Dear All,
Please be advised:
"From 2017 onwards, at least 50 of the available places in the Graduate Entry Medicine program will be reserved for students who have completed Monash University's Bachelor of Biomedical Science. Generally, only students who start a first year undergraduate Biomedical Science degree at Monash University will be considered eligible for entry via the direct pathway into Graduate Entry Medicine at Monash University."
External applications will still be assessed on the basis of their GAMSAT but with relegated priority. Undergraduate entrance will also remain an option with equal weighting given to (1) ATAR, (2) UMAT and (3) Interview.
Sources:
Transition to Graduate Entry MBBS
Undergraduate Entry
Saturday, August 22, 2015
Sunday, July 12, 2015
Simple Kinematic Problem
Problem: Find the magnitude of the force $P$ in the figure below.
Let $F_{d}=(m_{1}+m_{2})\cdot \overline{a}$ where $\overline{a}$ is the acceleration to the right.
Note the following relationships:
$$tan(\theta)=\frac{F_{v}}{F_{h}} \quad\rightarrow\quad F_{h}=\frac{F_{v}}{tan(\theta)}$$
$$F_{1}=\mu N_{1}=\mu m_{1}g$$
$$F_{2}=\mu N_{2} \quad where \quad m_{2}g=N_{2}+F_{v}$$
$$F_{h}=F_{d}+F_{1}+F_{2}$$
Making the appropriate substitutions give:
$$\frac{F_{v}}{tan(\theta)}=(m_{1}+m_{2})\cdot \overline{a}+\mu m_{1}g+\mu (m_{2}g-F_{v})$$
After some algebraic rearrangement, we arrive at:
$$F_{v}=\frac{tan(\theta)}{1+\mu tan(\theta)}\bigg[ m_{1}+m_{2}(\mu g + \overline{a}) \bigg]$$
Hence, $P=\frac{F_{v}}{sin(\theta)}=\frac{tan(\theta)}{sin(\theta)[1+\mu tan(\theta)]}\bigg[ m_{1}+m_{2}(\mu g + \overline{a}) \bigg]$
Note the following relationships:
$$tan(\theta)=\frac{F_{v}}{F_{h}} \quad\rightarrow\quad F_{h}=\frac{F_{v}}{tan(\theta)}$$
$$F_{1}=\mu N_{1}=\mu m_{1}g$$
$$F_{2}=\mu N_{2} \quad where \quad m_{2}g=N_{2}+F_{v}$$
$$F_{h}=F_{d}+F_{1}+F_{2}$$
Making the appropriate substitutions give:
$$\frac{F_{v}}{tan(\theta)}=(m_{1}+m_{2})\cdot \overline{a}+\mu m_{1}g+\mu (m_{2}g-F_{v})$$
After some algebraic rearrangement, we arrive at:
$$F_{v}=\frac{tan(\theta)}{1+\mu tan(\theta)}\bigg[ m_{1}+m_{2}(\mu g + \overline{a}) \bigg]$$
Hence, $P=\frac{F_{v}}{sin(\theta)}=\frac{tan(\theta)}{sin(\theta)[1+\mu tan(\theta)]}\bigg[ m_{1}+m_{2}(\mu g + \overline{a}) \bigg]$
Thursday, June 11, 2015
Problem Statement:
A wealthy and successful businessman decides to showcase his wealth by wearing a tailor made 'gilded' silk shirt. However, in order to ward off potential muggers, he hires four (4) bodyguards to follow him around as he flaunts his way about town.
The guards are well compensated for their services and, in time, they make enough money to afford their own gilded silk shirts. And so that's what they did. Now we have the boss plus his four guards all wearing gilded silk shirts. Now that the guards are well off, they each decide to hire four (4) bodyguards of their own to ward off potential muggers.
If the above scenario perpetuates, then we can envision each successive generation of employees (guards) becoming wealthy enough so that they can afford their own gilded shirts and bodyguards. Guards in the n-th generation will concurrently become wealthy enough to guy their gilded silk shirt and each will, concurrently, hire 4 of their own bodyguards.
Assume that the population of India is 1.3 billion. Answer the following questions:
$(a)$
What proportion (\rho) of the total population have gilded silk shirts?
