Post by: EspoirTron on April 23, 2014, 12:03:49 pm
Enjoy the Maths!
Post by: kinslayer on April 23, 2014, 02:11:01 pm
Post by: m.Chemia on April 23, 2014, 07:49:32 pm
Post by: LaLaLouise on April 23, 2014, 08:31:30 pm
Was wondering if anyone is doing MTH2010 and is attempting to do assignment 2? What the hell is question 2 even about hahaha. Anyone want to give me some hints on 2b and c? I've got a and d :)
Post by: kinslayer on April 23, 2014, 08:57:49 pm
Post by: keltingmeith on April 24, 2014, 04:01:16 pm
Post by: LaLaLouise on April 24, 2014, 07:31:26 pm
I've attached the pdf of the assignment. I've done all of the questions except for 2b and c.
For 2b I understand how to get a critical point, take the derivative of the function and equate it to zero. From 2a we get the equation and I take the derivative the function with respect to a and b so we have 2 equations and then attempt to solve for a and b but the answer just doesn't come out right. My friend also found this pdf, http://web.williams.edu/Mathematics/sjmiller/public_html/BrownClasses/54/handouts/MethodLeastSquares.pdf , and got to 3.12 , I can get these equations but MTH2010 doesn't teach those steps afterwards. So confusing haha
For 2c I'm not really sure. With the condition the denominator will be negative for a and b. I understand what a local minimum is, I think it may have to do the second derivative test??
Thanks again and sorry for so much writing :)
Post by: kinslayer on April 24, 2014, 09:50:54 pm
I've done the first part of 2b), see attached.
Showing that it is a local minimum is just a matter of applying the second derivative test for functions of two variables. It's in Stewart somewhere I think or you can see here:
http://mathworld.wolfram.com/SecondDerivativeTest.html
It works out to be very simple and you just have to use the fact that
Post by: LaLaLouise on April 24, 2014, 10:45:54 pm
Yeah I thought we has to use the second derivative test for 2c and I figured out the answer right after I posted the question haha
Thanks so much for you help especially since it's time out of your holidays! :)
Post by: EspoirTron on May 03, 2014, 04:27:34 pm
Q1. A right circular cylinder is inscribed in a cone with height h and base r. Find the largest possible volume of such a cylinder.
Q2. The base of a solid is a triangular region with vertices (0,0), (1,0) and (0,1). Cross-sections perpendicular to the y-axis are equilateral triangles. Find the volume of such a solid.
Q3. Set up an integral for the volume of a solid torus with radii r and R.
Q4. Find the volume common to two spheres, each with radius r, if the center of each sphere lies on the surface of the other sphere. (This answer is in terms of r).
If anyone could help I would really appreciate that!
Post by: mrb3n on May 04, 2014, 02:13:33 pm
I've got two questions regarding limits. I'll post a picture because trying type them would be very hard.
Any guidance you could give me would be appreciated.
Post by: kinslayer on May 04, 2014, 02:54:11 pm
Hi guys,
I've got two questions regarding limits. I'll post a picture because trying type them would be very hard.
Any guidance you could give me would be appreciated.
1.a) i) This is an indeterminate form of type
1.a) ii) Expand the denominator, then divide numerator and denominator by
1.b) f(x) = -3 for all x < 0 and f(x) = -1 for all x > 0. So the left-hand limit is -3 and the right-hand limit is -1.
Not sure what the limit laws are that you are supposed to use but I assume it's just things like;
- the limit of a sum/difference is the sum/difference of limits
- the limit of a ratio is the ratio of the limits (for nonzero denominator)
- the limit of a constant times a function is constant times the limit of a function
- etc...
Just remember to write down which law you are using when you use it.
Post by: mrb3n on May 04, 2014, 03:03:52 pm
Post by: DisaFear on May 04, 2014, 04:16:33 pm
I can do b), given a) - It will just be the inverse
I can't seem to grasp the process to figure out a) though. I've looked at my lecture notes, and I think he does it sort of intuitively. I'm not sure about whether which bit should be a column or a row. (Yea...basic math flaws :( )
If anyone could outline the steps I'd need to take for a), would be thankful :)
Post by: kinslayer on May 04, 2014, 07:27:54 pm
I used the procedure here: http://www.math.hmc.edu/calculus/tutorials/changebasis/changebasis.pdf
For part a) you should end up with this matrix for the change of basis (I think):
Verifying: if you have a vector
Post by: Kanon on May 06, 2014, 02:57:37 pm
How are you guys studying for university maths? I'm doing MTH1020 and it just seems that when I get a question wrong I make that mistake in the future again, any advice?
