Honestly, I can't believe I'm almost done Calculus. It was a lot of work, but I still can't believe it.
Over the past semester, I have definitely acquired more knowledge of mathematics than I had before; I've learned about and gained a pretty decent understanding of concepts like limits and derivatives, as well as an idea as how to model certain things in the natural world. I certainly feel more proficient in some subjects than others, particularly in growth models as compared to things like continuity and derivatives (though I still understand them, I'm just not quite so good at solving their problems). I held an A in the class most of the semester, which I'm very proud of and somewhat surprised at, because as I mentioned in one of my blog posts before, I am not the best mathematician and certainly my middle school self would be astonished. Things do change (ha-ha calculus ha-ha mathematics of change).
Achieving these goals were probably most helped by in class examples followed by homework problems that were achievable/able to be checked. I often found that homework problems that couldn't be checked/compared to something often were fairly useless in my learning because I had nothing to compare them to, and so it was pretty easy for me to accidentally go down a wrong path. Additionally, guidance in class was also very useful, and projects often helped apply the knowledge to what would likely be real world scenarios.
I would definitely advise incoming students that if they want to perform well on exams and quizzes, homework is probably the best way to study, but not to stress on problems that are profoundly difficult- sometimes it just takes good judgement as to what constitutes good studying and what is no longer productive.
I would probably give myself an overall grade of around a high B to a low A. I've put in quite a lot of time to this course and have definitely learned a lot, but obviously there have been some concepts that I've needed working on, and there were times when I just couldn't do homework to gain a better understanding of the concepts. Overall, I did understand most of the material though (at least so I think), so I feel as though I'm pretty "alright" with calculus concepts, hence the B to a low A reasoning.
Friday, May 6, 2016
Sunday, May 1, 2016
Reflection 11: Walk or Run in the Rain
In this article, the modelling of a common problem- whether or not we should walk or run in the rain- was created to get an idea of what factors constitute which form of movement. This was designed by integrating parameters into the original equation to dictate what may effect the ultimate outcome; things like surface area of your body, the density and angle of the rain, the distance to your front door, etc. The derivative of this equation was used to find what may be the optimum running velocity (an optimization of speed in this scenario, as related to the rain coming down). All of these concepts have been ideas covered in class, and can be applied to other scenarios of interest.
For example, I used to be an avid airsofter (essentially paintball for definition purposes), and a lot of situations can be modeled/optimized in the sport. Optimizing time spent on objectives, modelling the accuracy/shot placement of the BBs, and modelling the velocity/FPS speed of a BB leaving the barrel based on things like length, power of the spring in the gun, compression of the air, etc. are all possibilities. For this assignment, however, I will be modelling the optimal team size for succeeding at an objective (let's say capturing a base or rescuing a "hostage").
There are quite a few factors to take into account for. First off, our output from the equation should be a probability of success of sorts (above or below a certain value will indicate the probability of success or failure), which will be referred to as a Success/Fail Ratio (S/F). As for parameters, there should be three main portions to the equation; parameters relating to your team, parameters relating to the opposing team, Parameters relating to your team and the opposing team could be as follows; team size (x=number of individuals on team, or may be thought of as "number of weapons" since each player is only considered if they have a weapon), number of medics on team that can heal players back into game (typically game rules allow for one per ten players, so x/10), a constant assigned based on team skill (perhaps something on a scale of 1-10, ten being most skilled, 1 being least skilled, represented as a_skill), and a coefficient which would represent the gear being used by the players, which may include the probability of weapon/gear malfunction, which can be assigned a constant (a_malfunction, which is about 1 in every 15 rifles, so 0.067) and the availability of spare gear (how many spare batteries, gas, weapons, ammo, etc. is available), which can be represented by Gp- a coefficient of the supplies needed for the situation and the supplies currently held (S_h/S_n).
a_team skill(0.067(x_t+x_t/10)+Gp)-a_opponent skill(0.067(x_o+x_t/10)+Gp)
As for the environment, things such as area of cover as a proportion to area where combat is likely (Cover/Combat Area= Co/Ca) (integrated later) and desired amount of time to complete vs amount of time available in minutes (Tc/Ti).
a_team skill(0.067(x_t+x_t/10)+Gp)-a_opponent skill(0.067(x_o+x_t/10)+Gp)*(Tc/Ti)
Finally, none of this matters if your accuracy is poor, and you can't perform better than your accuracy except by chance, so it will act as the "carrying capacity" for the equation. The likelihood of hitting a target vs the likelihood of getting hit could be modeled as average accuracy at any distance in the combat area per 100 shots, represented as a percentage or a ratio related to the number of your team members versus the number of your opponents team members. Accuracy may be thrown off by cover, so cover available to your team vs cover available to the enemy team is now in consideration.
