An Introduction to Mathematical Reasoning
by Peter J. Eccles · first published 1997
79% recommend21% neutral
Why HN recommends it
A short, example-driven introduction to mathematical proofs, logic, sets and functions, showing how mathematicians actually reason. Suited to students and self-learners starting proof-based math.
Summarised by Claude from recommending comments
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
Mentions per year
What Hacker News says
Related books
2008–2022Problem-solving strategies
Arthur Engel
Recommended by 9 · mentioned by 99 recommend · 9 mention9 recommend · 99 recommend
2009–2024Maths
Jenny Olive
Recommended by 7 · mentioned by 87 recommend · 8 mention7 recommend · 87 recommend
2009–2023Chapter Zero
Carol Schumacher
Recommended by 5 · mentioned by 75 recommend · 7 mention5 recommend · 75 recommend
Book of Proof
Richard Hammack
Recommended by 54 · mentioned by 6654 recommend · 66 mention54 recommend · 6654 recommend
2013–2026How to think like a mathematician
Kevin Houston
Recommended by 8 · mentioned by 108 recommend · 10 mention8 recommend · 108 recommend
2010–2026Understanding Analysis
Stephen Abbott
Recommended by 31 · mentioned by 3831 recommend · 38 mention31 recommend · 3831 recommend
2008–2025Mathematics
Andrei Nikolaevich Kolmogorov, M. A. Lavrentʹev, A.D Alexsandrov
Recommended by 12 · mentioned by 1512 recommend · 15 mention12 recommend · 1512 recommend
2007–2026How to prove it
Daniel J. Velleman
Recommended by 78 · mentioned by 10478 recommend · 104 mention78 recommend · 10478 recommend
…https://www.amazon.com/Mathematics-Million-Master-Magic-Numb... Of the two I prefered Kline's book but they are both good, albeit a bit heavy on geometery as that was a big focus of early math research. Another great starting point is "Book of Proofs" and "Introduction to Mathematical Reasoning" to give you a deeper sense of how to approach the subject. https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472... https://www.amazon.com/Introduction-Mathematical-Reasoning-N... From there…
on “Georgia Tech's free math textbook collective” ↗Atlas Shrugged, The Fountainhead, Stranger in a Strange Land, The Rules of Life, Catch-22, 1984, Brave New World, and An Introduction to Mathematical Reasoning (by Peter Eccles)
on “Books That Changed My Life” ↗…applies to more advanced concepts, explains Rings/Fields and has a really good introduction to Logic. I wish this book existed 5 years ago when I started http://press.princeton.edu/titles/10697.html "An Introduction to Mathematical Reasoning" by Eccles is short and excellent. You can also download the lecture notes here from CMU's course on proofs http://math.cmu.edu/~svasey/concepts-summer-1-2014/ and try some of the homework if you want…
on “Ask HN: Which areas of math are practical to programming/algorithms and why?” ↗…things are omitted. once you have that knowledge it makes sense, but before that it seems like giant leaps are being taken without a rigorous line of reasoning between them. to answer op's question: "an introduction to mathematical reasoning" by peter eccles was helpful for me. it's basically an expanded version of what you'll find at the start of many intro cs/math courses. another option, if sets, number theory and such are confusing to…
on “Ask HN: How to learn mathematical proofs from scratch?” ↗Another book to read that I recommend to all my friends: An Introduction to Mathematical Reasoning: Numbers, Sets and Functions by Peter J. Eccles. You can find it on Amazon.
on “A course of pure mathematics, by G.H. Hardy (full text online)” ↗Run, don't walk, and get "An Introduction to Mathematical Reasoning"by Peter Eccles. That will open your eyes to mathematics, as done by mathematicians. After that, anything by Serge Lang. He is a first-rate mathematician and a fine educator. A master of mathematical…
on “Ask HN: Math books like SICP?” ↗…chapters of 'The Art and Craft of Problem Solving' by Zeitz and 'How to Solve it' by Polya. The Zeitz book specifically refers to the issues in abstract word problems and strategies for understanding them. 'Introduction to Mathematical Reasoning' by Eccles was another great book to explain the meaning of mathematical statements and how to think like a mathematician. If you read some of those, and want to learn more math, start with functional…
on “University of Tokyo Graduate School Entrance Exam – Mathematics (2016) [pdf]” ↗…Concepts of Modern Mathematics by Stewart https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo... Dover Version with Google Preview Button http://store.doverpublications.com/0486284247.html Introduction to Mathematical Reasoning: Numbers, Sets, and Functions https://www.amazon.com/Introduction-Mathematical-Reasoning-N... How to Prove It by Velleman https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/...
on “Ask HN: How to self-learn math?” ↗…solely with learning the art of mathematical proofs. I had an excellent professor, so I can't really say how much this book helps with the learning process when used by itself, but we were assigned An Introduction to Mathematical Reasoning: Numbers, Sets and Functions, by Peter J. Eccles. Might be a good place to start!
on “The Feynman Lectures on Physics: Algebra (1963)” ↗I've personally read An Introduction to Mathematical Reasoning: Numbers, Sets and Functions Paperback by Peter Eccles and Chapter Zero by Carol Schumacher and would recommend them both. Sadly, this is not an easy thing to learn and requires a lot of work and most…
on “Ask HN: What is the best way to learn proof based math without a teacher?” ↗"An Introduction to Mathematical Reasoning" by Peter J Eccels. Teaches the vocabulary of mathematics, just the basics you need to think like a mathematician, not a mathematics user like most science texts. "How To Solve It" George Polya. Heurists…
on “Ask HN: Best Mathematics book for complete noobie?” ↗If you truely want a really great, small, book, purchase Peter J. Eccle's An Introduction to Mathematical Reasoning. http://books.google.com/books?id=ImCSX_gm40oC&dq=an+intr...
on “Ask YC: Math problems” ↗…recommend a couple of books from that thread: http://www.springer.com/physics/book/978-0-306-45036-5 http://www.amazon.com/Mathematics-Short-Introduction-Timothy... I agree with the recommendation of An Introduction to Mathematical Reasoning in this thread. Another participant has already recommended my favorite for background reading, Concepts of Modern Mathematics by Ian Stewart. http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...…
on “Ask HN: Best Mathematics book for complete noobie?” ↗…examples in mind is very useful! Basically I would try to round out the basic pure math stuff for sure, but I think youre better equipped than most. Another intro book I thought of was Peter Eccle's introduction to mathematical reasoning. Might be worth looking at. If you want a nice leisurely introduction to groups Nathan Carter's Visual group theory is nice. I got a lot of use out of the princeton encyclopedias of math. Dont expect…
on “A Programmer’s Introduction to Mathematics” ↗…someone else here on HN put it, I'd prefer them to "be written by mathematicians, for mathematicians". 4. Good exercises with solutions. I've already found a few suggestions in other threads: * An Introduction to Mathematical Reasoning: Numbers, Sets and Functions (Eccles) * How to Solve it: A New Aspect of Mathematical Method (Conway, Polya) * Calculus (Spivak) * Linear Algebra Done Right (Axler) Can I read those in order before…
on “Ask HN: Math books for a CS autodidact?” ↗