Post by: EspoirTron on May 07, 2014, 01:54:35 pm
I'm not really that great at maths, so I'm thinking maybe I'm going about it the wrong way.
How are you guys studying for university maths? I'm doing MTH1020 and it just seems that when I get a question wrong I make that mistake in the future again, any advice?
Hey Kanon, I am doing MTH1020 as well. I suggest that when you get a question wrong you identify why you got it wrong. Perhaps it was arithmetic or just forgetting to factorize properly? Often I find it is trivial issues rather than actually having a gap in your knowledge. As silly as this may sound working on exercises that just test simple skills like understanding surds, fractions and factorising can often really help you speed up you thinking and allow yourself to avoid making mistakes. Since I am doing MTH1020 if you ever would like to form a study group or something I am more than happy too since no one else I know actually studies much for this unit.
I was wondering if anyone here could tell me if Euler's method is actually used in later units to numerically solve differential equations? We spent about 20 minutes on but I am not sure if it is really important. Having a quick glance over the MTH1030 unit book Euler's Method is not mentioned, so if anyone could clarify that for me that'd be great!
Post by: LaLaLouise on May 07, 2014, 09:44:46 pm
Monsieur Kebab I'm doing MTH2010 atm and I don't think we use Euler's method (but I may be wrong). I did MTH1030 last year but I can't remember if it was used sorry!
Also I have a question for everyone, it's more of a wording issue I'm having then needing help with solving. So basically I have a cardioid and a circle and the question says I have to find the area of 'the region contained inside both the cardioid and circle'.
(Picture attached for reference)
So do you think this implies the entire region of both (green) or just the part where they both intersect (blue)?
Post by: DisaFear on May 07, 2014, 09:55:02 pm
I have not done 2021 so I'm not sure how it's laid out in the lectures. The basis B' looks like the "standard" basis forso finding the change of basis matrix isn't as hard as it could be :P.
I used the procedure here: http://www.math.hmc.edu/calculus/tutorials/changebasis/changebasis.pdf
For part a) you should end up with this matrix for the change of basis (I think):
Verifying: if you have a vectorwith respect to B then
AKA
.
Thanks you :)
Post by: kinslayer on May 07, 2014, 10:20:09 pm
So do you think this implies the entire region of both (green) or just the part where they both intersect (blue)?
It would be the region that is inside the cardioid and inside the circle. So the blue one on the left is correct.
np DisaFear!
Post by: BigAl on May 08, 2014, 12:06:01 am
(http://i.imgur.com/qeDQmIm.jpg)Lecture notes are bit vague...I had to watch couple of YouTube videos to do that question...but basically what you're doing is writing p as a combination of q1 q2 and q3 and write these coefficients as a column..for future reference :)
I can do b), given a) - It will just be the inverse
I can't seem to grasp the process to figure out a) though. I've looked at my lecture notes, and I think he does it sort of intuitively. I'm not sure about whether which bit should be a column or a row. (Yea...basic math flaws :( )
If anyone could outline the steps I'd need to take for a), would be thankful :)
Post by: Kanon on June 02, 2014, 11:37:34 pm
Quote
Which of the following functions has an inverse for x > 2?So I got that b and c have a function has an inverse for x > 2 but I also selected a which is wrong.
a. sqrt(x - 4)
b. |x^2 - x|
c. ln(x + 2)
d. |x - 3|
interchange x and y
Which can be defined for all x > 2? ???
Post by: EspoirTron on June 03, 2014, 12:14:11 am
fmllllll, so bad at dis.
So I got that b and c have a function has an inverse for x > 2 but I also selected a which is wrong.
interchange x and y
Which can be defined for all x > 2? ???
Okay so sqrt(x-4) is only considering x>0 first off, since there is a positive sign in front of the square root. However, since we have a horizontal translation of 4 units in the positive direction of the x-axis, we are only considering x>4, since if x<4 f(x) would be undefined. I am just saying that f(x)=sqrt(x-4). Let's check the domain of the inverse by observing the range of f(x), well we can see that it is [0,infinity). So let's look at the question, it says all x>2. From our orginal function we see that x=3 is an undefined point and hence a is excluded as an option. Putting in x=3 would give sqrt(-1) which is undefined on the real number line, and hence, we say there is no solution.
Post by: duhherro on June 07, 2014, 01:27:45 pm
Post by: mrb3n on June 11, 2014, 05:47:24 pm
This is quite a rudimentary question, but I need some help determining the range of this function analytically.
H(x)=1-√(x+1)
They are really pedantic about full sentence answers in ENG1090, so an explanation would be really appreciated.
Cheers
Post by: EspoirTron on June 11, 2014, 10:36:34 pm
I hope that helped.
