Mathematical Thinking: Problem-Solving and Proofs (2nd Edition) 2nd Edition by John P. D’Angelo (PDF)

Description

This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and Functions. Language and Proofs. Properties of Functions. Induction. PROPERTIES OF NUMBERS. Counting and Cardinality. Divisibility. Modular Arithmetic. The Rational Numbers. DISCRETE MATHEMATICS. Combinatorial Reasoning. Two Principles of Counting. Graph Theory. Recurrence Relations. CONTINUOUS MATHEMATICS. The Real Numbers. Sequences and Series. Continuity. Differentiation. Integration. The Complex Numbers. For anyone interested in learning how to understand and write mathematical proofs, or a reference for college professors and high school teachers of mathematics.

User’s Reviews

Editorial Reviews: From the Back Cover This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and Functions. Language and Proofs. Properties of Functions. Induction. PROPERTIES OF NUMBERS. Counting and Cardinality. Divisibility. Modular Arithmetic. The Rational Numbers. DISCRETE MATHEMATICS. Combinatorial Reasoning. Two Principles of Counting. Graph Theory. Recurrence Relations. CONTINUOUS MATHEMATICS. The Real Numbers. Sequences and Series. Continuity. Differentiation. Integration. The Complex Numbers. For anyone interested in learning how to understand and write mathematical proofs, or a reference for college professors and high school teachers of mathematics.

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

⭐Most of the chapters on discrete mathematics are very well-written with concise and fully explained proofs, although can’t say the same about the chapters on continuous mathematics. Has enough english explanations to merit a couch read, but not enough for a full self-study I’d like to think. Chapter on induction is so-so. Exercises are similar enough to examples that most can be done (although certain exercises with (!) require an unrealistic amount of prior knowledge/experience).All in all, this is a great book if you’re just transitioning from Calculus into proof-based mathematics and have a professor who is somewhat lenient about the exercises assigned.

⭐This book contain a little bit too much for someone who has no experience with discrete math or proofs. Overall, its decent.

⭐Good but the book is just too old to be such price.

⭐I was extremely disappointed by this book. This book is a required textbook at the University of Illinois at Urbana-Champaign, class MATH 347-348. I think the only reason the department has chosen this book is because John D’Angelo is a faculty at UIUC and the interests of the department are placed above the learning outcomes of the students. The book did not teach me anything, I ended up learning proof techniques on my own, using you-tube videos, professor’s office hours, and peer-led study group sessions. The only purpose the textbook served was a collection of exercises for Homework. If you are buying this book for self study, stay away from it.

⭐I originally purchased this book as a text for a math course and quite enjoyed the selections that we worked through in it. It has been about a year since I took that course and I still find myself going back for references in the book. It is a must have for someone who is interested in proofs or will be doing them on a semi-regular basis.

⭐The book was coming a loose from the center binder. It has a big orange sticker on the front of the cover that is hard to come off.

⭐Um, I had a really hard time understanding the way that this book was written. Maybe you need to be a true mathematician or a wizard to understand it. I did not like it.

⭐quick shipment and nice good, exactly the one required by my course. The content itself is hard though, if you are going to use this book for your course, probably you need to try hard to succeed in it.

⭐It likes to be easy to know and this product has a reliable and reliant.

⭐The cover and pages seem to be in excellent condition. Several pages on the inside have been tarnished by a dark stain, leaking through and damaging several pages. The cause of the stain is unidentifiable and is quite disgusting.

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