Overview

This Guide supports study and revision for IBDP Mathematics HL Paper 3, for students planning to answer questions on Topic 8 Option: Sets, Relations, and Groups. Coverage includes: a review of key aspects of the syllabus relating to abstract algebra; how to apply mathematical concepts to exam-style questions; concise definitions of important concepts, laws, theorems, and proofs; and guidance on boosting exam performance. Key features: worked examples to demonstrate how to solve exam problems; practice questions to test understanding; margin boxes with key points, hints, and tips; and clearly presented equations, diagrams, and tables.

Full Product Details

Author:   Peter Gray
Publisher:   OSC Publishing
Imprint:   OSC Publishing
Edition:   2nd Revised edition
Dimensions:   Width: 21.00cm , Height: 0.30cm , Length: 29.50cm
Weight:   0.094kg
ISBN:  

9781907374609

ISBN 10:   1907374604
Pages:   28
Publication Date:   12 February 2013
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Sets Set notation Number systems Venn Diagrams The algebra of sets Commutative law Associative law Distributive law De Morgan's laws The formal proof of the first de Morgan Law Practice Questions Answers Relations Cartesian product Relations Equivalence relations Functions (Mappings) Definitions Injection Surjection Bijection Practice Questions Answers Binary Operations Properties of S under a binary operation Commutativity Associativity The existence of an identity element Inverse elements Algebra of binary operations Groups Definition Common examples of groups Modulo arithmetic Symmetry transformations Functions Permutations Cycle notation Finite Groups Order of an element Order of a group Cyclic group Subgroups Lagrange's theorem Cosets Isomorphism Isomorphism and finite groups Practice Questions Answers Infinite Groups Homomorphisms Practice Questions Answers Groups Theorems Theorem 3 Subgroup Tests Theorem 4 Theorem 5 Homomorphism and Isomorphism Proofs Theorem 6 Theorem 7 Theorem 8 Theorem 9 Theorem 10 Practice Questions Answers

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Author Information

Peter Gray studied Mathematics at Cambridge University and has taught IB Mathematics in the UK and Germany since 1996, currently teaching at Munich International School, Germany. He has experience as an examiner and moderator and has taught revision since 2000.

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