Sequences, combinations, limits

What Hacker News says

1. nikofeynFeb 2020
   israel gelfand, a top russian mathematician, has books aimed at high school students that served as education materials for distance learning in russia. the series covers algebra, functions, trigonometry, graphs, geometry, and more.

   https://www.amazon.com/Functions-Graphs-Dover-Books-Mathemat...

   https://www.amazon.com/Sequences-Combinations-Limits-Dover-M...

   https://www.amazon.com/Geometry-Israel-M-Gelfand/dp/10716029...

   https://www.amazon.com/Algebra-Israel-M-Gelfand/dp/081763677...

   https://www.amazon.com/Trigonometry-I-M-Gelfand/dp/081763914...

   https://www.amazon.com/Method-Coordinates-Dover-Books-Mathem...

   the books by sanjoy mahajan are also a treat and teach real-world applications of mathematical and scientific thinking.

   https://www.amazon.com/Street-Fighting-Mathematics-Educated-...

   https://www.amazon.com/Art-Insight-Science-Engineering-Compl...

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2. MugwortNov 2019
   A bird in the hand is worth three in the bush. If I could give someone from a non-mathematician background, e.g. programmer, who sincerely wants to get a peek behind the curtain and know what calculus really IS without diluting anything in an unacceptable way I'd show them I. Gelfand et al "Sequences, Combinations, Limits". Once you have the idea of a limit of a sequence down it isn't hard to learn the limit of a function (epsilon, delta) and move on from there. A good second step is Apostol's calculus vol. 1 just the first chapter where he calculates an integral from scratch with no "fluff" (details you don't need just yet). (Yes, learning integration first actually makes more sense than learning derivates.) Once you do that you can continue with Apostol (highly recommended.) or use Spivak's calculus (tougher but even more highly recommended).

   To wrap up Gelfand is one bird in the hand, Apostol chapter 1? with integration from stratch is another bird in the hand. That would be a good first two steps to get a sense of what calculus is really about.

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3. svanderbleekSep 2016
   This approach is what took my math skills to the next level. I would also frequently skip exercises and forget material that I learned previously. Since I started adding exercise books to my study routine I have seen enormous gains in knowledge retention and my ability to build on concepts already learned. It also doesn't have to be Olympiad style, there are also Math Circles and the general Problems in {Area} book, like one of my favorites Sequences, Combinations, Limits.
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4. tokenadultMay 2009
   I think it would be enlightening if you could provide the textbooks you buy.

   Interpreting that as a request to name the textbooks I find useful, I'll do that here.

   Elementary mathematics:

   Primary Mathematics

   http://www.singaporemath.com/Primary_Math_s/21.htm

   and

   Miquon Math

   http://www.keypress.com/x6252.xml

   Secondary mathematics:

   The Gelfand Correspondence Program series

   http://www.amazon.com/Algebra-I-M-Gelfand/dp/0817636773

   http://www.amazon.com/Functions-Graphs-Dover-Books-Mathemati...

   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 student has those materials well in hand, it is time to work on AMC and Olympiad style problem solving,

   http://www.artofproblemsolving.com/Books/AoPS_B_CP_AMC.php

   http://www.artofproblemsolving.com/Books/AoPS_B_CP_Olympiad....

   and also the best calculus textbooks, such as those by Spivak or Apostol.

   http://www.amazon.com/Calculus-Michael-Spivak/dp/0914098918/

   http://www.amazon.com/Calculus-Vol-One-Variable-Introduction...

   http://www.amazon.com/Calculus-Vol-Multi-Variable-Algebra-Ap...

   Elementary reading:

   By far the best initial reading text is

   Let's Read: A Linguistic Approach

   http://www.amazon.com/Lets-Linguistic-Approach-Leonard-Bloom...

   but there are many other good reading series, including

   Primary Phonics

   http://www.epsbooks.com/dynamic/catalog/series.asp?seriesonl...

   and

   Teach Your Child to Read in Ten Minutes a Day

   (I devote more time than that to reading instruction, typically, because I use multiple materials)

   http://www.amazon.com/Teach-Your-Child-Read-Minutes/dp/14120...

   and quite a few others. There is more junk than good stuff among elementary reading materials, alas.

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