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About this book :-
Cambridge IGCSE Mathematics written by Karen Morrison, Lucille Dunne .
This book is the culmination of a set of notes that has been growing and fermenting in a bottom drawer of my desk for over 30 years. The goal was that after the right amount of pedantic aging, they would be ready to uncork the bottle and share with the world. It is my hope that the finished product harbors the perfect blend of intuition and rigorous preciseness, theory versus pragmatism, hard-nosed mathematics, and an enjoyable learning experience.
This book provides a "crash course" in beginning pure mathematics. The book contains six chapters. Chapter 1 covers logic and proofs, introducing the reader to sentential and predicate calculus and mathematical induction. After two introductory sections of sentential logic and the connectives -- and, or, not, if then, if and only if - the author moves up the logical ladder to predicate logic and the universal and existential quantifiers and variables. Chapter 2 examines sets and counting, including an introduction to counting, including permutations, combinations, and the pigeonhole principle. Next, Chapter 3, introduces order relations and the idea of the image and inverse image of a set, concepts important in analysis and topology. A brief tutorial on the complex numbers, a subject often overlooked in undergraduate curricula, is covered in Chapter 4. Next, Chapter 5 introduces a number of sides to topology and covers the basic ideas of point-set topology required for hard analysis, including open and closed sets, limit points, interior, exterior and boundary of a set, and so on. Finally, Chapter 6 provides a brief introduction to symmetries and abstract groups, rings and fields. The book contains many problems for readers of all interests and abilities in each section.
Book Detail :-
Title: Cambridge IGCSE Mathematics
Author(s): Karen Morrison, Lucille Dunne
Publisher: Cambridge University Press
Type: Read Online
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About Author :-
The author Charles Terence Clegg "Terry" Wall (December 1936) is a British mathematician, educated at Marlborough and Trinity College, Cambridge. He is an emeritus professor of the University of Liverpool, where he was first appointed professor in 1965. From 1978 to 1980 he was the president of the London Mathematical Society.
His early work was in cobordism theory in algebraic topology; this includes his 1959 Cambridge PhD thesis entitled "Algebraic aspects of cobordism", written under the direction of Frank Adams and Christopher Zeeman. His research was then mainly in the area of manifolds, particularly geometric topology and related abstract algebra included in surgery theory, of which he was one of the founders. In 1964 he introduced the Brauer–Wall group of a field. His 1970 research monograph "Surgery on Compact Manifolds" is a major reference work in geometric topology.
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Book Contents :-
Cambridge IGCSE Mathematics written by Karen Morrison, Lucille Dunne cover the following topics. '
Unit 1; 1. Reviewing number concepts; 2. Making sense of algebra; 3. Lines, angles and shapes; 4. Collecting, organising and displaying data; Unit 2. 5. Fractions and standard form; 6. Equations and transforming formulae; 7. Perimeter, area and volume; 8. Introduction to probability; Unit 3. 9. Sequences and sets; 10. Straight lines and quadratic equations; 11. Pythagoras' theorem and similar shapes; 12. Averages and measures of speed; Examination practice; Unit 4. 13. Understanding measurement; 14. Further solving of equations and inequalities; 15. Scale drawings, bearings and trigonometry; 16. Scatter diagrams and correlation; Unit 5. 17; Managing money; 18. Curved graphs; 19. Symmetry; 20. Histograms and frequency distribution diagrams; Unit 6. 21. Ratio, rate and proportion; 22. More equations, formulae and functions; 23. Vectors and transformations; 24. Probability using tree diagrams and Venn diagrams; Examination practice; Answers.
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