Passage to abstract mathematics pdf

Add to Cart. Passage to Abstract Mathematics helps students progress from a facility with computational procedures to an understanding of abstract mathematical concepts. Students develop their ability in mathematical communication through reading proofs, constructing proofs, and writing proofs in correct mathematical language. Concise, practical, and highly valuable, the text is ideal for students who have taken lower-division mathematics courses and need the tools requisite to study more advanced, abstract mathematics.

The text features material that instructors of upper-level courses in set theory, analysis, topology, and modern algebra presume students have already learned by the time they enter advanced courses.

It places emphasis on complete and correct definitions, as well as expressing mathematics in correct syntax. The core material consists of the first five closely knit chapters: Logic, Numbers, Sets, Functions, and Induction. To support active and continuous learning, exercises are embedded within the text material immediately following a definition or theorem. The explanatory comments, hints to solutions, and thought-provoking questions that appear within brackets throughout the text all serve to deepen the student's understanding of the material.

In the second edition, the chapter entitled Functions precedes the chapter entitled Induction, and select material has been clarified or corrected. Number theoretic digressions such as Euclid's Algorithm and the Chinese Remainder Theorem have been deleted.

Mark E. Watkins holds a Ph. He is a professor emeritus of mathematics at Syracuse University. Watkins has published over 70 research articles, mainly in algebraic and topological graph theory, and has coauthored the books Combinatorics with Emphasis on the Theory of Graphs and Locally Finite, Planar, Edge-Transitive Graphs.

Jeffrey L. Meyer holds a Ph. He is an associate teaching professor of mathematics at Syracuse University. Meyer has published both research and expository papers in analytic number theory, especially Dedekind Sums. Instructors: Next Step Bookstore Orders. With brief and focused sections, copious well-chosen exercises, and a flexible format, it adapts well to both on-line and in-person instruction.

I think the students actually read and understood the book, a rarity in a math text. Company Info Contact Us. You have successfully signed out and will be required to sign back in should you need to download more resources. Out of print. Passage to Abstract Mathematics.

Watkins, Syracuse University Jeffrey L. Meyer, Syracuse University. Description Passage to Abstract Mathematics facilitates the transition from introductory mathematics courses to the more abstract work that occurs in advanced courses.

Content - The text covers logic and proof, numbers, sets, induction, functions, cardinality, and more—-material which many instructors of upper-level courses presume their students have already mastered but is often missing from lower-level courses. Exercise Sets — At the end of each section and each chapter, students will encounter many exercises ranging from routine to challenging, including applications of learned material to further topics.

Logic and Proof 1. Numbers 2. Sets 3. Induction 4. Functions 5. Binary Relations 6. Infinite Sets and Cardinality 7. Algebraic Systems 8. About the Author s. Previous editions. This implies that. By Exercise 1. From Exercise 1. Do we agree that gold glitters? If so, then the second statement is true. The statements are not negations of each other. The midpoint of DF is , 0.

Verify that , 0 lies on the 2 2 tangent line. Thus the tangent line is the perpendicular bisector of DF. Open navigation menu. Close suggestions Search Search.

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