Mathematical proofs
by Gary Chartrand, Albert D. Polimeni, Zhang, Ping, Ping Zhang · first published 2002
85% recommend15% neutral
Why HN recommends it
Starts from first principles with many simple examples, teaching how to structure a proof and use set notation. Suits self-learners and students bridging to upper-level math; only high school algebra is needed.
Summarised by Claude from recommending comments
Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. Written in a student-friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such as number theory, combinatorics, and calculus. The exercises receive consistent praise from users for their thoughtfulness and creativity. They help students progress from understanding and
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…to get you started: Book of Proof by Richard Hammack: https://www.people.vcu.edu/~rhammack/BookOfProof/ Discrete Math by Susanna Epp: https://www.amazon.com/Discrete-Mathematics-Applications-Sus... Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al: https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... How to Think About Analysis by Lara Alcock: https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0...…
on “Ask HN: Resources on how to improve abstract thinking skills?” ↗…Chartrand et al, [3] How to Think about Analysis by Lara Alcock, [4] Learning to Reason by Nancy Rodgers [1] https://books.google.com/books?id=PPc_2qUhXrAC&pg=PA1&source... [2] https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... [3] https://books.google.com/books?id=n0tuBAAAQBAJ&pg=PA4&source... [4] https://books.google.com/books?id=J9RLuhDRWGQC&pg=PR6&source... If you're on a budget, check out the free…
on “Ask HN: Any resources to learn the fundamentals of critical thinking?” ↗…plan on going to graduate school later on. For a coverage of the material that emphasizes a proof-based approach, you can supplement your reading with a book on general proof strategies, such as: 1. Mathematical Proofs by Chartrand, Polmeni, Zhang 2. How to Prove It by Daniel Velleman The first book by Chartrand et al is more of a traditional textbook and gives a comprehensive introduction to set theory in the context…
on “Ask HN: Resources to learn Discrete Mathematics?” ↗Read an introduction to proofs oriented book such as Book of Proof or my personal favorite: https://www.amazon.ca/Mathematical-Proofs-Transition-Advance...
on “How MIT OpenCourseWare transformed a learner's life” ↗Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand Polimeni and Zhang. This was the textbook used in my intro to proofs course and it was fantastic. Worth the steep price. Another good one that was optional…
on “Ask HN: Have you been able to teach yourself advanced mathematics as an adult?” ↗…by Susanna Epp https://www.amazon.com/Discrete-Mathematics-Applications-Sus... [2] Pure Mathematics for Beginners by Steve Warner https://www.amazon.com/Pure-Mathematics-Beginners-Rigorous-I... [3] Mathematical Proofs by Gary Chartrand et al https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... [4] Data Structures and Algorithms: Concepts, Techniques and Applications by G.A.V. Pai https://www.amazon.com/gp/product/0070699577/ref=ppx_yo_dt_b...…
on “Ask HN: What's Wrong with Me?” ↗First read https://artofproblemsolving.com/news/articles/avoid-the-calc... By one of my early mathematics tutors in San Diego math circle Then buy something like: Mathematical Proofs: A Transition to Advanced Mathematics (3rd Edition) (Featured Titles for Transition to Advanced Mathematics) https://www.amazon.com/dp/0321797094/ref=cm_sw_r_cp_api_i_K4...
on “Ask HN: Recommend a maths book for a teenager?” ↗…some examples of the kinds of books I mean, and you can find others by following Amazon recommendations from those: http://www.amazon.com/Nuts-Bolts-Proofs-Fourth-Edition/dp/01... http://www.amazon.com/Mathematical-Proofs-Transition-Advance... With math textbooks especially, it pays to look for a previous edition, as the current edition can be ridiculously expensive, and the previous edition might be only 20% of the price,…
on “Great books about mathematics” ↗…which math is usually taken in the US is not the optimal one! I recently took calc-1,2,3 and linear algebra through my local community college, and then started working my way through a wonderful book on mathematical proofs:(http://www.amazon.com/Mathematical-Proofs-Transition-Advance...), as preparation for working on higher level math. I would now argue that being able to understand and write proofs is a (the?) key mathematical…
on “A Software Engineer’s Adventures in Learning Mathematics” ↗Not an overall answer, but some parts of an answer: - Notes on Discrete Mathematics (James Aspnes) - Mathematical Proofs (Chartrand, Polimeni et al) - TrevTutor videos on YouTube - Professor Leonard videos on YouTube
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗…foundational it is to really understanding what you're looking at when it comes to math. If you're interested in learning how proofs work, and you've missed out on a course like I did, I'd recommend "Mathematical Proofs", by Albert D. Polimeni, Gary Chartrand, and Ping Zhang. You should be able to find a paperback for some bucks. Usually mathematics texts are thick and difficult to follow for me, I'm not the brightest,…
on “Ask HN: Why is math often taught without explanation?” ↗…etc. Obviously, such books don't get carried away by ditching epsilon-delta/balls arguments in favor of more general open sets to define continuity, for example. One such book that comes to mind is "Mathematical Proofs: A Transition to Advanced Mathematics" by Chartrand, Polimeni, Zhang. I think the best book in this introductory genre is "Book Of Proof" by Richard Hammack. It's freely available. I see the latest edition…
on “Ask HN: The book that did it for you in math and/or CS?” ↗If anyone is interested in how mathematicians think and do proofs there are many helpful books. For example, Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand and others. How to Prove It: A Structured Approach by Velleman. Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers.…
on “A Software Engineer’s Adventures in Learning Mathematics” ↗…anything above high school algebra to learn proofs, so you don't have to wait, you can just get started now! My favorite book, that I strongly recommend despite the high price of around $100 in the US is "Mathematical Proofs" by Chartrand. You can get an international copy off eBay for around $45. If you're weak on basic algebra etc, then you should instead start with "engineering mathematics" by Stroud, which has a foundations…
on “Georgia Tech's free math textbook collective” ↗I can second the Chartrand book (I believe you mean "Mathematical Proofs: A Transition to Advanced Mathematics"). I used this book in a "bridge" class and loved it; it really starts from first principles and gives you a lot of simple examples that you can build on.
on “Ask HN: Resources to learn real analysis?” ↗