The Australian Academy of Science and The Australian Mathematical Sciences Institute are currently preparing a Decadal Plan for the Mathematical Sciences in Australia.
Michael A. B. Deakin
The earth, as we all know, rotates about its axis once every twenty-four hours, giving us the cyclic alternation of night and day.
Jihoon Kim
This method generalizes the disk method of integration to find the volume of a rotated function by utilizing a differential dependent on both the axis of rotation and the rotated function.
Jihoon Kim
This method generalizes the disk method of integration to find the volume of a rotated function by utilizing a differential dependent on both the axis of rotation and the rotated function.
Q1400 Using the method of previous problems (for example, problem 1393), we rewrite the recurrence as
a(n)−ra(n−1)=s[a(n−1)−ra(n−2)] with r=s=3 .
Prepare to be MOOCed! The MOOCs are upon us and there is no turning back. MOOC is an acronym for Massively Open Online Course.
David Angell
Many popular and well-known puzzles can be approached by setting up and solving equations. Frequently, however, it will be necessary to find solutions which are not just any old real numbers, but integers. Here are two examples.
Michael A. B. Deakin
Sometimes mathematicians seem to be overcautious in their assertions, overcautious even to the point of pedantry, requiring proofs of things that seem so clearly obvious that surely no proof is required.
Peter Nguyen
In order to make use of and regulate glucose in the blood stream, the body alters the rate of passage of glucose into and out of cells.
Q1421 Find all integer solutions of the equation 2013x+49y=2 .
Q1411 How many three-digit numbers are there which do not contain any digit more than once? What do you get if you add them all up?
The Nobel Prize in Physics this year was awarded jointly to Francois Englert and Peter W. Higgs "for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles".
Michael A. B. Deakin
One of the most used methods of proof applies to those situations in which an infinite set of propositions follow one another in a sequence.
Hartwig Fuchs
In the Australian outback there are 20 cattle ranches which are visited every month by a veterinarian. On one of these aerial trips the veterinarian took along his assistant as a copilot. When they were flying between two ranches the assistant suddenly said:
Problem 1. Suppose that x,y,z are non-zero integers with no common factor except 1 such that
x2+y2=z2.
Prove that exactly one of these integers is a multiple of 5
Competition Winners – Senior Division
First Prize
Leo Jiang Trinity Grammar School
Q1431. Find a four-digit number with the following property: if the last digit of the number is moved to the front and 7 is added to the result, the answer is exactly twice the original number. Is there more than one such number?
Q1421 Find all integer solutions of the equation 2013x+49y=2 .