$(b)$
Find ratio (R) of gilded silk shirt-wearers to 'ungilded' bodyguards.
$(c)$
What proportion (\epsilon) of the population are neither gilded shirt-wears or bodyguards?
Suggested Solution:
Let $\zeta(t)$ be the number of gilded silk shirt wearers at time $t$ and note that $\zeta(0)=1$.
Let $\eta(t)$ be the number of guards without gilded silk shirts where $eta(0)=4$.
Let $L=1.3\cdot10^{9}$ be the total population.
The value of $\zeta(t)$ and $\eta(t)$ respectively grows as follows:
$$\zeta(t)=\sum_{k=0}^{t}4^{k}$$ and $$\eta(t)=4^{t+1}$$
This is a deterministic branching process whereby each instance of $\zeta$ in the current iteration spawns four new instances of $\eta$ in the next iteration. Other examples of (probabilistic) branching processes include nuclear fission, population growth and cellular division.
We choose some time $t=T$ such that $\zeta(T) + \eta(T) \leq L$ and $\zeta(T+1) + \eta(T+1) > L$
$(a)$
The proportion of the total population have gilded silk shirts:
$$\rho=\frac{\zeta(T)}{L}=\frac{\sum_{k=0}^{T}4^{k}}{L}$$
$(b)$
The ratio of gilded silk shirt-wearers to 'ungilded' bodyguards.
$$R=\frac{\zeta(T)}{\eta(T)}=\frac{\sum_{k=0}^{T}4^{k}}{4^{T+1}}$$
$(c)$
The proportion of the population who are neither gilded nor bodyguards?
$$\epsilon=\frac{L-\zeta(T)-\eta(T)}{L}=\frac{L-\sum_{k=0}^{T+1}4^{k}}{L}$$
Now solve the above using recursion.
A wealthy and successful businessman decides to showcase his wealth by wearing a tailor made 'gilded' silk shirt. However, in order to ward off potential muggers, he hires four (4) bodyguards to follow him around as he flaunts his way about town.
The guards are well compensated for their services and, in time, they make enough money to afford their own gilded silk shirts. And so that's what they did. Now we have the boss plus his four guards all wearing gilded silk shirts. Now that the guards are well off, they each decide to hire four (4) bodyguards of their own to ward off potential muggers.
If the above scenario perpetuates, then we can envision each successive generation of employees (guards) becoming wealthy enough so that they can afford their own gilded shirts and bodyguards. Guards in the n-th generation will concurrently become wealthy enough to guy their gilded silk shirt and each will, concurrently, hire 4 of their own bodyguards.
Assume that the population of India is 1.3 billion. Answer the following questions:
$(a)$
What proportion (\rho) of the total population have gilded silk shirts?
$(b)$
Find ratio (R) of gilded silk shirt-wearers to 'ungilded' bodyguards.
$(c)$
What proportion (\epsilon) of the population are neither gilded shirt-wears or bodyguards?
Suggested Solution:
Let $\zeta(t)$ be the number of gilded silk shirt wearers at time $t$ and note that $\zeta(0)=1$.
Let $\eta(t)$ be the number of guards without gilded silk shirts where $eta(0)=4$.
Let $L=1.3\cdot10^{9}$ be the total population.
The value of $\zeta(t)$ and $\eta(t)$ respectively grows as follows:
$$\zeta(t)=\sum_{k=0}^{t}4^{k}$$ and $$\eta(t)=4^{t+1}$$
This is a deterministic branching process whereby each instance of $\zeta$ in the current iteration spawns four new instances of $\eta$ in the next iteration. Other examples of (probabilistic) branching processes include nuclear fission, population growth and cellular division.
We choose some time $t=T$ such that $\zeta(T) + \eta(T) \leq L$ and $\zeta(T+1) + \eta(T+1) > L$
$(a)$
The proportion of the total population have gilded silk shirts:
$$\rho=\frac{\zeta(T)}{L}=\frac{\sum_{k=0}^{T}4^{k}}{L}$$
$(b)$
The ratio of gilded silk shirt-wearers to 'ungilded' bodyguards.
$$R=\frac{\zeta(T)}{\eta(T)}=\frac{\sum_{k=0}^{T}4^{k}}{4^{T+1}}$$
$(c)$
The proportion of the population who are neither gilded nor bodyguards?
$$\epsilon=\frac{L-\zeta(T)-\eta(T)}{L}=\frac{L-\sum_{k=0}^{T+1}4^{k}}{L}$$
Now solve the above using recursion.
