Selected Problems of the Vietnamese Mathematical Olympiad (1962-2009).
Title:
Selected Problems of the Vietnamese Mathematical Olympiad (1962-2009).
Author:
Chau, Le Hai.
ISBN:
9789814289603
Personal Author:
Physical Description:
1 online resource (328 pages)
Series:
Mathematical Olympiad Series
Contents:
Contents -- Foreword -- Preface -- Chapter 1 The Gifted Students -- 1.1 The Vietnamese Mathematical Olympiad -- The Mathematical Olympiad, 2009 -- How to study mathematics wisely? -- 3.1. In Arithmetic. -- 3.2. In Algebra. -- 3.3. In Geometry. -- Case 1. -- Case 2. -- 1.2 High Schools for the Gifted in Maths -- 1.3 Participating in IMO -- Chapter 2 Basic Notions and Facts -- 2.1 Algebra -- 2.1.1 Important inequalities -- 1) Mean quantities -- 2) Arithmetic-Geometric Mean (or Cauchy) inequality -- 3) Cauchy-Schwarz inequality -- 4) Bernoulli inequality -- 5) Holder inequality -- 2.1.2 Polynomials -- 1) Definition -- 2) Properties -- 3) Polynomials with integer coefficients -- 2.2 Analysis -- 2.2.1 Convex and concave functions -- 1) Definition -- 2) Properties -- 3) Jensen inequality -- 2.2.2 Weierstrass theorem -- 1) Monotone sequences -- 2) Necessary condition for convergence -- 3) Weierstrass theorem -- 2.2.3 Functional equations -- 2.3 Number Theory -- 2.3.1 Prime Numbers -- 1) Some divisibility rules -- 2) Prime numbers -- 3) The greatest common divisor (g.c.d) and least common multiple (l.c.m.) -- 4) Euclidean algorithm -- 2.3.2 Modulo operation -- 1) Definition -- 2) Properties -- 3) Chinese Remainder Theorem -- 2.3.3 Fermat and Euler theorems -- 1) Fermat (Little) Theorem -- 2) Euler Theorem -- 2.3.4 Numeral systems -- 1) Definition -- 2) Decimal system -- 3) Other numeral systems -- 2.4 Combinatorics -- 2.4.1 Counting -- 1) Permutations -- 2) Arrangements -- 3) Combinations -- 2.4.2 Newton binomial formula -- 2.4.3 Dirichlet (or Pigeonhole) principle -- 1) Principle -- 2) Some applications -- 2.4.4 Graph -- 1) Definitions -- 2) Some problems -- 2.5 Geometry -- 2.5.1 Trigonometric relationship in a triangle and a circle -- 1) Right triangle -- 2) Sine, cosine, tangent and cotangent laws -- 3) Formulas of triangle area -- 4) The power.
2.5.2 Trigonometric formulas -- 1) Addition -- 2) Double, triple angles -- 3) Sum-to-product, Product-to-sum -- 4) Rationalization -- 2.5.3 Some important theorems -- 1) Thales' theorem -- 2) Menelaus' theorem -- 3) Ceva's theorem -- 4) Euler formula -- 2.5.4 Dihedral and trihedral angles -- 2.5.5 Tetrahedra -- 2.5.6 Prism, parallelepiped, pyramid -- 2.5.7 Cones -- Chapter 3 Problems -- 3.1 Algebra -- 3.1.1 (1962) -- 3.1.2 (1964) -- 3.1.3 (1966) -- 3.1.4 (1968) -- 3.1.5 (1969) -- 3.1.6 (1970) -- 3.1.7 (1972) -- 3.1.8 (1975) -- 3.1.9 (1975) -- 3.1.10 (1976) -- 3.1.11 (1976) -- 3.1.12 (1977) -- 3.1.13 (1977) -- 3.1.14 (1978) -- 3.1.15 (1978) -- 3.1.16 (1979) -- 3.1.17 (1979) -- 3.1.18 (1980) -- 3.1.19 (1980) -- 3.1.20 (1980) -- 3.1.21 (1981) -- 3.1.22 (1981) -- 3.1.23 (1981) -- 3.1.24 (1981) -- 3.1.25 (1982) -- 3.1.26 (1982) -- 3.1.27 (1983) -- 3.1.28 (1984) -- 3.1.29 (1984) -- 3.1.30 (1984) -- 3.1.31 (1985) -- 3.1.32 (1986) -- 3.1.33 (1986) -- 3.1.34 (1987) -- 3.1.35 (1988) -- 3.1.36 (1989) -- 3.1.37 (1990 B) -- 3.1.38 (1991 B) -- 3.1.39 (1992 B) -- 3.1.40 (1992 B) -- 3.1.41 (1992) -- 3.1.42 (1994 B) -- 3.1.43 (1994) -- 3.1.44 (1995) -- 3.1.45 (1996) -- 3.1.46 (1996) -- 3.1.47 (1997) -- 3.1.48 (1998 B) -- 3.1.49 (1998) -- 3.1.50 (1999) -- 3.1.51 (1999) -- 3.1.52 (2001 B) -- 3.1.53 (2002) -- 3.1.54 (2003) -- 3.1.55 (2004 B) -- 3.1.56 (2004) -- 3.1.57 (2004) -- 3.1.58 (2005) -- 3.1.59 (2006 B) -- 3.1.60 (2006 B) -- 3.1.61 (2006) -- 3.1.62 (2007) -- 3.1.63 (2008) -- 3.2 Analysis -- 3.2.1 (1965) -- 3.2.2 (1975) -- 3.2.3 (1980) -- 3.2.4 (1983) -- 3.2.5 (1984) -- 3.2.6 (1984) -- 3.2.7 (1985) -- 3.2.8 (1986) -- 3.2.9 (1986) -- 3.2.10 (1987) -- 3.2.11 (1987) -- 3.2.12 (1988) -- 3.2.13 (1989) -- 3.2.14 (1990 B) -- 3.2.15 (1990) -- 3.2.16 (1990) -- 3.2.17 (1991) -- 3.2.18 (1991) -- 3.2.19 (1992 B) -- 3.2.20 (1992) -- 3.2.21 (1993 B) -- 3.2.22 (1993).
3.2.23 (1993) -- 3.2.24 (1994 B) -- 3.2.25 (1994 B) -- 3.2.26 (1994) -- 3.2.27 (1994) -- 3.2.28 (1995 B) -- 3.2.29 (1995 B) -- 3.2.30 (1995) -- 3.2.31 (1996 B) -- 3.2.32 (1996) -- 3.2.33 (1997 B) -- 3.2.34 (1997) -- 3.2.35 (1998 B) -- 3.2.36 (1998 B) -- 3.2.37 (1998) -- 3.2.38 (1998) -- 3.2.39 (1999 B) -- 3.2.40 (1999 B) -- 3.2.41 (1999 B) -- 3.2.42 (2000 B) -- 3.2.43 (2000) -- 3.2.44 (2000) -- 3.2.45 (2001 B) -- 3.2.46 (2001) -- 3.2.47 (2001) -- 3.2.48 (2002 B) -- 3.2.49 (2002 B) -- 3.2.50 (2002) -- 3.2.51 (2003 B) -- 3.2.52 (2003 B) -- 3.2.53 (2003 B) -- 3.2.54 (2003) -- 3.2.55 (2004) -- 3.2.56 (2005) -- 3.2.57 (2006 B) -- 3.2.58 (2006) -- 3.2.59 (2007) -- 3.2.60 (2007) -- 3.2.61 (2008) -- 3.2.62 (2008) -- 3.3 Number Theory -- 3.3.1 (1963) -- 3.3.2 (1970) -- 3.3.3 (1971) -- 3.3.4 (1972) -- 3.3.5 (1974) -- 3.3.6 (1974) -- 3.3.7 (1975) -- 3.3.8 (1976) -- 3.3.9 (1977) -- 3.3.10 (1978) -- 3.3.11 (1981) -- 3.3.12 (1982) -- 3.3.13 (1983) -- 3.3.14 (1983) -- 3.3.15 (1984) -- 3.3.16 (1985) -- 3.3.17 (1985) -- 3.3.18 (1987) -- 3.3.19 (1989) -- 3.3.20 (1989) -- 3.3.21 (1990) -- 3.3.22 (1991) -- 3.3.23 (1992) -- 3.3.24 (1995) -- 3.3.25 (1996 B) -- 3.3.26 (1997 B) -- 3.3.27 (1997) -- 3.3.28 (1999 B) -- 3.3.29 (1999) -- 3.3.30 (2001) -- 3.3.31 (2002 B) -- 3.3.32 (2002 B) -- 3.3.33 (2002) -- 3.3.34 (2003) -- 3.3.35 (2004 B) -- 3.3.36 (2004) -- 3.3.37 (2004) -- 3.3.38 (2005 B) -- 3.3.39 (2005) -- 3.3.40 (2006) -- 3.3.41 (2007) -- 3.3.42 (2008) -- 3.4 Combinatorics -- 3.4.1 (1969) -- 3.4.2 (1977) -- 3.4.3 (1987) -- 3.4.4 (1990) -- 3.4.5 (1991) -- 3.4.6 (1992) -- 3.4.7 (1993) -- 3.4.8 (1996) -- 3.4.9 (1997) -- 3.4.10 (2001) -- 3.4.11 (2004 B) -- 3.4.12 (2005) -- 3.4.13 (2006) -- 3.4.14 (2007) -- 3.4.15 (2008) -- 3.5 Geometry -- Plane Geometry -- 3.5.1 (1963) -- 3.5.2 (1965) -- 3.5.3 (1968) -- 3.5.4 (1974) -- 3.5.5 (1977) -- 3.5.6 (1979) -- 3.5.7 (1982).
