About the Book

Year Published: 2014
Page Count: 240
ISBN: 978-1-921972-34-8 (9781921972348)
Online ISBN: 978-1-921972-81-2 (9781921972812)

Table of Contents

Mathematics HL (Option): Discrete Mathematics

  SYMBOLS AND NOTATION USED IN THIS BOOK 6
       
1 NUMBER THEORY 9
  A Mathematical induction 13
  B Recurrence relations 18
  C Divisibility, prime numbers, and the Division Algorithm 41
  D GCD, LCM, and the Euclidean Algorithm 49
  E Prime numbers 62
  F Congruences 66
  G The Chinese Remainder Theorem 75
  H Divisibility tests 79
  I Fermat's Little Theorem 82
  J The Pigeonhole Principle (Dirichlet's Principle) 86
       
2 GRAPH THEORY 89
  A Terminology 91
  B Fundamental results of graph theory 97
  C Journeys on graphs 100
  D Planar graphs 110
  E Trees and algorithms 117
  F The Chinese Postman Problem (CPP) 128
  G The Travelling Salesman Problem (TSP) 132
       
    THEORY OF KNOWLEDGE (NP problems) 140
    Review set A 142
    Review set B 145
    Review set C 148
    APPENDIX (Methods of proof) 151
    THEORY OF KNOWLEDGE (Axioms and Occam's razor) 160
       
  WORKED SOLUTIONS 161
       
  INDEX 236

Authors

Author

Catherine Quinn

Author

Peter Blythe

Author

Chris Sangwin

Chris completed a BA in Mathematics at the University of Oxford, and an MSc and PhD in Mathematics at the University of Bath. He spent thirteen years in the Mathematics Department at the University of Birmingham, and from 2000-2011 was seconded half time to the UK Higher Education Academy “Maths Stats and OR Network“ to promote learning and teaching of university mathematics. He was awarded a National Teaching Fellowship in 2006. Chris Sangwin joined the University of Edinburgh in 2015 as Professor of Technology Enhanced Science Education.   

 

What are your learning and teaching interests in mathematics?

I teach mathematics at university but am particularly interested in core pure mathematics which starts in school and continues to be taught at university. Solving mathematical problems is at the heart of mathematics, and I enjoy teaching problem solving at university.

 

What interests you outside mathematics?

I really enjoy hill walking and mountaineering, particularly spending time with friends in the hills.

 

Why do you choose to collaborate with a small publisher on the other side of the world?

There is a unique team spirit in Haese which other publishers don't have. This makes authorship much more collaborative than my previous experiences, which is really enjoyable and I'm sure leads to much better quality books for students which are, after all, the whole point.

Author

Robert Haese

Author

Michael Haese

Michael completed a Bachelor of Science at the University of Adelaide, majoring in Infection and Immunity, and Applied Mathematics. He studied laminar heat flow as part of his Honours in Applied Mathematics, and finished a PhD in high speed fluid flows in 2001. He has been the principal editor for Haese Mathematics since 2008.

 

What motivates you to write mathematics books?

My passion is for education as a whole, rather than just mathematics. In Australia I think it is too easy to take education for granted, because it is seen as a right but with too little appreciation for the responsibility that goes with it. But the more I travel to places where access to education is limited, the more I see children who treat it as a privilege, and the greater the difference it makes in their lives. But as far as mathematics goes, I grew up with mathematics textbooks in pieces on the kitchen table, and so I guess it continues a tradition.

 

What do you aim to achieve in writing?

I think a few things:

  • I want to write to the student directly, so they can learn as much as possible from the text directly. Their book is there even when their teacher isn't.
  • I therefore want to write using language which is easy to understand. Sure, mathematics has its big words, and these are important and we always use them. But the words around them should be as simple as possible, so the meaning of the terms can be properly explained to ESL (English as a Second Language) students.
  • I want to make the mathematics more alive and real, not by putting it in contrived "real-world" contexts which are actually over-simplified and fake, but rather through its history and its relationship with other subjects.

 

What interests you outside mathematics?

Lots of things! Horses, show jumping and course design, alpacas, badminton, running, art, history, faith, reading, hiking, photography ....

Features

Fully worked solutions are included for every question.

Theory of Knowledge is a core requirement in the International Baccalaureate Diploma Programme.

Students are encouraged to think critically and challenge the assumptions of knowledge. Students should be able to analyse different ways of knowing and kinds of knowledge, while considering different cultural and emotional perceptions, fostering an international understanding.

Graphics calculator instructions for Casio fx-9860G Plus, Casio fx-CG20, TI-84 Plus, and TI-nspire are included with this textbook. The textbook will either have comprehensive instructions at the start of the book, specific instructions available from icons located throughout, or both. The extensive use of graphics calculators and computer packages throughout the book enables students to realise the importance, application, and appropriate use of technology.

Early prints of this textbook came with a Student CD. Recent prints of this book include 27 months of access for electronic devices through our Snowflake learning platform.

Where relevant, Snowflake or the Student CD include a complete electronic copy of the book with interactive geometry, graphing, and statistics software, demonstrations, games, spreadsheets, and a range of printable worksheets, tables, and diagrams. Teachers are provided with a quick and easy way to demonstrate concepts, and students can discover for themselves and re-visit when necessary.

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