Wednesday, June 10, 2015
To my MEC2010 group members,
The test function you should implement in your expression is as follows:
$$\theta(i,j)=\varepsilon \cdot \sin \bigg( \frac{ij\pi}{n_{x}} \bigg)$$
The test case was the diffusion (heat) equation:
$$\frac{\partial U}{\partial t}=\kappa\frac{\partial^{2}U}{\partial x^2}$$
In your response, you need to discuss the conditions that ensure numerical stability and produce a plot using meshgrid() to show the stable and unstable cases respectively.
Email me if further clarification is required.
The test function you should implement in your expression is as follows:
$$\theta(i,j)=\varepsilon \cdot \sin \bigg( \frac{ij\pi}{n_{x}} \bigg)$$
The test case was the diffusion (heat) equation:
$$\frac{\partial U}{\partial t}=\kappa\frac{\partial^{2}U}{\partial x^2}$$
In your response, you need to discuss the conditions that ensure numerical stability and produce a plot using meshgrid() to show the stable and unstable cases respectively.
Email me if further clarification is required.
Thursday, April 23, 2015
Hi All,
I wanted to make this post to address some of the concerns expressed in your emails regarding 'distributions' and 'functions'. This is covered extensively by online resources. I've had a brief look at the Wikipedia page and it seems fit for consumption. Please don't ask me anything about compact support. I don't know anything about it. Anyway, there are many different flavours of explanations and the preference of one over others differs between authors. I'm going to offer one of those flavours.
A distribution has some 'function-like' properties but not enough of those to make it a function. One of those properties is that it houses a class or family of functions AND, for each of those functions, points to a set of numbers (a field) that relates to that function. The class of functions that lie inside the distribution MUST be well-behaving. I think distributions are only accepted very reluctantly by mathematicians and recognition comes on the basis that (1) it is valuable as an analysis tool and (2) they have an explicit, analytic form.
Linearity is preferred but not necessary; see examples from stochastic calculus and operational calculus for additional explanation. This is not an issue for us because we only look at linear problems that do not involved coupled dependent variables and their derivatives. The only distributions we will EVER look at (maybe) are the PDF and the Dirac Delta. And yes, it is possible to multiply PDFs but there are constraints that limit those possibilities. I will talk more about these in class. There are a number of transforms that can change distributions to 'nicer' forms to allow for that operation.
I'll go through a few concrete examples during our next extension class on Tuesday 28 April. Email me if you have any special requests.
I wanted to make this post to address some of the concerns expressed in your emails regarding 'distributions' and 'functions'. This is covered extensively by online resources. I've had a brief look at the Wikipedia page and it seems fit for consumption. Please don't ask me anything about compact support. I don't know anything about it. Anyway, there are many different flavours of explanations and the preference of one over others differs between authors. I'm going to offer one of those flavours.
A distribution has some 'function-like' properties but not enough of those to make it a function. One of those properties is that it houses a class or family of functions AND, for each of those functions, points to a set of numbers (a field) that relates to that function. The class of functions that lie inside the distribution MUST be well-behaving. I think distributions are only accepted very reluctantly by mathematicians and recognition comes on the basis that (1) it is valuable as an analysis tool and (2) they have an explicit, analytic form.
Linearity is preferred but not necessary; see examples from stochastic calculus and operational calculus for additional explanation. This is not an issue for us because we only look at linear problems that do not involved coupled dependent variables and their derivatives. The only distributions we will EVER look at (maybe) are the PDF and the Dirac Delta. And yes, it is possible to multiply PDFs but there are constraints that limit those possibilities. I will talk more about these in class. There are a number of transforms that can change distributions to 'nicer' forms to allow for that operation.
I'll go through a few concrete examples during our next extension class on Tuesday 28 April. Email me if you have any special requests.
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