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Principles of Mathematics A Primer 1st Edition by Vladimir Lepetic 9781119131649 1119131642

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Principles of Mathematics A Primer 1st Edition Vladimir Lepetic Digital Instant Download

Author(s): Vladimir Lepetic
ISBN(s): 9781119131649, 1119131642
Edition: 1
File Details: PDF, 2.66 MB
Year: 2016
Language: english
SKU: EB-5318550 Category: Tag:

Principles of Mathematics A Primer 1st Edition by Vladimir Lepetic – Ebook PDF Instant Download/Delivery: 9781119131649, 1119131642

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Product details:

ISBN 10: 1119131642

ISBN 13: 9781119131649

Author: Vladimir Lepetic

Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics

An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra.

The author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, Principles of Mathematics: A Primer features:

  • Detailed explanations of important theorems and their applications
  • Hundreds of completely solved problems throughout each chapter
  • Numerous exercises at the end of each chapter to encourage further exploration
  • Discussions of interesting and provocative issues that spark readers’ curiosity and facilitate a better understanding and appreciation of the field of mathematics

Principles of Mathematics: A Primer is an ideal textbook for upper-undergraduate courses in the foundations of mathematics and mathematical logic as well as for graduate-level courses related to physics, engineering, and computer science. The book is also a useful reference for readers interested in pursuing careers in mathematics and the sciences.

Table of contents:

1 SET THEORY
1.1 Introduction
1.2 Set Theory – Definitions, Notation, and Terminology – What Is a Set?
1.3 Sets Given by a Defining Property
1.4 The Algebra of Sets
1.5 The Power Set
1.6 The Cartesian Product
1.7 The Sets N, Z, and Q
1.8 The Set R – Real Numbers I
1.9 A Short Musing on Transfinite Arithmetic
1.10 The Set R – Real Numbers II
1.11 Supplementary Problems

2 LOGIC
2.1 Introduction
2.2 Propositional Calculus
2.3 Arguments I
2.4 Arguments II
2.5 A Short Revisit to Set Theory
2.6 Boolean Algebra
2.7 Supplementary Problems

3 PROOFS
3.1 Introduction
3.2 Direct Proof
3.3 Indirect Proof
3.4 Mathematical Induction
3.5 Supplementary Problems

4 FUNCTIONS
4.1 Introduction
4.2 Relations
4.3 Functions
4.4 Supplementary Problems

5 GROUP THEORY
5.1 Introduction
5.2 Fundamental Concepts of Group Theory
5.3 Subgroups
5.4 Cyclic Groups
5.5 Homomorphisms and Isomorphisms
5.6 Normal Subgroups

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