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Mathematics Higher Level for the IB Diploma Option Topic 10 Discrete Mathematics [Pehme köide]

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  • Formaat: Paperback / softback, 187 pages, kõrgus x laius x paksus: 295x210x10 mm, kaal: 740 g, Worked examples or Exercises
  • Sari: IB Diploma
  • Ilmumisaeg: 25-Apr-2013
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1107666945
  • ISBN-13: 9781107666948
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Mathematics Higher Level for the IB Diploma Option Topic 10 Discrete MathematicsSuurem pilt
  • Formaat: Paperback / softback, 187 pages, kõrgus x laius x paksus: 295x210x10 mm, kaal: 740 g, Worked examples or Exercises
  • Sari: IB Diploma
  • Ilmumisaeg: 25-Apr-2013
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1107666945
  • ISBN-13: 9781107666948
Teised raamatud teemal:
Teised raamatud sellest sooduspakkumisest: Valik IB Diploma õppematerjale 15% allahindlusega
Püsilink: https://www.kriso.ee/db/9781107666948.html
Märksõnad:
This title forms part of the completely new Mathematics for the IB Diploma series. This highly illustrated book covers topic 10 of the IB Diploma Higher Level Mathematics syllabus, the optional topic Discrete Mathematics. It is also for use with the further mathematics course. Based on the new group 5 aims, the progressive approach encourages cumulative learning. Features include: a dedicated chapter exclusively for mixed examination practice; plenty of worked examples; questions colour-coded according to grade; exam-style questions; feature boxes throughout of exam hints and tips.

Muu info

This title forms part of the completely new Mathematics for the IB Diploma series.
How to use this book v
Acknowledgements viii
Introduction 1(2)
1 Methods of proof
3(10)
1A Proof by contradiction
4(2)
1B Pigeonhole principle
6(3)
1C Strong induction
9(4)
2 Divisibility and prime numbers
13(20)
2A Factors, multiples and remainders
13(6)
2B Greatest common divisor and least common multiple
19(4)
2C The Euclidean algorithm
23(3)
2D Prime numbers
26(7)
3 Representation of integers in different bases
33(9)
3A How many fingers do we need to count?
33(2)
3B Changing between different bases
35(1)
3C Arithmetic in different bases
36(6)
4 Linear Diophantine equations
42(9)
4A Examples of equations with integer solutions
42(2)
4B How many solutions are there?
44(2)
4C Finding the general solution
46(1)
4D Solutions subject to constraints
47(4)
5 Modular arithmetic
51(16)
5A Introduction: working with remainders
51(2)
5B Rules of modular arithmetic
53(3)
5C Division and linear congruences
56(3)
5D Chinese remainder theorem
59(3)
5E Fermat's little theorem
62(5)
6 Graph theory
67(31)
6A Introduction to graphs
67(2)
6B Definitions
69(10)
6C Some important theorems
79(6)
6D Subgraphs and complements
85(2)
6E Moving around a graph
87(2)
6F Eulerian graphs
89(4)
6G Hamiltonian graphs
93(5)
7 Algorithms on graphs
98(36)
7A Weighted graphs
98(4)
7B Minimum spanning tree: Kruskal's algorithm
102(4)
7C Finding the shortest path: Dijkstra's algorithm
106(6)
7D Travelling along all the edges: Chinese postman problem
112(6)
7E Visiting all the vertices: Travelling salesman problem
118(16)
8 Recurrence relations
134(15)
8A Defining sequences recursively
134(2)
8B First order linear recurrence relations
136(3)
8C Second order recurrence relations
139(4)
8D Modelling using recurrence relations
143(6)
9 Summary and mixed examination practice
149(9)
Answers 158(14)
Glossary 172(5)
Index 177
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