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Explaining and Exploring Mathematics
Explaining and Exploring Mathematics is designed to help you teach key mathematical concepts in a fun and engaging way by developing the confidence that is vital for teachers. This practical guide focuses on improving students’ mathematical understanding, rather than just training them for exams. Covering many aspects of the secondary mathematics curriculum for ages 11–18, it explains how to build on students’ current knowledge to help them make sense of new concepts and avoid common misconceptions. Focusing on two main principles to improve students’ understanding: spotting patterns and extending them to something new, and relating the topic being taught to something that the pupils already understand, this book helps you to explore mathematics with your class and establish a successful teacher-student relationship.
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Cheva va Menelay teoremalari hamda ular yordamida masalalar yechish
Tekislikda uchta to’g’ri chiziqning bir nuqtada kesishishi ya’ni konkurentlik masalasi juda qiziq geometrik muammolardan biridir. Odatda maktab kursidagi geometriya kitoblarda uchburchak bissektrisa yoki balandliklari yoki medianalarining konkurentligi haqidagi tasdiqlar isbotsiz keltiriladi. Shuning uchun mazkur malakaviy bitiruv ishi uchburchak kesmalarining bir nuqtada kesishishi uchun yetarli va zaruriy shartlarini topish masalasiga bag’ishlanadi.
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Қалбимдасан, Аллох
Турк адиби Муҳаммад Бўздағ қаламига мансуб ушбу асар банданинг Аллоҳга нисбатан тутган ўрнини тушунишимиз учун катта ёрдам бериши шубҳасиз. Муаллиф “Биз киммиз?”, “Қандай қилиб Аллоҳнинг розилигини топамиз ва Унга дўст бўламиз?” каби саволларга жавобни Қуръони карим ва Ҳадиси шарифлар асосида тушунтиришга уринади. “Робб” ва “банда” тушунчаларини “тавҳид”га кўра изоҳлайди. Китобдан “ҲАК ’ни топишга интилаётган ўқувчилар муҳим йўриқнома сифатида фойдаланишлари ҳам мумкин.
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Dynamic Programming
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers.
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Challenges in Geometry
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer.
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Bulgarian Mathematical Olympiad 1960 - 2008
In a cone is inscribed a sphere. Then it is inscribed another sphere tangent to the first sphere and tangent to the cone (not tangent to the base). Then it is inscribed third sphere tangent to the second sphere and tangent to the cone (not tangent to the base). Find the sum of the surfaces of all inscribed spheres if the cone’s height is equal to h and the angle throught a vertex of the cone formed by a intersection passing from the height is equal.
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Langkah Emas Menuju Sukses OSN Matematika
Alhamdulillah Penulis ucapkan kepada Allah, SWT karena dengan karunia-Nya Penulis dapat menyelesaikan penulisan buku ini. Buku ini Penulis tulis dalam rangka mempermudah tugas dalam mempersiapkan siswa-siswa SMA Darul Ulum 2 Unggulan BPPT CIS ID 113 Jombang menghadapi olimpiade matematika pada tahap-tahap awal, yakni OSK dan OSP 2016. Buku ini merupakan hasil revisi 03 dari buku edisi 2012. Ucapan terima kasih kepada semua pihak yang telah membantu dalam penyelesaian buku ini, khususnya kepada isteri tercinta Penulis, Rahayu Lestari, S.Pd., yang telah memberi dukungan yang besar kepada Penulis serta juga telah melahirkan puteri pertama kami, Qonitah Ayu Nabilah Nuruljannah pada 23 Nopember 2010.
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9 Tahun Penyelenggaran OSN
Alhamdulillah Penulis ucapkan kepada Allah, SWT karena dengan karunia-Nya Penulis dapat menyelesaikan penulisan buku ini. Buku ini Penulis tulis sebagai salah satu jawaban akan masih kurangnya buku-buku Olimpiade Matematika yang ada di Indonesia. Buku ini berisi soal dan solusi Olimpiade Matematika Tingkat Kabupaten/Kota, Tingkat Provinsi dan Tingkat Nasional yang berlangsung di Indonesia dari tahun 2002-2010 dan dapat dipergunakan dalam menyiapkan siswa-siswa menuju Olimpiade Sains Nasional pada tahun-tahun berikutnya. Ucapan terima kasih kepada semua pihak yang telah membantu dalam penyelesaian buku ini, khususnya buat rekan-rekan dalam forum www.olimpiade.org yang telah memberikan dorongan moril kepada Penulis, baik yang pernah bertemu secara langsung dengan Penulis maupun yang sampai saat ini belum pernah bertemu langsung dengan Penulis. Tak lupa terima kasih juga Penulis ucapkan kepada isteri tercinta Penulis, Rosya Hastaryta, S. Si, yang telah memberi dukungan yang besar kepada Penulis serta juga telah melahirkan puteri pertama kami, Kayyisah Hajidah, pada tanggal 2 Desember 2009.
