Introduction to Advanced Mathematics, 2nd edition

Focused on “What Every Mathematician Needs to Know,” this text provides material necessary for students to succeed in upper-division mathematics courses, and more importantly, the analytical tools necessary for thinking like a mathematician. It begins with a natural progression from elementary logic, methods of proof, and set theory, to relations and functions; then provides application examples, theorems, and student projects.

• NEW - Streamlined Ch. 1—Gets more quickly to proofs involving topics more commonly encountered in mathematics courses.

• NEW - Functions are now covered before relations (Chs. 4 and 5).

• NEW - New chapter on rings and integral domains (Ch. 8).

• NEW - Extensively revised chapter on number theory and algebra. (Chs. 6, 7, and 9).

  • The flow from cardinality to rings is now very smooth. Ex.___

• NEW - “Find the Flaw” problems—At the beginning of exercise sets in Chs. 1-5.

  • Help students learn to read proofs critically. Ex.___

• NEW - A collection of True/False questions—Begins each set of review exercises in Chs. 2-5.

• NEW - Many new exercises of all kinds—More than in any other textbook of its kind.

• Five core chapters (Chs. 1-5)—In a natural progression: elementary logic, methods of proof, set theory, functions, and relations. Each chapter contains a full exposition of topics with many examples and practice problems to reinforce the concepts as they are introduced.

  • Anticipates many of the questions students might have and develops the subject slowly and carefully. Students are then able to work more independently—and with much greater understanding of the material. Ex.___

• Four chapters of examples, theorems, and projects (Chs. 6-9)—Many theorems have no proof or only a hint or outline for the proof. Likewise, the examples may have no solutions or just a hint for the solution.

  • The intent is that the material be used as a basis for students to construct their own proofs or solutions and perhaps present them to the class. Ex.___

• Clearly written examples and practice problems— Provides solutions to practice problems, odd-numbered exercises, and review problems.

• Supplementary exercises—Extend or relate to some of the concepts discussed in the text but are not necessary for the continuity of the subject matter.

• Streamlined Ch. 1—Gets more quickly to proofs involving topics more commonly encountered in mathematics courses.

• Functions are now covered before relations (Chs. 4 and 5).

• New chapter on rings and integral domains (Ch. 8).

• Extensively revised chapter on number theory and algebra. (Chs. 6, 7, and 9).

  • The flow from cardinality to rings is now very smooth. Ex.___

• “Find the Flaw” problems—At the beginning of exercise sets in Chs. 1-5.

  • Help students learn to read proofs critically. Ex.___

• A collection of True/False questions—Begins each set of review exercises in Chs. 2-5.

• Many new exercises of all kinds—More than in any other textbook of its kind.