Post by: mrb3n on June 12, 2014, 08:31:50 am
Post by: LaLaLouise on August 02, 2014, 09:57:40 pm
Looking to get the solutions to the tutorial questions for MTH2032 (particularly the first half of the course). So if anyone happened to save them and could send them to me I'd appreciate it a lot!
Thanks!
(Also I've still got the MTH2010 soultions if anyone wants them)
Post by: m.Chemia on August 02, 2014, 10:30:20 pm
Hey hope everyone's first week back was good :)
Looking to get the solutions to the tutorial questions for MTH2032 (particularly the first half of the course). So if anyone happened to save them and could send them to me I'd appreciate it a lot!
Thanks!
(Also I've still got the MTH2010 soultions if anyone wants them)
I have the solutions to the tutorial questions for MTH2032. PM me your email if you haven't got them already :D (solutions to Problem Set 3 is missing somehow, but you can always ask questions in this thread :D)
Post by: emchun on August 08, 2014, 12:46:16 am
I have a question I don't know how to do...so I'm hoping someone could help.
I have to prove this statement true or either counter-example to demonstrate it is false:
"For any function
Thank you!
Post by: kinslayer on August 08, 2014, 12:48:55 am
Hello,
I have a question I don't know how to do...so I'm hoping someone could help.
I have to prove this statement true or either counter-example to demonstrate it is false:
"For any function."
Thank you!
What does
Post by: Phy124 on August 08, 2014, 12:52:59 am
Edited to clarify and give a proper answer as kinslayer was correct in saying:
Strictly speaking, in Phy's example, equality does hold if x=y=0, so you would need to allow for that, at least on the last line.
Post by: kinslayer on August 08, 2014, 01:11:20 am
c^2 = c only when c = 1 or 0; a contradiction. Therefore, with this f, f(x)f(y) does not equal f(xy).
Example: if f(x) = 2, then f(x)f(y) = 4, but f(xy) = 2.
Strictly speaking, in Phy's example, equality does hold if x=y=0, so you would need to allow for that, at least on the last line.
Post by: keltingmeith on August 08, 2014, 08:48:06 am
I need to show that
So, since delta in this case represents the radius of a circle closing in at (0, 1), I substituted that into the bottom, giving
Post by: kinslayer on August 08, 2014, 05:19:47 pm
I recommend starting with
Doing it this way, I came up with
PS: No more 2015? :P
Post by: keltingmeith on August 08, 2014, 06:35:24 pm
I don't follow your logic here. In particular, I'm not sure what you are doing in the step after you substituted delta. Also, delta should be a function of epsilon, not the other way around.
I recommend starting withand then write down a bunch of inequalities. What you want ultimately is a function of delta on the RHS (which you can then set equal to epsilon and solve for delta). Hint: the triangle inequality may help.
Doing it this way, I came up with.
PS: No more 2015? :P
Yeah, every example I've found online seems to include the triangle inequality, but I haven't been able to include it. Guess I'll just have to play around with adding random things and see what comes out, hahah.
And yeah, I had to drop it for health reasons. But I may appear in random workshops to learn fun things. :P
Post by: BigAl on August 08, 2014, 06:37:09 pm
Hey guys, this is for the MTH2010 assignment, so I'd rather not have the answer given to me. However, I'm a little unsure as to my reasoning.This question is same as last year's assignment...I had so much difficulty with Cartesian coordinates..but polar coordinates simplify this question..give it a go!
I need to show thatby the definition of a limit.
So, since delta in this case represents the radius of a circle closing in at (0, 1), I substituted that into the bottom, givingand from this, I let
. However, then if I let epsilon get infinitely small, delta must be infinitely large. Similarly, if delta is infinitely small, epsilon become infinitely large, and that would sort of destroy the whole proof.
Post by: keltingmeith on August 08, 2014, 06:39:00 pm
Post by: BigAl on August 08, 2014, 06:50:35 pm
so I'm solving a separable differential equation and the left hand side has this form
Post by: keltingmeith on August 08, 2014, 06:51:05 pm
Sorry for the double post, but I forgot to ask - what does this actually mean? Namely the "min{...}" part, I've never seen it before.
EDIT: Then you save me from the double post, BA. :P
While I'm here..I have a question about differential equations..feeling a bit rusty :(
so I'm solving a separable differential equation and the left hand side has this formso I have to exclude
and
But the wording in the assignment confuses me..it's insisting as if
exists and wants me to draw the solutions given two initial conditions...Not really sure what to do :(
Depends on how you got to that form, pretty sure (granted, haven't done MTH2032, so I don't know all the technicalities there).