So, finally:
S/F=
((a_team skill(0.067(x_t+x_t/10)+Gp))/(Cot/Ca*Accuracy(x_o)*100))-((a_opponent skill(0.067(x_o+x_t/10)+Gp))/(Coo/Ca*Accuracy(x_t)*100))*(Tc/Ti)
Given my experience with modelling anything like this, this equation is probably not set up quite right and likely needs things to be shuffled around. However, it definitely delves into the ideas of what may control the outcome of certain things, which would lead to another portion of my model; what numbers constitute success, and which ones failures.
From this point one may optimize the equation to decide what the optimum time would be to complete an objective, what the optimum team size would be, the optimum amount of cover, the optimum amount of gear, the optimum area of combat, etc., depending on which variables are known and which ones are desired for manipulation.
For example, I used to be an avid airsofter (essentially paintball for definition purposes), and a lot of situations can be modeled/optimized in the sport. Optimizing time spent on objectives, modelling the accuracy/shot placement of the BBs, and modelling the velocity/FPS speed of a BB leaving the barrel based on things like length, power of the spring in the gun, compression of the air, etc. are all possibilities. For this assignment, however, I will be modelling the optimal team size for succeeding at an objective (let's say capturing a base or rescuing a "hostage").
There are quite a few factors to take into account for. First off, our output from the equation should be a probability of success of sorts (above or below a certain value will indicate the probability of success or failure), which will be referred to as a Success/Fail Ratio (S/F). As for parameters, there should be three main portions to the equation; parameters relating to your team, parameters relating to the opposing team, Parameters relating to your team and the opposing team could be as follows; team size (x=number of individuals on team, or may be thought of as "number of weapons" since each player is only considered if they have a weapon), number of medics on team that can heal players back into game (typically game rules allow for one per ten players, so x/10), a constant assigned based on team skill (perhaps something on a scale of 1-10, ten being most skilled, 1 being least skilled, represented as a_skill), and a coefficient which would represent the gear being used by the players, which may include the probability of weapon/gear malfunction, which can be assigned a constant (a_malfunction, which is about 1 in every 15 rifles, so 0.067) and the availability of spare gear (how many spare batteries, gas, weapons, ammo, etc. is available), which can be represented by Gp- a coefficient of the supplies needed for the situation and the supplies currently held (S_h/S_n).
a_team skill(0.067(x_t+x_t/10)+Gp)-a_opponent skill(0.067(x_o+x_t/10)+Gp)
As for the environment, things such as area of cover as a proportion to area where combat is likely (Cover/Combat Area= Co/Ca) (integrated later) and desired amount of time to complete vs amount of time available in minutes (Tc/Ti).
a_team skill(0.067(x_t+x_t/10)+Gp)-a_opponent skill(0.067(x_o+x_t/10)+Gp)*(Tc/Ti)
So, finally:
S/F=
((a_team skill(0.067(x_t+x_t/10)+Gp))/(Cot/Ca*Accuracy(x_o)*100))-((a_opponent skill(0.067(x_o+x_t/10)+Gp))/(Coo/Ca*Accuracy(x_t)*100))*(Tc/Ti)
Given my experience with modelling anything like this, this equation is probably not set up quite right and likely needs things to be shuffled around. However, it definitely delves into the ideas of what may control the outcome of certain things, which would lead to another portion of my model; what numbers constitute success, and which ones failures.
From this point one may optimize the equation to decide what the optimum time would be to complete an objective, what the optimum team size would be, the optimum amount of cover, the optimum amount of gear, the optimum area of combat, etc., depending on which variables are known and which ones are desired for manipulation.
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