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Sets, Functions, and Logic: An Introduction to Abstract Mathematics
Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students.
Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead.
Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read…and enjoy…and learn from.
About the Author
Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,.
Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.
Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead.
Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read…and enjoy…and learn from.
About the Author
Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,.
Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.
- GenresMathematicsLogic
153 pages, Kindle Edition
First published January 1, 1981
6 people are currently reading
69 people want to read
About the author
Keith Devlin
85 books166 followersDr. Keith Devlin is a co-founder and Executive Director of the university's H-STAR institute, a Consulting Professor in the Department of Mathematics, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 26 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. He is "the Math Guy" on National Public Radio.
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Displaying 1 - 5 of 5 reviews
May 3, 2013
I approached this book with a little trepidation as it is some time since I have done any real mathematics. However, I am doing a philosophy degree I wanted to improve my use of logic and understanding of set theory. It is not exactly a light read, but that would not be expected. It is a well structured, if brief, introduction to sets, functions and logic.
Take time to read it with care and go through the exercises and the book does what it sets out to achieve. The author has kept it short. It reflects his experience teaching mathematics as the contents are clear and sufficiently comprehensive. Choose this if you are a reasonably confident student who wants a friendly, but concise introduction to these topics - or if you are looking for a refresher to bring stale knowledge back to life. If you are really starting from zero knowledge you may find this a little too concise.
The book is targeted at those who have done calculus and are moving onto the next level of mathematics. It is a long time (over 20 years) since I did any calculus, and yet I found this book reasonably straightforward to follow and did not find myself having to recall much from those distant times!
It would have been better for me if the exercises had answers. The author leaves these out, reasoning this is not a book for individual study, but to be used as part of a course and as such you should discuss your answers with colleagues and tutors. However, this is not a fatal problem and I used the book successfully for independent study.
Take time to read it with care and go through the exercises and the book does what it sets out to achieve. The author has kept it short. It reflects his experience teaching mathematics as the contents are clear and sufficiently comprehensive. Choose this if you are a reasonably confident student who wants a friendly, but concise introduction to these topics - or if you are looking for a refresher to bring stale knowledge back to life. If you are really starting from zero knowledge you may find this a little too concise.
The book is targeted at those who have done calculus and are moving onto the next level of mathematics. It is a long time (over 20 years) since I did any calculus, and yet I found this book reasonably straightforward to follow and did not find myself having to recall much from those distant times!
It would have been better for me if the exercises had answers. The author leaves these out, reasoning this is not a book for individual study, but to be used as part of a course and as such you should discuss your answers with colleagues and tutors. However, this is not a fatal problem and I used the book successfully for independent study.
December 13, 2020
Sets, Functions, and Logic is a lovely short book written for students preparing to attend Pure Mathematics classes. It's supposed to be a transition between calculus and courses on Abstract Algebra, Analysis, Math Fundamentals.
The first chapter provides an overview of Contemporary Math, presenting some historical perspective.
The second chapter introduces math notation very gently. Some concepts from mathematical logic are presented in a friendly way, as well as a raw account of mathematical proofs. The topic on negation and quantifiers is particularly good.
The third chapter deals with the basics of Set Theory, and it is straightforward and objective. Devin adds a section on the history of set theory, which is enlightening.
The fourth chapter focuses on Functions. It also adds discussions on denumerability and uncountability. Since readers are students making a transition to Pure Mathematics, those topics are a bit harder to grasp. The reader can find a clearer presentation of those topics in Barbara Partee, Alice ter Meulen, and Robert E. Wall’s book Mathematical Methods in Linguistics.
Finally, the fifth and last chapter is about Relations. Devlin chose to present Functions before the chapter on Relation, which is an unusual choice. The section on Upper Bounds and completeness is the most challenging topic in the chapter.
Something to consider: this book isn't intended for self-study. It provides no answers to exercises. Exercises are used as a tool to sharpen readers' math skills and develop some concepts. Readers need to study in a group and consult the instructor for feedback.
Overall, this book is an excellent introductory book. However, the reader will probably need other introductory books to grasp the content fully. How to prove it, by Daniel Velleman, would be an excellent complementary source.
The first chapter provides an overview of Contemporary Math, presenting some historical perspective.
The second chapter introduces math notation very gently. Some concepts from mathematical logic are presented in a friendly way, as well as a raw account of mathematical proofs. The topic on negation and quantifiers is particularly good.
The third chapter deals with the basics of Set Theory, and it is straightforward and objective. Devin adds a section on the history of set theory, which is enlightening.
The fourth chapter focuses on Functions. It also adds discussions on denumerability and uncountability. Since readers are students making a transition to Pure Mathematics, those topics are a bit harder to grasp. The reader can find a clearer presentation of those topics in Barbara Partee, Alice ter Meulen, and Robert E. Wall’s book Mathematical Methods in Linguistics.
Finally, the fifth and last chapter is about Relations. Devlin chose to present Functions before the chapter on Relation, which is an unusual choice. The section on Upper Bounds and completeness is the most challenging topic in the chapter.
Something to consider: this book isn't intended for self-study. It provides no answers to exercises. Exercises are used as a tool to sharpen readers' math skills and develop some concepts. Readers need to study in a group and consult the instructor for feedback.
Overall, this book is an excellent introductory book. However, the reader will probably need other introductory books to grasp the content fully. How to prove it, by Daniel Velleman, would be an excellent complementary source.
December 31, 2017
2.5 stars
Not much new here. The book was intended for college students between calculus and analysis. I should have read it back in the 60s
Not much new here. The book was intended for college students between calculus and analysis. I should have read it back in the 60s
July 12, 2020
A decent book. (∃ Better book) ∧ (∃ Worse book) than this
June 16, 2025
Excellent primer for learning proof-based logic and abstract mathematics. Great for the student entering mathematical analysis.
The author does an impeccable job of demystifying the mathematical basis by incorporating real world explanations in-line with the text.
This book changed the way I think, and has had an immeasurable impact on my studies.
Highly recommend!
The author does an impeccable job of demystifying the mathematical basis by incorporating real world explanations in-line with the text.
This book changed the way I think, and has had an immeasurable impact on my studies.
Highly recommend!
Displaying 1 - 5 of 5 reviews