A Transition to Advanced Mathematics 7th Edition by Douglas Smith (PDF)

Description

A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically–to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students’ ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they’ll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems.

User’s Reviews

Editorial Reviews: About the Author The authors are the leaders in this course area. They decided to write this text based upon a successful transition course that Richard St. Andre developed at Central Michigan University in the early 1980s. This was the first text on the market for a transition to advanced mathematics course and it has remained at the top as the leading text in the market. Douglas Smith is Professor of Mathematics at the University of North Carolina at Wilmington. Dr. Smith’s fields of interest include Combinatorics / Design Theory (Team Tournaments, Latin Squares, and applications), Mathematical Logic, Set Theory, and Collegiate Mathematics Education.Maurice Eggen is Professor of Computer Science at Trinity University. Dr. Eggen’s research areas include Parallel and Distributed Processing, Numerical Methods, Algorithm Design, and Functional Programming.Richard St. Andre is Associate Dean of the College of Science and Technology at Central Michigan University. Dr. St. Andre’s teaching interests are quite diverse with a particular interest in lower division service courses in both mathematics and computer science.

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

⭐Three stars seems a bit low, but four definitely would be too high for this book. There seem to be a lot of reviews here of the fifth and sixth editions; I can’t speak to them because my copy is the seventh edition. (It would seem to me that reviews for the various edition should be separate, since problems with one might not be in another, but Amazon, in their infinite wisdom, considers all editions to be the same book and lumps all the reviews in together.)On the good side, this book seems to have a good variety of exercises to work, from easy to extremely challenging; unlike some reviewers, I consider this a feature, not a bug. And if there aren’t solutions to all (or even half) of the problems, it is a fair defense to point out that in a book of this sort, there may be many possible solutions to the same problem, and it would be doing students a disservice to provide “the” solution. Still, I’ll agree with the reviewers who complain that the “the second half of this proof is left as an exercise for the student” copout is the lazy author’s way out.The real problem with this book, however, is that even more so than most math textbooks (which is saying something) the explanations are impenetrable for someone who isn’t already fluent in the language of math. I was fortunate enough to have a good prof, who was able to explain concepts clearly and with a translation to standard english; as such, concepts that were impenetrable when I read them prior to class made perfect sense by the time class was finished. But not everyone is so fortunate; the value of a math textbook is that if the student doesn’t understand something in the lecture, he/she can supplement the lecture with the textbook. My suspicion is that anyone trying to do that with this book would be left at least as baffled as they were before reading it.And no, it doesn’t help that it’s outrageously overpriced.

⭐Consider this book your first investment in your mathematical education. While its a great read, its not worth the price, and if you’re buying it anyways, chances are you were sucked into it by university requirement. While this might be the case, its still a great reference for introductory logic, proof writing, how to approach proofs, and theories and axioms for topics in mathematics. After reading it, you’ll definitely feel stronger in mathematics, but again, not worth the price. Also the extra chapters on cardinality, introductory algebra, and introductory analysis, aren’t that enlightening considering specific texts for those subjects combined is still less than the cost of this textbook. The problem is there is no decent undergraduate level textbook that incorporates all of the skills to write proofs, while still learning mathematics, hence the ability of the publisher to sell this at such a high price.As for the people that hate this book, my first time reading it for a class was a struggle, but I recommend for those who don’t need it for their studies to try reading it during a break. Its much easier to work through questions and issues when you have an unlimited amount of time to thoroughly read and practice the material.I swear I would give it a 4 out of 5 if the book was a $75. If you have to get it for class, better luck next time. If you want it for personal reading to gain a better understanding of mathematics, and to add it to your personal library, consider previous editions at a more reasonable price.

⭐We’ve been using this in our Introduction to Mathematical Proofs class (an upper-level undergraduate math class). I was a little nervous after seeing so many bad reviews here, but it’s been a fine textbook. It’s easy to learn the material from the book, and the question/problem sets are useful too. I don’t have any other books of this type to compare it to, of course, but the layout of the text and material is clear, with definitions and properties given as needed.

⭐I had to use this book for my proofs course in college. Since this is a introductory proof course, they should have done a more thorough job of explaining concepts and guiding the student. What I mean by that is, they’ll introduce a theorem, but won’t prove it. Instead, the proof will be left as a exercise for the student. Then another problem will reference that answer, but there is no answer in the back of the book! I utilized my professor’s office hours which gave me more detailed explanations and guidance. I would advise that for anyone who is required to use this book for their class.With regard to the solutions, not even all of the odd numbered solutions are given in the back, and again, I had to consult others to verify my answers.Concepts seemed solid for the most part, but more work is necessary for the next edition.

⭐With all due respects to all the Math books I’ve learned in the past 21 years, this book is one of the least benefitial book ever written.1) The theorem is poorly proofed and illustrated. Don’t even bother talking about explaining here because there’s only statements instead of explanation.2) Exercises are so hard, there are problems you don’t even understand the questions. Plus this book is so ridiculous, it doesn’t give the answer to all the odd problems. Some chapter, there are like 2, 3 answers to the 20 problems they give out.After all we’re all mathematician reading this book to understand or learn about the theorem in the book. But if there is not anything to explain why the theorem is what it is, then I question myself, WHY YOU EVEN BOTHER OWN THIS BOOK if it doesn’t help you learn at all????????DO NOT BUY IT, it’s a waste of money!

⭐I was very satisfied with the overall condition of the book for such an economical price; The cover was not damaged or faded and there were no marks, no torn pages and no dog ears. Books R Good provided excellent service and responded quickly to my emails. In spite of shipping difficulties encountered, Books R Good shipped the book 3 times at their own expense. I cannot recommend this particular purveyor of books highly enough. It is a pleasure to do business with Books R Good.

⭐The book was in good condition. It’s a dual-colour edition, the way it looked in the ebook version. Good quality pages. I have yet to read it, so I cannot comment on the content of the book.

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