CSC165 Lecture Week 3

I was always told that university would come with a lot of new challenges, and I think I faced my first one this week. In high school I grasped most topics very quickly and very easily. The only thing I really struggled with were proofs in math, but we didn't have to know them for tests, so I am ashamed to say that I pretty much just ignored them. Now that I actually have to learn this stuff, I have to figure out how to approach these problems. The tutorial exercise for this week took me two hours to do and I had to have a lot of outside help. Hopefully, in the future I will get better at this kind of problem solving.

Question 2 from the tutorial:

To help me solve answer this question, I first went to the CS help centre. I got two bits of information that helped me. First the x on the left and within each set of brackets is not necessarily the same x, but they could be the same x. I also figured out from looking at the online notes that (a) and (b) are actually laws and they are called quantifier distributive laws.

I then Googled quantifier distributive laws to see if I could get a different perspective that would help me. This website http://goose.ycp.edu/~dbabcock/PastCourses/mat235/lecture/lecture06.html, gave me concrete definitions of the predicates, which helped me to finally solve the problems. Let D be the set of people. Let P(x) mean x likes pie and Q(x) mean x likes cake.

Three things to keep in mind:
1. An implication can only be proven false if the antecedent is true while the consequent is false.
2. Or (V) is true when one statement is true and false when both statements are false.
3. And (^) is true when both statements are true and false when one statement is false.

And now my answers to the questions:
(a) is true in both directions. Translating it into English makes it obvious. Everybody likes pie and cake, therefore everybody likes pie and everybody likes cake. Everybody likes pie and everybody likes cake, therefore everybody likes pie and cake.

(b) is always true from left to right. When someone likes cake and pie (proving the right true), that same someone likes pie and that same someone likes cakes, so the left cannot be false. The other way however is sometimes false. Let's say person A likes pie and person B likes cake (proving the left true). There does not have to exist a single person C who like both (proving the left false). The antecedent can therefore be proven true when the consequent is false.

(c) is always true from right to left. Everyone likes pie (proving the left true), therefore everyone likes pie (proving the right true). The other way is false because everyone likes pie or cakes could mean that, for example, half of everyone likes pie while the other half only like cake (proving the right true), therefore there may exist some person A who does not like pie and some person B who does not like cake (proving the left false).

(d) is true in both directions. It's the same as saying: someone likes pie/cake therefore someone likes pie/cake, which makes both sides true.

These are, of course, not formal proofs and I can't Google around for answers on assignments and test, but I'm hoping that this was a decent first step. I learned some new strategies for understanding problems (rewording into something I understand, coming up with concrete examples) so I'm getting better at this.

Now I shall move onto my next challenge of learning to do laundry because I cannot take it home this weekend.

CSC165 Lecture Weeks 1 and 2

This is my first post for CSC165, so just a quick housekeeping note. This used to be a physics blog for physics class, but from this point forward all posts will be dedicated to CSC165.

Learning about mathematical expression and reasoning or logic is pretty much the same as learning a new language. Instead of learning new words we are leaning new symbols such as ∀ for universal quantification and ∃ for existential quantification. Instead of learning grammar, we are learning new, more precise ways to interpret the English language. Surprisingly, I am actually really enjoying this course, which is odd since I hated those years where I was forced to learn French.

The first week’s topic was very intuitive for me. Universal quantifiers like ‘all’ and ‘every’ can only be proven by looking at every element in the set, and can be disproven by one counter example. Existential quantifies like ‘some’ and ‘there exists’ can be proven by one example and disproven only by looking at all the elements of a set. I think this duality is really elegant and really makes sense in everyday English.

On the other hand, the topic from the past two weeks that I have found most interesting is the vacuous truth and it seems very counter intuitive. It’s pretty weird to think that a statement such as, ‘If the sun does not rise, then pigs will fly’, is true. In everyday English, this whole sentence is absurd. None of these things will ever happen, so it would seem as if this sentence where completely false. Although, once I think about it, the fact that this statement is true starts to make a lot more sense. If P, then Q implications can only be proven false if there is an example where P is true but Q is false. In the case of the statement above, P is never true, so this statement can never be proven false, and is therefore true. I really like how precisely this the rules for implication are defined. It definitely trips me up sometimes, but I do often find everyday English to be too loose and ambiguous, so maybe that’s why I’m liking this course.