3.5.8 (1983) -- 3.5.9 (1989) -- 3.5.10 (1990) -- 3.5.11 (1991) -- 3.5.12 (1992) -- 3.5.13 (1994) -- 3.5.14 (1997) -- 3.5.15 (1999) -- 3.5.16 (2001) -- 3.5.17 (2003) -- 3.5.18 (2004 B) -- 3.5.19 (2005) -- 3.5.20 (2006 B) -- 3.5.21 (2007) -- 3.5.22 (2007) -- 3.5.23 (2008) -- Solid Geometry -- 3.5.24 (1962) -- 3.5.25 (1963) -- 3.5.26 (1964) -- 3.5.27 (1970) -- 3.5.28 (1972) -- 3.5.29 (1975) -- 3.5.30 (1975) -- 3.5.31 (1978) -- 3.5.32 (1984) -- 3.5.33 (1985) -- 3.5.34 (1986) -- 3.5.35 (1990) -- 3.5.36 (1990 B) -- 3.5.37 (1991) -- 3.5.38 (1991 B) -- 3.5.39 (1992) -- 3.5.40 (1993) -- 3.5.41 (1995 B) -- 3.5.42 (1996) -- 3.5.43 (1996 B) -- 3.5.44 (1998) -- 3.5.45 (1998 B) -- 3.5.46 (1999) -- 3.5.47 (2000 B) -- 3.5.48 (2000) -- Chapter 4 Solutions -- 4.1 Algebra -- 4.1.1 -- 4.1.2 -- 4.1.3 -- 4.1.4 -- 4.1.5 -- 4.1.6 -- 4.1.7 -- 4.1.8 -- 4.1.9 -- 4.1.10 -- 4.1.11 -- 4.1.12 -- 4.1.13 -- 4.1.14 -- 4.1.15 -- 4.1.16 -- 4.1.17 -- 4.1.18 -- 4.1.19 -- 4.1.20 -- 4.1.21 -- 4.1.22 -- 4.1.23 -- 4.1.24 -- 4.1.25 -- 4.1.26 -- 4.1.27 -- 4.1.28 -- 4.1.29 -- 4.1.30 -- 4.1.31 -- 4.1.32 -- 4.1.33 -- 4.1.34 -- 4.1.35 -- 4.1.36 -- 4.1.37 -- 4.1.38 -- 4.1.39 -- 4.1.40 -- 4.1.41 -- 4.1.42 -- 4.1.43 -- 4.1.44 -- 4.1.45 -- 4.1.46 -- 4.1.47 -- 4.1.48 -- 4.1.49 -- 4.1.50 -- 4.1.51 -- 4.1.52 -- 4.1.53 -- 4.1.54 -- 4.1.55 -- 4.1.56 -- 4.1.57 -- 4.1.58 -- 4.1.59 -- 4.1.60 -- 4.1.61 -- 4.1.62 -- 4.1.63 -- 4.2 Analysis -- 4.2.1 -- 4.2.2 -- 4.2.3 -- 4.2.4 -- 4.2.5 -- 4.2.6 -- 4.2.7 -- 4.2.8 -- 4.2.9 -- 4.2.10 -- 4.2.11 -- 4.2.12 -- 4.2.13 -- 4.2.14 -- 4.2.15 -- 4.2.16 -- 4.2.17 -- 4.2.18 -- 4.2.19 -- 4.2.20 -- 4.2.21 -- 4.2.22 -- 4.2.23 -- 4.2.24 -- 4.2.25 -- 4.2.26 -- 4.2.27 -- 4.2.28 -- 4.2.29 -- 4.2.30 -- 4.2.31 -- 4.2.32 -- 4.2.33 -- 4.2.34 -- 4.2.35 -- 4.2.36 -- 4.2.37 -- 4.2.38 -- 4.2.39 -- 4.2.40 -- 4.2.41 -- 4.2.42 -- 4.2.43 -- 4.2.44 -- 4.2.45 -- 4.2.46 -- 4.2.47 -- 4.2.48 -- 4.2.49.
