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Sequences, Combinations, Limits (Dover Books on Mathematics)

S. I. Gelfand, M. L. Gerver, A. A. Kirillov, N. N. Konstantinov · 2 HN comments
HN Books has aggregated all Hacker News stories and comments that mention "Sequences, Combinations, Limits (Dover Books on Mathematics)" by S. I. Gelfand, M. L. Gerver, A. A. Kirillov, N. N. Konstantinov.
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Amazon Summary
In a departure from traditional teaching methods, this text focuses on theory more than computations, relying on independent study. Its material is geared toward aspects of high-school mathematics that promise to prove particularly useful for future studies and work. The first of three chapters deals with sequences, their definitions, and methods of mathematic induction. The next chapter addresses combinations, and the final chapter examines limits through a series of introductory problems, problems related to the definition of limit, and problems related to the computation of limits. Answers and hints to the test problems are provided, and "road signs" appear in the margins, marking passages requiring particular attention. 1969 edition.
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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...

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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