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An Elementary Transition to Abstract Mathematics
Taschenbuch von Gove Effinger (u. a.)
Sprache: Englisch

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Beschreibung
An Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role.

The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, functions, cardinality, complex numbers, permutations, and matrices; the third part introduces basic number theory including applications to cryptography; the fourth part introduces key objects from abstract algebra; and the final part focuses on polynomials.


Features:





The material is presented in many short chapters, so that one concept at a time can be absorbed by the student.



Two "looking back" chapters at the outset (pre-calculus and calculus) are designed to start the student's transition by working with familiar concepts.



Many examples of every concept are given to make the material as concrete as possible and to emphasize the importance of searching for patterns.



A conversational writing style is employed throughout in an effort to encourage active learning on the part of the student.
An Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role.

The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, functions, cardinality, complex numbers, permutations, and matrices; the third part introduces basic number theory including applications to cryptography; the fourth part introduces key objects from abstract algebra; and the final part focuses on polynomials.


Features:





The material is presented in many short chapters, so that one concept at a time can be absorbed by the student.



Two "looking back" chapters at the outset (pre-calculus and calculus) are designed to start the student's transition by working with familiar concepts.



Many examples of every concept are given to make the material as concrete as possible and to emphasize the importance of searching for patterns.



A conversational writing style is employed throughout in an effort to encourage active learning on the part of the student.
Inhaltsverzeichnis
A Look Back: Precalculus Math

A Look Back: Calculus



About Proofs and Proof Strategies



Mathematical Induction



The Well-Ordering Principle



Sets



Equivalence Relations



Functions



Cardinality of Sets



Permutations



Complex Numbers



Matrices and Sets with Algebraic Structure



Divisibility in Z and Number Theory



Primes and Unique Factorization



Congruences and the Finite Sets Zn



Solving Congruences



Fermat's Theorem



Diffie-Hellman Key Exchange



Euler's Formula and Euler's Theorem



RSA Cryptographic System



Groups-Definition and Examples



Groups-Basic Properties



Groups-Subgroups



Groups-Cosets



Groups-Lagrange's Theorem



Rings



Subrings and Ideals



Integral Domains



Fields



Vector Spaces



Vector Space Properties



Subspaces of Vector Spaces



Polynomials



Polynomials-Unique Factorization



Polynomials over the Rational, Real and Complex Numbers



Suggested Solutions to Selected Examples and Exercises

Inhaltsverzeichnis
A Look Back: Precalculus Math

A Look Back: Calculus



About Proofs and Proof Strategies



Mathematical Induction



The Well-Ordering Principle



Sets



Equivalence Relations



Functions



Cardinality of Sets



Permutations



Complex Numbers



Matrices and Sets with Algebraic Structure



Divisibility in Z and Number Theory



Primes and Unique Factorization



Congruences and the Finite Sets Zn



Solving Congruences



Fermat's Theorem



Diffie-Hellman Key Exchange



Euler's Formula and Euler's Theorem



RSA Cryptographic System



Groups-Definition and Examples



Groups-Basic Properties



Groups-Subgroups



Groups-Cosets



Groups-Lagrange's Theorem



Rings



Subrings and Ideals



Integral Domains



Fields



Vector Spaces



Vector Space Properties



Subspaces of Vector Spaces



Polynomials



Polynomials-Unique Factorization



Polynomials over the Rational, Real and Complex Numbers



Suggested Solutions to Selected Examples and Exercises

Sicherheitshinweis