A transition to advanced mathematics
by Smith, Douglas · first published 1983
88% recommend12% neutral
Why HN recommends it
Bridges high-school math to reading and writing proofs, starting from first principles with many simple examples. Suits self-learners and undergraduates in an intro-to-proofs course.
Summarised by Claude from recommending comments
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There is some distance from this to antenna design, electromagnetism, etc, but I think you have to be fluent in proofs to actually follow along on those. Math is a big subject; ymmv. A Transition to Advanced Mathematics by Douglas Smith (Author), Maurice Eggen (Author), Richard St. Andre (Author) ISBN-13: 978-0495562023 ISBN-10: 0495562025 Edition: 7th It shows up on Abebooks which could help with the price. It's…
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗"A Transition to Advanced Mathematics" (0-534-38214-2) at the end of my 6th grade school year, just as summer was starting. I would give this book to myself because it's a bridge between finishing the final class in high school math and…
on “If you could give a book to your younger self, what would it be?” ↗…Approach 2. Elements of Set Theory - Enderton 2a. Naive Set Theory - Halmos 3. Foundations of Analysis - Landau 4. Basic Mathematics - Lang 5. Principles of Mathematics - Allendoerfer & Oakley 6. A Transition to Advanced Mathematics 6a. Concept of Modern Mathematics - Stewart 7. Calculus - Apostol or Spivak Don't skip any
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗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. Elementary Discrete Math books make…
on “A Software Engineer’s Adventures in Learning Mathematics” ↗…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... Learning…
on “Ask HN: Resources on how to improve abstract thinking skills?” ↗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?” ↗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 reading was Book of Proof, it's…
on “Ask HN: Have you been able to teach yourself advanced mathematics as an adult?” ↗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?” ↗…Proofs: Just pick one of these that speaks to you the most. All three are good. Discrete Mathematics with Applications - Epp Discrete Mathematics and Its Applications - Rosen Mathematical Proofs: A Transition to Advanced Mathematics - Chartrand, et al. Abstract Algebra: How to Think about Abstract Algebra - Alcock Abstract Algebra - Pinter Abstract Algebra: A First Course - Saracino Algebra - Artin Abstract Algebra - Herstein…
on “Physics Student Earns PhD at Age 89” ↗I would recommend coming to terms with "A Transition To Advanced Mathematics". Once you feel like you can plumb Cantor's Diagonalization without nausea :), then read on Godel. GEB is excellent but frothy ( not pointed and a slog ) but is worth it for other reasons. I think that…
on “Gödel and the limits of logic” ↗…reorder some class offerings to improve the "throughput" of a math program. I can divide my math education career into before and after the semester I took the course based on Smith/Eggen/St. Andre's "A transition To Advanced Mathematics." Mathematics is proofs, and knowing how to speak them is completely critical. After that course, I could do mathematics much more easily than before. I feel that this book is fundamental to learning…
on “Why does it take so long to learn mathematics?” ↗…course: https://www.udacity.com/course/viewer#!/c-ma008 There is also a good introductory class on Statistics: https://www.udacity.com/course/viewer#!/c-st101 After these classes, hopefully, reading "Transition to Advanced Mathematics" will not be a pain.
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗The course that made it for me was based on "Transition To Advanced Mathematics" by Egger , Smith and St. Andre. Just learning the actual proofs ( beyond calculus style proofs ) techniques was a big leg up, especially induction and contradiction.
on “Top Myths About Teaching Computer Science (2015)” ↗I'm going through the books - 1.How to Prove It: A Structured Approach; 2.Mathematical Proofs: A Transition to Advanced Mathematics The are very different books on how to read/write proofs, but complement each other nicely. On top of that, I'm doing though few elementary logic and set theory books, they also have what I would call…
on “Ask HN: How can I learn to read mathematical notation?” ↗I used the book “A Transition to Advanced Mathematics” in undergraduate and I loved it. Many but not all exercises have answers in the back
on “Classic Mathematics Books for Lifelong Learners” ↗