture;Hasse Diagram;Mathematical writing;Research Articles;probability;Axiomatic Method;Reduced Row Echelon Form;Quotient Set;Original Research Articles;Choice Function;Mathematical Expressions;Pigeonhole Principle;Greatest Lower Bound;In-text Citation;Combinatorial Proof;LaTeX Code;Vocational Discernment;Partial Order;Ancient Greece;Vocational Pathway;Backward Learning;Mathematical Associations;Peer Reviewed Journal Articles;Equivalence Relation;Binary Operation;National Libraries;Axiomatic System
