Bridge to abstract mathematics: Mathematical proof and structures 0th Edition by Ronald P Morash (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐When I took a so-called “bridge” class, which is a pre-requisite to more advanced math courses, I suffered. The text the instructor chose was VERY difficult, yet it was better than two others I had seen previously.I’m using Prof. Morash’s book to review before I take more classes, and it’s better than wonderful. He’s not too snobby to actually explain concepts, which (apparently) a lot of math types don’t want to do.There are lots of “Intro to Set Theory and Proofs” books now on the market, yet none I have used comes close to this one. (And, believe me, I bought several texts through Amazon to try to fully understand that class.)My copy of Morash’s book is older than the one pictured here, which has a 1991 publication date, yet I don’t see any newer editions. Not that they need to change anything, just keep publishing it, please.And you math instructors out there, get a grip! A book being new doesn’t make it good.My copy was published by Random House, with a 1987 date. So – whomever has the pub. rights, do students a favor and don’t let this book slip away into Out-of-Print anonymity.ADDENDUM: If you can deal with not having an actual book in your hand, the first edition of this book is available for direct (free) download at: […]And, P.S. FYI, I’m not eighteen. I’m a “mature” adult (as they currently say) who has two degrees and works full-time in a non-math-related job. I’m taking math classes in preparation for a career change.

⭐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.ContentsBook One. The Foundation: Sets, Logic, and Mathematical Argument1.Sets2.Logic, part I: the propositional calculus2.Logic, part II: the predicate calculus4.Elementary applications of logic5.Methods of mathematical proof, part I: elementary methods6.Methods of mathematical proof, part II: advanced methodsBook Two. Bridging Topics: Relations, Functions, and Number Systems7.Relations, part I: equivalence relations and partial orderings8.Relations, part II: functions and mappings9.Properties of the number systems of undergraduate mathematics10.Construction of the number systems of undergraduate mathematics

⭐I concur with the other reviewers: this is a clear, helpful text. Many other math books present complicated proofs without much explanation of what is actually being done, but this book has simple proofs that demonstrate proof methods without having to deal at the same time with difficult mathematics.

⭐Thanks!

⭐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.

⭐This is my first review even though I’ve been using Amazon.com for years. I had to write because this books is understandable and entertaining (for a math book). It’s as though he’s having a conversation with the reader. After being confused by an intro math theory class, I picked up this book and Professor Morash has helped me immensely.

⭐Simply a must for any upper division math student or any one heading into rigorous theory.

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