This text is designed for students who are preparing to take a post-calculus abstract algebra and analysis course. Morash concentrates on providing students with the basic tools (sets, logic and proof techniques) needed for advanced study in mathematics. The first six chapters of the text are devoted to these basics, and these topics are reinforced throughout the remainder of the text. Morash guides students through the transition from a calculus-level courses upper-level courses that have significant abstract mathematical content.
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6 of 6 people found the following review helpful:
5.0 out of 5 stars
Premier Text on Proofing!,
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This review is from: Bridge to Abstract Mathematics: Mathematical Proof and Structures (International Series in Pure and Applied Mathematics) (Hardcover)
I am currently taking a 300 level course on proofing and Bridge to Abstract Mathematics is one of the required texts. This book is an excellent introduction to proofing. There is a huge intellectual leap between 200 level and 300 level proof based math courses that is often very difficult for college math students to make. This text does an wonderful job of bridging that gap. Many teachers and curriculum's in proof based courses expect students to somehow magically pick up the art and skill of proofing on their own. Morash takes the time to show the logic and art behind proofing that teachers often don't or can't teach. (Because they consider it trivial or they don't really understand it themselves!) The logic sections can be boring if you're not into truth tables but it is infinitely useful material if you want to learn to proof well. I've seen other books on proofing and they don't hold a candle to this one. Many of my math profs. recommend this book because it is the one they learned from when they were undergrads.
5 of 5 people found the following review helpful:
5.0 out of 5 stars
Best intro to true mathematics I've ever read or seen,
By Todd Riggs (Riverside, California, USA) - See all my reviews
This review is from: Bridge to Abstract Mathematics: Mathematical Proof and Structures (International Series in Pure and Applied Mathematics) (Hardcover)
Simply a must for any upper division math student or any one heading into rigorous theory.
4 of 4 people found the following review helpful:
5.0 out of 5 stars
Best book on the subject in my collection,
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This review is from: Bridge to Abstract Mathematics: Mathematical Proof and Structures (International Series in Pure and Applied Mathematics) (Hardcover)
I kept buying books on the subject and none of them were exactly what I was looking for. Then I found this book and realized that it was the best. If you are looking for good, clear explanations, you will find them here.
Contents Book One. The Foundation: Sets, Logic, and Mathematical Argument 1.Sets 2.Logic, part I: the propositional calculus 2.Logic, part II: the predicate calculus 4.Elementary applications of logic 5.Methods of mathematical proof, part I: elementary methods 6.Methods of mathematical proof, part II: advanced methods Book Two. Bridging Topics: Relations, Functions, and Number Systems 7.Relations, part I: equivalence relations and partial orderings 8.Relations, part II: functions and mappings 9.Properties of the number systems of undergraduate mathematics 10.Construction of the number systems of undergraduate mathematics
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