4.2.50 -- 4.2.51 -- 4.2.52 -- 4.2.53 -- 4.2.54 -- 4.2.55 -- 4.2.56 -- 4.2.57 -- 4.2.58 -- 4.2.59 -- 4.2.60 -- 4.2.61 -- 4.2.62 -- 4.3 Number Theory -- 4.3.1 -- 4.3.2 -- 4.3.3 -- 4.3.4 -- 4.3.5 -- 4.3.6 -- 4.3.7 -- 4.3.8 -- 4.3.9 -- 4.3.10 -- 4.3.11 -- 4.3.12 -- 4.3.13 -- 4.3.14 -- 4.3.15 -- 4.3.16 -- 4.3.17 -- 4.3.18 -- 4.3.19 -- 4.3.20 -- 4.3.21 -- 4.3.22 -- 4.3.23 -- 4.3.24 -- 4.3.25 -- 4.3.26 -- 4.3.27 -- 4.3.28 -- 4.3.29 -- 4.3.30 -- 4.3.31 -- 4.3.32 -- 4.3.33 -- 4.3.34 -- 4.3.35 -- 4.3.36 -- 4.3.37 -- 4.3.38 -- 4.3.39 -- 4.3.40 -- 4.3.41 -- 4.3.42 -- 4.4 Combinatorics -- 4.4.1 -- 4.4.2 -- 4.4.3 -- 4.4.4 -- 4.4.5 -- 4.4.6 -- 4.4.7 -- 4.4.8 -- 4.4.9 -- 4.4.10 -- 4.4.11 -- 4.4.12 -- 4.4.13 -- 4.4.14 -- 4.4.15 -- 4.5 Geometry -- Plane Geometry -- 4.5.1 -- 4.5.2 -- 4.5.3 -- 4.5.4 -- 4.5.5 -- 4.5.6 -- 4.5.7 -- 4.5.8 -- 4.5.9 -- 4.5.10 -- 4.5.11 -- 4.5.12 -- 4.5.13 -- 4.5.14 -- 4.5.15 -- 4.5.16 -- 4.5.17 -- 4.5.18 -- 4.5.19 -- 4.5.20 -- 4.5.21 -- 4.5.22 -- 4.5.23 -- Solid Geometry -- 4.5.24 -- 4.5.25 -- 4.5.26 -- 4.5.27 -- 4.5.28 -- 4.5.29 -- 4.5.30 -- 4.5.31 -- 4.5.32 -- 4.5.33 -- 4.5.34 -- 4.5.35 -- 4.5.36 -- 4.5.37 -- 4.5.38 -- 4.5.39 -- 4.5.40 -- 4.5.41 -- 4.5.42 -- 4.5.43 -- 4.5.44 -- 4.5.45 -- 4.5.46 -- 4.5.47 -- 4.5.48 -- Chapter 5 Olympiad 2009.
Abstract:
Vietnam has actively organized the National Competition in Mathematics and since 1962, the Vietnamese Mathematical Olympiad (VMO). On the global stage, Vietnam has also competed in the International Mathematical Olympiad (IMO) since 1974 and constantly emerged as one of the top ten. To inspire and further challenge readers, we have gathered in this book selected problems of the VMO from 1962 to 2008. A number of Selection Test problems are also included to aid in the formation and training of a national team for IMO. The book is highly useful for high school students and teachers, coaches and instructors preparing for mathematical olympiads, as well as non-experts simply interested in having the edge over their opponents in mathematical competitions.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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