Basic Mathematics
by Serge Lang · first published 1971
81% recommend19% neutral
Why HN recommends it
Rigorous, proof-minded refresher on high school math that builds from first principles, with some beauty along the way. Suits self-learners relearning math before calculus or pure math.
Summarised by Claude from recommending comments
This is a text in basic mathematics with multiple uses for either high school or college level courses. Readers will get a firm foundation in basic principles of mathematics which are necessary to know in order to go ahead in calculus, linear algebra or other topics. The subject matter is clearly covered and the author develops concepts so the reader can see how one subject matter can relate and grow into another.
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Ive never read this book in particular, but had a similar experience with another book (Serge Lang, Basic Mathematics) that changed my life trajectory. If you find this stuff remotely interesting please give it a go! Math is really wonderful! Learning math in some prescribed way (book or sequence of books) is the mathematics…
on “A Programmer’s Introduction to Mathematics” ↗…the steps to get the right answer, get my A, forget it all, and wait for whatever was coming next. Years later I go straight back to the beginning and figure everything out, starting with Serge Lang's Basic Mathematics. I didn't even know where the Pythagorean Theorem came from, and when I learned it the second time around, it was damn beautiful. my advice is to go back all the way to the beginning and get a book written…
on “How I faced my fears and learned to be good at math” ↗…background in math and want to get up to speed before going into calculus and beyond, I have 2 suggestions. 1) Lial's Basic College Math[1] is adequate and will get you up to speed. 2) Serge Lang's "Basic Mathematics" is great and will cover all you need to go into a rigorous theory based college math class. [1] http://www.amazon.com/s?ie=UTF8&field-keywords=lials%20basic... The editions basically the same... pick…
on “How I Rewired My Brain to Become Fluent in Math” ↗…you were younger. This is... not the majority view? But I am attempting to teach myself math right now, as an older (late 30s) person with a job. The best tools I've found are Serge Lang's books (Basic Mathematics) and Khan Academy. I would be super interested in recommendations for better tools and resources; Money isn't really an object, at least at student scale, but time is limited. Khan academy, for me,…
on “The World Might Be Better Off Without College for Everyone” ↗…very detrimental towards doing mathematics. Without further details, it's hard to know what your current level is. Most math bootcamps cover algebra and calculus. A great high school level one is: * Basic Mathematics by Lang * Calculus Made Easy by Thompson If that is too simplistic, try a Math 55 like approach: * Linear Algebra Done Right by Axler * Principles of Mathematical Analysis by Rudin You can replace…
on “Any recommended crash course on Maths?” ↗I personally find Serge Lang's "Basic Mathematics" to be super useful in explaining the "why" of a particular formula in pre-college level math, as most books at my current level just seem to say "memorize this" He has an explanation of why x^0 is…
on “Just teach my kid the math” ↗Two books: Basic Mathematics by Serge Lang and Calculus Made Easy by Silvanus P Thompson.
on “The Best Textbooks on Every Subject” ↗There's Serge Lang's Basic Mathematics which discusses algebra and geometry, including a bit of linear algebra. Introduction to Linear Algebra, by the same author is a bit deeper. Those are the textbooks I would pair with Calculus Made Easy.…
on “Calculus Made Easy (1910)” ↗…http://www.amazon.com/Method-Coordinates-I-M-Gelfand/dp/0817... http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144... http://www.amazon.com/Sequences-Combinations-Limits-Library-... and Basic Mathematics by Serge Lang http://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/038796... and The Art of Problem Solving expanded series http://www.artofproblemsolving.com/Books/AoPS_B_Texts_FAQ.ph... When a…
on “A Textbook Example of What’s Wrong with Education” ↗…Mathematician's Delight is surely also good (I've read other books by Sawyer). http://www.amazon.co.uk/gp/product/0486462404/ Read those for background as you get my favorite overviews of mathematics: Basic Mathematics by Serge Lang and Numbers and Geometry by Joseph Stillwell. http://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/038796... (Basic Mathematics is mostly high school level math, with a minimum of fuss…
on “Ask HN: Best Mathematics book for complete noobie?” ↗…there is a wide selection of "intro to higher mathematics" books meant for people like that, and if that level is still too high you might need to review high school math, e.g. Serge Lang has a good "Basic Mathematics" review book, or you can use Khan Academy videos etc. I myself had to review a lot of high school math when I was starting. MIT OCW has excellent courses for discrete math, calculus and linear algebra…
on “I cannot afford to go back to engineering school” ↗…responses, and many of the answers ignored the actual request, and plugged their favorite math books instead. In case you missed it, there was at least one suggestion that gave a real answer to the question: 'Basic Mathematics' by Serge Lang[1]. It's a streamlined but somewhat dry textbook that starts with the properties of arithmetic and ends with precalculus. You might try reading through the table of contents to get a better…
on “The Best Textbooks on Every Subject” ↗…but they heavily focus on building up deep insight rather than mechanical problem solving -- https://brilliant.org. That said, for a rigorous proof-based approach to high school math, you may enjoy "Basic Mathematics" by Lang: https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/03879...
on “Show HN: HN.Academy – Top online courses recommended by Hacker News users” ↗Try "Basic Mathematics" by Serge Lang. This will be particularly useful for learning basic algebra.
on “Ask HN: What are the best textbooks for high school level math?” ↗I've had the same thoughts before. 'Basic Mathematics' by Serge Lang helped me a lot.
on “Math Basics for Computer Science and Machine Learning [pdf]” ↗