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9781119131694 English 1119131693 Designed to be an accessible treatment of the foundations of modern mathematics, the book uniquely bridges introductory mathematics and more advanced topics. The author introduces a variety of mathematical concepts, all of which are typically introduced in logic, foundations, and transitions courses to fulfill general mathematical requirements. Beginning with comprehensive coverage of the necessary building blocks in mathematics, the book quickly explores interesting and provocative treatments of current issues in the field of mathematics and science. While the book can be used as a primer for more advanced mathematical work, the author maintains a useful balance of introductory coverage and mathematical rigor in order to facilitate complete understanding of the presented topics. The book utilizes numerous theorems and proofs to increase comprehension of the concepts, as well as hundreds of completely solved problems at the end of each chapter. The author also includes additional exercises throughout the book for the readers to work through in order to supplement the presented topics. Topical coverage includes: set theory; mathematical logic; proof theory; group theory; theory of functions; and linear algebra., 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. Vladimir Lepetic, PhD, is Professor in the Department of Mathematical Sciences at DePaul University. His research interests include mathematical physics, set theory, foundations of mathematics, and the philosophy of mathematics.
9781119131694 English 1119131693 Designed to be an accessible treatment of the foundations of modern mathematics, the book uniquely bridges introductory mathematics and more advanced topics. The author introduces a variety of mathematical concepts, all of which are typically introduced in logic, foundations, and transitions courses to fulfill general mathematical requirements. Beginning with comprehensive coverage of the necessary building blocks in mathematics, the book quickly explores interesting and provocative treatments of current issues in the field of mathematics and science. While the book can be used as a primer for more advanced mathematical work, the author maintains a useful balance of introductory coverage and mathematical rigor in order to facilitate complete understanding of the presented topics. The book utilizes numerous theorems and proofs to increase comprehension of the concepts, as well as hundreds of completely solved problems at the end of each chapter. The author also includes additional exercises throughout the book for the readers to work through in order to supplement the presented topics. Topical coverage includes: set theory; mathematical logic; proof theory; group theory; theory of functions; and linear algebra., 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. Vladimir Lepetic, PhD, is Professor in the Department of Mathematical Sciences at DePaul University. His research interests include mathematical physics, set theory, foundations of mathematics, and the philosophy of mathematics.