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Thinking in Java
This is the best book on Java that I have ever found! You have done a great job. Your depth is amazing. I will be purchasing the book when it is published. I have been learning Java since October 96. I have read a few books, and consider yours a “MUST READ.” These past few months we have been focused on a product written entirely in Java. Your book has helped solidify topics I was shaky on and has expanded my knowledge base. I have even used some of your explanations as information in interviewing contractors to help our team. I have found how much Java knowledge they have by asking them about things I have learned from reading your book (e.g., the difference between arrays and Vectors). Your book is great!
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Elementary Differential Equations and Boundary Value Problems
This edition, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may be sometimes quite theoretical, sometimes intensely practical, and often somewhere in between. We have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for reading the book is a working knowledge of calculus, gained from a normal two- or three-semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
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MORE MATHEMATICAL ACTIVITIES
This book has been written in response to the enthusiastic reception given to my earlier book Mathematical Activities which was written to provide teachers with a readily available resource of ideas to enrich their teaching of mathematics. That book contained a mix of investigations, puzzles, games and practical activities, together with a commentary, to stimulate mathematical thinking. That format was clearly approved of, so it has been retained. The emphasis in the early activities is on spatial thinking, with details of interesting models to make from fascinating folding polyhedra and linkages to harmonographs. Chess board tours, matchstick puzzles, coin puzzles, shunting problems, ways to produce ellipses, parabolas and other curves continue themes introduced in the earlier book but can be attempted independently. The activity on building a matchbox computer can be seen on one level as fun, but has much significance in terms of artificial intelligence. Rigid structures in two and three dimensions have endless possibilities for linking model building in the classroom with structures in the real world, and a box of drinking straws goes a long way!
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MATHEMATICAL CAVALCADE
This book has been written in response to the success of my earlier mathematical puzzle books. When half way through writing it, I was privileged to lecture to the South East Asian Conference on Mathematical Education in Brunei Darussalam, where the theme was The Enchantment of Mathematics'. This reinforced my experience that, given the right context, mathematics appeals to a very wide audience the world over. Mathematical recreations, whether puzzles, games or models, provide stimulating contexts. This book contains 131 such activities ranging from matchstick and coin puzzles through ferrying, railway shunting, dissection, topological and domino problems to a variety of magical number arrays with surprising properties. There are some intriguing models to make including flexagons, and a tetrahedron covered in pentominoes, while the Knight's Solitaire game is a real challenge which can amuse you for many hours.
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MATHEMATICAL ACTIVITIES
With the present pattern of schools and the current vogue for mixed ability teaching there is a very real danger that the children with an aptitude for mathematics will rarely have their appetite for the subject whetted. It is my own opinion and that of many of my colleagues that our own interest in mathematics grew from the stimulation we received from teachers and books at an early age - long before decisions about examinations were taken. This interest was generated not only by the formal mathematics lessons but often by ideas which come from unusual puzzles or games, or patterns which a teacher introduced or were seen in some publication.
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EVEN MORE MATHEMATICAL ACTIVITIES
The widespread interest shown by colleagues in both primary and secondary schools to my earlier activities books has encouraged me to put together this third collection of ideas for stimulating children's mathematical thinking. Problem solving has always been at the heart of mathematics and this has been reinforced by the Cockcroft Report and the paper by the mathematics inspectorate, Mathematics from 5 to 16. Investigations and project work also feature strongly in all the GCSE proposals, so there is a growing awareness by teachers of a need to work in new ways. But to do this they need new resources. This book, together with the earlier books, goes some way towards this in providing a resource of puzzles, investigations, games, projects and applications to challenge the reader and give insights into the fascinating world of mathematics.
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A MATHEMATICAL PANDORA'S BOX
This is the fourth in my series of mathematical puzzle books. But this last is something of a misnomer for they contain, in addition to many puzzles, a mix of mathematical games, tricks, models to make, and explanations of interesting ideas and phenomena. The collection put together here contains, in all, 142 new items gleaned from many sources. Some of the ideas are hundreds of years old while others are entirely original and published here for the first time. Just before starting this book I was privileged to lecture at a conference of mathematics teachers in Japan, and the ongoing correspondence this has generated reinforces my belief in the world-wide interest in the kind of activities included here. They not only stimulate creative thinking, but make the reader aware of areas of mathematics in which they might otherwise be quite ignorant. The experienced mathematician will often be aware of the underlying theory which is the basis of a puzzle, but its solution does not normally require any great mathematical knowledge; rather it requires mathematical insight and tenacity. The ability to persist, to reflect, to research, and to call on other experiences is the key to a successful conclusion. When all else fails there is the detailed, but essential, commentary at the end of the book which will often add more insight even when you have found a solution, and will sometimes offer a follow-up problem.
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Разговорный английский по уровням. Уровень В1.
Курс "Разговорный английский по уровням. Уровень В1" предназначен для тех, кто уже освоил уровни А1 и А2 и стремится улучшить свои навыки общения на английском языке.Уровень B1 в английском языке предполагает, что студент может спокойно и без внутреннего страха говорить на повседневные темы, употребляя в речи знакомые грамматические конструкции и лексику.