By Koh Khee Meng, Tay Eng Guan

Publication Description

Publication Date: January 25, 2013

This e-book in its moment version is an invaluable, beautiful creation to easy counting options for top secondary to undergraduate scholars, in addition to academics. more youthful scholars and lay those who savour arithmetic, let alone avid puzzle solvers, also will locate the ebook attention-grabbing. many of the difficulties and functions listed here are strong for increase talent in counting. also they are necessary for honing easy talents and strategies regularly challenge fixing. a number of the difficulties keep away from regimen and the diligent reader will usually become aware of multiple means of fixing a specific challenge, that's certainly an enormous knowledge in challenge fixing. The booklet therefore is helping to provide scholars an early begin to studying problem-solving heuristics and considering skills.

New chapters initially from a supplementary booklet were additional during this version to considerably elevate the assurance of counting thoughts. the hot chapters comprise the primary of Inclusion and Exclusion, the Pigeonhole precept, Recurrence family members, the Stirling Numbers and the Catalan Numbers. a few new difficulties have additionally been extra to this edition.

**Read or Download Counting (2nd Edition) PDF**

**Best mathematics books**

**Calculus II For Dummies (2nd Edition)**

An easy-to-understand primer on complicated calculus topics

Calculus II is a prerequisite for lots of renowned collage majors, together with pre-med, engineering, and physics. Calculus II For Dummies bargains professional guideline, recommendation, and easy methods to aid moment semester calculus scholars get a deal with at the topic and ace their exams.

It covers intermediate calculus subject matters in simple English, that includes in-depth assurance of integration, together with substitution, integration options and while to exploit them, approximate integration, and flawed integrals. This hands-on advisor additionally covers sequences and sequence, with introductions to multivariable calculus, differential equations, and numerical research. better of all, it contains useful routines designed to simplify and improve realizing of this complicated subject.

advent to integration

Indefinite integrals

Intermediate Integration themes

endless sequence

complex themes

perform exercises

Confounded by means of curves? puzzled through polynomials? This plain-English consultant to Calculus II will set you straight!

**Didactics of Mathematics as a Scientific Discipline**

This e-book describes the state-of-the-art in a brand new department of technological know-how. the elemental proposal was once to begin from a common standpoint on didactics of arithmetic, to spot definite subdisciplines, and to indicate an total constitution or "topology" of the sphere of study of didactics of arithmetic. the amount presents a pattern of 30 unique contributions from 10 diverse nations.

- Séminaire Bourbaki, Vol. 44, 2001-2002, Exp. 894-908
- Angewandte Mathematik fur Physiker
- Partial Differential Equations in Classical Mathematical Physics (CUP 1998)
- Fist Course on Fuzzy Theory & Apps

**Extra info for Counting (2nd Edition)**

**Example text**

How many shortest P—Q routes in the grid are there? Solution Certainly, we can solve the problem directly by listing all the possible shortest routes. This, however, would not be practical if we wish to solve the same problem in, say, a 190 x 100 rectangular grid. We look for a more efficient way. There are two types of segments: horizontal and vertical. Let us use a "0" to represent a horizontal segment, and a " 1 " to represent a vertical segment. 6 can accordingly be represented by the binary sequence with four "0"s and two "l"s as shown below: -> 010100 P •- Likewise, we can have: _J -> 000101 and so on.

3 shows five distinct points on the circumference of a circle. How many chords can be formed by these points? Let A be the set of such chords, and B, the set of 2-element subsets of {1,2,3,4,5}. 4). Then / is a mapping from A to B. )• Thus, / is injective. 4 The Bijection Principle 39 q = 5), there is a chord a in A (in this instance, a is the chord joining points 2 and 5) such that f(a) = {p,q}. Thus, / is onto. Hence, / : A ->• B is a bijection and, by (BP), we have \A\ = \B\. As 5 is the set of all 2-element subsets of {1,2,3,4,5}, \B\ = g ) .

While a "combination" of S is just a subset of S (and thus the ordering of elements is immaterial), a "permutation" of S is an arrangement of certain elements of S (and thus the ordering of elements is important). 2 r£) = (n-r + l ) ^ ) , where r > 1. +1 = P? _1; (ii) P r n + 1 = r! + r{P^ + P^1 + ••• + P;_ x ); (iii) (n - r)P? 3 Prove that the product of any n consecutive integers is divisible by n!. 4 Find the sum l - l ! + 2-2! + 3-3! + --- + n - n ! This page is intentionally left blank Chapter 4 Applications Having introduced the concepts of r-permutations and r-combinations of an n-element set, and having derived the formulae for P?