A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an ...
Read More
A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Throughout the text, some pieces (usually proofs) are left as exercises. Part V gives hints to help students find good approaches to the exercises. Part I introduces the language of mathematics and the methods of proof. The mathematical content of Parts II through IV were chosen so as not to seriously overlap the standard mathematics major. In Part II, students study sets, functions, equivalence and order relations, and cardinality. Part III concerns algebra. The goal is to prove that the real numbers form the unique, up to isomorphism, ordered field with the least upper bound. In the process, we construct the real numbers starting with the natural numbers. Students will be prepared for an abstract linear algebra or modern algebra course. Part IV studies analysis. Continuity and differentiation are considered in the context of time scales (nonempty, closed subsets of the real numbers). Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented.
Read Less
Add this copy of Bridge to Abstract Mathematics (Mathematical to cart. $16.11, good condition, Sold by Idaho Youth Ranch Books rated 5.0 out of 5 stars, ships from Boise, ID, UNITED STATES, published 2013 by Mathematical Association of America.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. A copy that has been read, but remains in clean condition. All pages are intact, and the cover is intact (including dust cover, if applicable). The spine may show signs of wear. Pages can include limited notes and highlighting, and the copy can include "From the library of" labels or limited small stickers. Book may have a remainder mark or be a price cutter.
Add this copy of A Bridge to Abstract Mathematics (Mathematical to cart. $20.11, fair condition, Sold by Goodwill Industries rated 4.0 out of 5 stars, ships from Miami, FL, UNITED STATES, published 2013 by American Mathematical Society.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Fair. Books may have damage such as dents creases and folded pages. Some books may have writing or highlighting inside. Extras or accessories are not guaranteed. Digital codes and CDs are not tested and may not work.
Add this copy of A Bridge to Abstract Mathematics (Mathematical to cart. $41.92, like new condition, Sold by FirstClassBooks rated 4.0 out of 5 stars, ships from Little Rock, AR, UNITED STATES, published 2013 by Mathematical Association of America.
Add this copy of A Bridge to Abstract Mathematics (Mathematical to cart. $41.92, very good condition, Sold by FirstClassBooks rated 4.0 out of 5 stars, ships from Little Rock, AR, UNITED STATES, published 2013 by Mathematical Association of America.
Add this copy of A Bridge to Abstract Mathematics (Mathematical to cart. $50.42, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2013 by American Mathematical Society.