Mathematics of Choice; Or, How to Count Without Counting

Anneli Lax New Mathematical Library

by Ivan Niven

A study of combinatorics--formulas used in solving problems that ask how many

Genres: Mathematics

202 pages, Hardcover

First published July 1, 1975

Reviews

[Hossein · Rating 4 out of 5]

سال اول دبیرستان که بودم کلاس آمادگی برای المپیاد ریاضی ثبت نام کردم و استاد اون کلاس مبحث ترکیبیات رو به ما آموزش داد و من از اونجا عاشق ریاضی شدم
هنوزم که هنوزه به نظرم شیرین ترین بخش ریاضی همین شمارشه
یادش به خیر

[Mobin Shakeri · Rating 5 out of 5]

An Amazing books.
a very fun and interesting text that makes you get involved with the basics of combination. I totally recommend it to every one who is even slightly interested in mathematics.
read it many times. one of my favorites.
and also I suggest other books of this great author, Ivan Niven. he is great.

[Farzad Naderi · Rating 5 out of 5]

این کتابی بود که منو خیلی علاقه مند به شمارش کرد: پایه همه علوم کامپیوتر.
از سال اول دبیرستان که این کتاب رو خوندم، ترکیبیات شد علاقه خیلی بزرگم و هنوز بعد از ۱۷ سال علاقه مندم و کماکان با مسائلش سر و کار دارم.

[Tom Schulte · Rating 3 out of 5]

This text is an engaging, even addictive, introduction to basic combinatorics. Written in a fun and inviting manner, reader interest is amplified by the author’s infectious enthusiasm. This is an excellent introduce to combinations and permutations. First published in 1975, before computers and calculators were assumed to be at the ready, the exercises in this book can all easily be done by hand on paper. Students finishing High School or in their first year of college will find this work an excellent adjunct to textbooks and lectures.

The work is arranged in a logical progression beginning with the definitions and motivations for factorials, combinations, and permutations. From there the reader moves to binomial coefficients, power sets, and Fibonacci numbers. The effect of repetitions on combinations makes a natural prelude in Chapter Four to the Inclusion-Exclusion Principle and the groundwork for basic probability. From partitions of integers the author moves into a brief and basic, yet cogent and enlightening, explanation of generating functions and some applications for them. The book also includes Pigeonhole Principle, induction, recursion, and allied topics.

Tom Schulte teaches mathematics at Oakland Community College in Michigan.


The William Lowell Putnam Mathematical Competition: Problems and Solutions 1965–1984 (MAA Problem Book Series)
Review by Tom Schulte

Unlike the rigorous and detailed prelude William Lowell Putnam Mathematical Competition Problems and Solutions: 1938-1964, this work covers a roughly similar time span in one-fifth the space. The competition problems are displayed in a straightforward presentation, chronologically in the first section. The second section is the solutions, roughly three to five per page taking up the last four-fifths of the book.

Students participating in competition mathematics will benefit from these actual species of problem, seen “in the field.” However, anyone interested in problem solving at the advanced collegiate level will find the quality and diversity of the problems presented here both challenging and fun. Having the official solution safely several pages away allows one to solve first and compare later.

Winning teams and students from 1965 through 1984 are listed in an appendix. An index of problems by type, ranging from abstract algebra to Wallis product, allows the work to serve as a reference for challenging student questions on many topics. This compendium is a problem solver’s delight and the unadorned presentation compared to the previous volume in no way distracts from the historical interest and value of this potpourri of mathematics.

[Fateme Najafi · Rating 5 out of 5]

شروع علاقه‌ی من به علوم کامپیوتر :)

[Hamlen · Rating 5 out of 5]

This is a wonderful text from an earlier era. It was published in 1965; there are probably more modern coverages of the material available. However, what he says, and how he says it remains valid and accurate.

The editing of content is wonderful. I would prefer a different font of larger size as it becomes difficult to distinguish subscripts in the denser sections of the text.

The first five chapters are just right. The last chapters become more perfunctory. I would have left out the chapter on Induction as he covered the entire book without resorting to sigma or pi notation for sums and products.

The hints and answer section gives explanations for the solutions offered.

This is mathematics as it should be presented to keep the reader engaged.

[Lime Street Labrador · Rating 3 out of 5]

Its contents are usually covered in the first 2 chapters in standard probability texts, before the concept of probability is discussed. Good probability texts do that better than this book.