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Complex vector spaces, duals, and duels: Fun with a number, or two, or four Daniel Mathews December 30, 2007 Contents

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• Linear algebra
• Complexification
• Algebra over a field
• Dual space
• Vector space
• Complex vector bundle
• Linear map
• Inner product space
• Complex number
• Product
• Duality
• Euclidean vector

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TOWARD A LANGUAGE THEORETIC PROOF OF THE FOUR COLOR THEOREM BOBBE COOPER, ERIC ROWLAND, AND DORON ZEILBERGER Abstract. This paper considers the problem of showing that every pair of binary trees with the same number of l

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THE FOUR NUMBERS GAME, WEEK 1 MATTHEW TAI We start the game by drawing a square, and placing a nonnegative whole number at each corner. Now we consider a side and the two adjacent corners. We take the (positive) differen

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