How to Make a Motor Video

The Many Types of North

[Untitled image of the Earth's poles]. Retrieved February 22, 2013, from:

     http://www.mnh.si.edu/earth/text/4_1_5_0.html

              Geographic north is based on the axis that the earth rotates around.  If we were to draw a line through the Earth that represents this axis, the point in the northern hemisphere where this line exits the Earth would be geographic north. This is also sometimes referred to as true north. All of our latitude and longitude lines are based off of the geographic north and south poles (DiSpezio, 2011).

EarthsMagneticField. Retrieved February 22, 2013, from:http://www.circulatethis.com/the-earths-magnetic-field-can-effect-more-than-just-your-compass-and-gps

              Magnetic north is determined by the Earth's magnetic field. This magnetic field is generated due to the liquid metal inside the Earth, the convection that takes place and the rotation of the Earth. Magnetic north is where the north end of a magnetic compass is attracted to. If you were to stand directly on top of the magnetic north pole, the compass would point straight down (Riddle, 2013). Since the opposite ends of magnets attract each other, the magnetic north pole is actually the Earth's physical south pole, and the magnetic south pole is the Earth's physical north pole. The magnetic field lines of the Earth move out from the pole in the southern hemisphere and into the pole in the northern hemisphere. Therefore when comparing to Earth to a bar magnet, the south pole is actually in the northern hemisphere as seen in the picture to above (Casselman, 2008).

                The geographic and magnetic poles are not in the same location, and the magnetic poles are constantly changing due to changes in the Earth. This difference can be determined through the use of magnetic declination or the degree of difference between the two poles (DiSpezio, 2011). 

References

(1) Casselman, A. (2008, February 28). Scientificamerican.com. Retrieved from                     

                    http://www.scientificamerican.com/article.cfm?id=the-earth-has-more-than-one-north-pole

(2) DiSpezio, M. A. (2011). Polar misunderstandings: Earth's dynamic dynamo. Science Scope, 35(2), 16-21.

(3) Riddle, B. (2013). Which way is north?. Science Scope, 36(5), 84-86.

The Energy Ball Report

Series and Parallel Circuits

                Series circuits and  parallel circuits are types of circuits. In a series circuit, there is only one path through which the electricity can pass. If this path is disrupted, any electrical devices that are connected would turn off. This disruption can be achieved using a switch or disconnecting a wire. In the energy ball lab, removing a finger from the metal conductor would open the circuit and stop the energy ball. Turning off a device can also cause a disruption (Henderson, n.d.). This is especially evident in things like older Christmas lights. If one light bulb burns out, then all of the light bulbs in the string will also turn off. It can be hard to determine where the problem is and it is therefore difficult to fix. A series circuit does however have its advantages as it can prevent an electrical  issue moving from one device to another since the current has been stopped. In a parallel circuit, there are multiple paths through which electricity could pass. As long as there is a closed circuit between a device and the power source, an open switch or broken device in another loop will not affect it . This type of circuit was created when we did the last activity with the whole class.  Houses are wired in parallel so that turning off the lights in a bedroom will not affect the lights in the kitchen.

Conductivity of the Human Body

                The human body is made up of covalent bonds and thus does not conduct electricity very well. However, the human body contains a lot of water with dissolved salts. Water has polar covalent bonds,  so pure water does not conduct electricity very well, but when salts are dissolved in water, it becomes a conductor. The body can then act like a wire and make the energy ball work. The brain needs salt to function, so if the ball does not work, a person must be dehydrated. Dehydrated, callused skin might not be able to make the energy ball work. The dry, dead skin cells can have a high resistance to electricity (Fish & Geddes, 2009).  The high resistance would mean that the skin no longer acts as a good conductor of electricity (Nave, n.d.) and the ball would not work in this case.

Self- Reflection

                I have learned that I have good collaboration skills and can work well in a group. During the lab, we discussed the answers and worked together to try and get the energy ball to work. At first we had some trouble finding metal to test our hypothesis for one of the questions, but eventually we were able to find some coins that we could use to test our answer. We, however, did not finish the whole lab, and could have improved on our time management by paying more attention to the clock and how many questions we had to answer. These time management skills are especially important to me because I get stressed when I don't think I have enough time to finish something.

Reference

(1) Fish, R. M. & Geddes, L.A. (2009, October 12). Conduction of electrical current to and through the   

                 human  body: A review. Retrieved February 3, 2013, from                  

                 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2763825/

(2) Henderson, T. (n.d.). Two Types of Connections. Retrieved February 3, 2013, from

                http://www.physicsclassroom.com/Class/circuits/u9l4b.cfm

(3) Nave, C.R. (n.d.). Conductors and insulators. Retrieved February 3, 2013, from

                http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html