title: The gcd-sum function

authors: Broughan, Kevin A.

subjects: mathematics

abstract: The gcd-sum is an arithmetic function defined as the sum of the gcd's of the first n integers with n: g(n) = sumi=1..n (i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of partial sums of the Dirichlet series at real values are derived, including estimates for error terms.

text: The gcd-sum function The gcd-sum is an arithmetic function defined as the sum of the gcd's of the first n integers with n: g(n) = sumi=1..n (i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of partial sums of the Dirichlet series at real values are derived, including estimates for error terms.

year: 2001

title: Making mathematics meaningful: Using student-initiated problems to situate mathematics

authors: Brough, Chris Jane

abstract: Mathematics is everywhere-from the minute we open our eyes to check the alarm clock and calculate how many minutes extra we can afford to lie in bed, to measuring out our cereal for breakfast and estimating if we have enough petrol to make the 18 kilometre journey to work. As teachers of mathematics. we must ask ourselves if the way we teach reflects the real-life problem-solving situations our students will experience within their everyday world.

text: Making mathematics meaningful: Using student-initiated problems to situate mathematics Mathematics is everywhere-from the minute we open our eyes to check the alarm clock and calculate how many minutes extra we can afford to lie in bed, to measuring out our cereal for breakfast and estimating if we have enough petrol to make the 18 kilometre journey to work. As teachers of mathematics. we must ask ourselves if the way we teach reflects the real-life problem-solving situations our students will experience within their everyday world.

year: 2014

title: Interface of gender and culture

authors: Tamasese, Kiwi

subjects: Maori

abstract: I greet you in the soothing waters of the Pacific. The birth waters of Hawai’i to the North, island of the dream time, and Aotearoa, to the south. Papua New Guinea to the West and Marquesas to the East.  These islands are the gathering places of the world’s largest Continent, the Pacific. We of this continent know that her birth waters are our connection.  We also know that she is woman identified. It is no surprise therefore that from Hawai’i to the north to Aotearoa in the south the positioning of women in each of these societies bears a different story to that of the women of the continent of Europe.  This reality lived out in Hawai’i means women shared with men the ultimate leadership of peoples.  This location of women power is named Kuhinanui. Many remarkable women of Hawai’i occupied this position.  From times of peace throughout to the first clash with imposed new culture, women of Hawai’i led, bled, struggled, defied and kept the kukui of self belief burning. Genealogically Hawai’i is connected to her other sisters throughout the Pacific.  The story of Kuhinanui Liliuokalani is poignant.

text: Interface of gender and culture I greet you in the soothing waters of the Pacific. The birth waters of Hawai’i to the North, island of the dream time, and Aotearoa, to the south. Papua New Guinea to the West and Marquesas to the East.  These islands are the gathering places of the world’s largest Continent, the Pacific. We of this continent know that her birth waters are our connection.  We also know that she is woman identified. It is no surprise therefore that from Hawai’i to the north to Aotearoa in the south the positioning of women in each of these societies bears a different story to that of the women of the continent of Europe.  This reality lived out in Hawai’i means women shared with men the ultimate leadership of peoples.  This location of women power is named Kuhinanui. Many remarkable women of Hawai’i occupied this position.  From times of peace throughout to the first clash with imposed new culture, women of Hawai’i led, bled, struggled, defied and kept the kukui of self belief burning. Genealogically Hawai’i is connected to her other sisters throughout the Pacific.  The story of Kuhinanui Liliuokalani is poignant.

year: 1993