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This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.
* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions * Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry * A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training
A Transition to Advanced Mathematics promotes the goals of a ``bridge'' course in mathematics, helping to lead students from courses in the calculus sequence to theoretical upper-level mathematics courses. The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics.
جلست جيدانكن في مقعدها وربطت الأحزمة، ثم قالت بجزم: "انطلق يا ديك... إلى القمر."+++أجابها الكمبيوتر: "أف! حسناً. افعل هذا، افعل ذاك، دائماً...". ضغطت جيدانكن على الزر الأحمر الكبير في لوحة التحكم أمامها. فدارت محركات المركبة وطغى هديرها على احتجاجات ديك.+++ما هو إلا وقت قصير حتى حطت المركبة على السطح القمر. وإذ ذاك، ذكرها ديك بأن ترتدي بزتها الفضائية قبل الخروج بسبب انعدام أي غلاف جوي. بدت البزة ضخمة، لكنها كانت مصممة جيداً ويسهل ارتداؤها. عبرت جيدانكن حجرة الضغط ثم نزلت الدرجات المعدنية وخرجت من المركبة إلى سطح القمر المغبر. وراحت تلهو بعض الوقت وتقفز صعوداً ونزولاً. وأعجبها أن تتمكن من الوثوب إلى مستوى أعلى مما تفعل على السطح الأرض. وفكرت أن الأمر "يشبه حتماً ما يفعله أبطال الوثب في الألعاب الأولمبية".

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