Proofs and Fundamentals (Undergraduate Texts in Mathematics)
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Proofs and Fundamentals: A First Course in Abstract Mathematics by Ethan D. Bloch
Please try again later. I have worked through Bloch's Proofs and Fundamentals the first edition and the book by Daniel Solow.
Bloch has written the best and clearest book for self-study of proofs. The back of the book has over 20 useful pages of Hints for Selected Exercises. For those reviewers who think Bloch is too wordy, perhaps he is if you already have an instructor in a class explaining everything to you. But if you are on your own, trying to learn by working through a book, Bloch's explanations are just right. This undergraduate book was required in my math class. Self teaching with this book is not impossible, but rather difficult if you do not know all the mathematical symbols.
One person found this helpful. The book is well structured and the topics are clearly explained, however the binding on my copy as well as the teacher's copy broke. Hopefully they will improve the quality of the binding in the next edition. This book was adequate in giving fundamentals however proofs might need a little work. If you are learning with a great advisor or professor you should have no problem however if the advisor or professor is not so great and you have to lean solely on the book I would recommend getting a supplementary book with better examples.
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I am currently selling the first edition of this book and I can also easily lease an online forum etext for the second edition if you are interested. While the first and second edition are the same for the first 3 pages, they are different quite a lot afterwards since the first edition had quite a lot of mistakes.
This book has NO solution guide or hints for excercises. The examples are obvious while the excercises are brutal. This book is designed for students who plan to live at their professors office hours. Sections written to help write proofs don't explain the setup and the why, Just the form.
This book has an innovative teaching approach that encourages the reader from the beginning to work independently on writing proofs and learning basics of the discipline.
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The text is written in a precise and enyojable way, and therefore recommend it for introductory courses, or for people interested in learning basic math topics. I found this book to be long and drawn out. The chapters are very wordy and dont really get to the point.
I picked this book up one day in the bookstore, started reading and left with it. I was a math major at one point in college, but I moved on for other reasons. These days most math programs offer courses such as "Introduction to Proofs. Now that I am back in college taking math courses again, I feel well prepared in my proof-oriented classes after going through about half of this book.
Proofs and Fundamentals: A First Course in Abstract Mathematics
The author does an excellent job of stressing the importance of proofs through language that is easy to understand. There is also a lot to read in the sense that concepts are explained and discussed in English. The exercises are adequate, although it would be better if more solutions were offered in the book only select ones are. I did most of the exercises and that is where the real learning took place. It's for those who have only taken computation-oriented classes who want to learn how to do basic proofs. I would recommend finding a copy and opening it up to see if it fits your style.
Anyone could learn from the beginning of this text, but it takes some mathematical sophistication to get through more advanced parts. The text seems technically precise clarity on the difference between range and codomain for instance and remains reader-friendly throughout. The author also does not hesitate on giving his opinions on how math proofs should be written. I liked the way that he emphasized writing proofs in complete sentences, and in keeping the scratch work and attempts at a proof separate from the proof itself.
Also, despite the language, rigor and mathematical symbolism are not sacrificed. At first glance I did not always see how the exercises related to the examples. After rereading the chapter, or trying out some different strategies, I usually was able to make sense of them. The exercises can sometimes be challenging in this manner, but that is not necessarily a bad thing.
They emphasize understanding rather than modeling. I found some satisfaction in struggling through some of the exercises upon figuring them out on my own.
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If you want to improve upon proof technique, I would look elsewhere. This book is definitely for those entering the world of mathematical proofs for the very first time. Unfortunately, there are not enough solutions of proofs in the back that you can compare to your own. See all 13 reviews. Vectrexgamer added it Aug 05, Felloherrera marked it as to-read Aug 12, Ed Ryan marked it as to-read Oct 01, Mig Palace added it Jan 04, Chris marked it as to-read Feb 12, Hasan marked it as to-read Jan 25, Nitin CR added it Mar 25, Santiago Gomez added it May 09, Ryan Smith marked it as to-read Aug 10, Cal marked it as to-read Sep 10, Cenker Akman marked it as to-read Dec 14, Franco marked it as to-read Feb 23, David Moreno is currently reading it Jan 31, BookDB marked it as to-read Oct 30, Charlotte marked it as to-read Nov 24, Bryce is currently reading it Nov 26, Jan marked it as to-read Dec 13, Paul Anthony marked it as to-read Jul 20, Sinan Apak marked it as to-read Nov 13, Ahmed Sabry Shalaby marked it as to-read Nov 29, Patrick marked it as to-read May 10, Jhoan Martinez marked it as to-read Aug 29, Sai Tej Paruchuri marked it as to-read Nov 17, Andreas added it Nov 18, Amadeo added it Apr 13, Manuel Monroy Correa marked it as to-read Mar 02, Thomas marked it as to-read Apr 18, There are no discussion topics on this book yet.
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