Basically, y= -1 and y = 1 COULD be solutions if y(c) = 1 or -1 are an initial condition. Just that the integral won't include those solutions. There are three possible solution curves in all, the solution to that integral, y=1 and y=-1. Which of the three you have depends on the initial condition.
Hope all that made sense. n.n;
Post by: BigAl on August 08, 2014, 06:56:40 pm
that's the problem..there is no c that satisfies that condition
Depends on how you got to that form, pretty sure (granted, haven't done MTH2032, so I don't know all the technicalities there).
Basically, y= -1 and y = 1 COULD be solutions if y(c) = 1 or -1 are an initial condition. Just that the integral won't include those solutions. There are three possible solution curves in all, the solution to that integral, y=1 and y=-1. Which of the three you have depends on the initial condition.
Hope all that made sense. n.n;
Post by: keltingmeith on August 08, 2014, 07:01:57 pm
that's the problem..there is no c that satisfies that condition
If may be easier to explain if I do this:
In this case, if y = -7, we have a gradient of zero. Nothing wrong with that, but then I go to solve by separation of variables:
Now, when I divided by y+7, we lost the solution y=-7. More specifically, we lost the solution y+7=0. So, we say that y+7=0 could still be a solution, since there was nothing wrong with that solution at the very start. So, if we have an initial condition of y(c)=-7, it will have the solution curve y=-7, as the possible solutions of the original differential equation are
If you're still unsure of what I'm trying to say, wait for someone else to come in and clarify, sorry. n.n;
Post by: kinslayer on August 08, 2014, 07:24:34 pm
Sorry for the double post, but I forgot to ask - what does this actually mean? Namely the "min{...}" part, I've never seen it before.
It just means the minimum. When I was doing the algebra I restricted delta to values between 0 and 1 to make it easier to deal with. If a given value of delta works for some epsilon, then it will also work for any larger epsilon.
Here, for any
Post by: keltingmeith on August 08, 2014, 07:28:12 pm
It just means the minimum. When I was doing the algebra I restricted delta to values between 0 and 1 to make it easier to deal with. If a given value of delta works for some epsilon, then it will also work for any larger epsilon.
Here, for any,
works. For
, we take
.
Don't we want epsilon and delta to be infinitely small, though? Would we still claim that the limit exists if we can only have it for delta = 1 or epsilon > 2?
Post by: kinslayer on August 08, 2014, 07:34:11 pm
Don't we want epsilon and delta to be infinitely small, though? Would we still claim that the limit exists if we can only have it for delta = 1 or epsilon > 2?
Epsilon can be whatever positive number, it's just that
Post by: keltingmeith on August 08, 2014, 07:39:51 pm
Post by: emchun on August 09, 2014, 01:22:57 am
Edited to clarify and give a proper answer as kinslayer was correct in saying:
Assuming the above interpretation is correct, a constant function would also work as a counter-example. If f(x) = c for all x and some c which is not equal to 1 or 0, then f(x)f(y) = c^2 for all x,y, but f(xy) = c.
c^2 = c only when c = 1 or 0; a contradiction. Therefore, with this f, f(x)f(y) does not equal f(xy).
Example: if f(x) = 2, then f(x)f(y) = 4, but f(xy) = 2.
Strictly speaking, in Phy's example, equality does hold if x=y=0, so you would need to allow for that, at least on the last line.
Thank you both for replying, but in Phy's example I don't really understand where you got
And for kinslayer's example, I also don't understand how you got
Sorry, these are probably really stupid questions but I'm not very good in maths. :-\
Post by: m.Chemia on August 09, 2014, 07:18:11 am
Thank you both for replying, but in Phy's example I don't really understand where you gotfrom?
And for kinslayer's example, I also don't understand how you gotand
Sorry, these are probably really stupid questions but I'm not very good in maths. :-\
In Phy's example, the function is
In kinslayer's example, the function is
Hope this clarifies a bit :)
Post by: emchun on August 10, 2014, 10:50:29 am
In Phy's example, the function is, that means the argument (variable) of the function is
. What
means is the value of the function when it is evaluated at the point
. Substituting
In kinslayer's example, the function isfor all
. In particular,
and
. Therefore
and as mentioned
Hope this clarifies a bit :)
Thanks! I finally understand both of them now.
If it's not too much trouble, could anybody please explain how to write
Post by: keltingmeith on August 10, 2014, 11:00:36 am
Thanks! I finally understand both of them now.You're right - a piecewise function is also called a hybrid function!
If it's not too much trouble, could anybody please explain how to writeas a piecewise defined function? I'm assuming piecewise is also called hybrid functions? The
in there is what is confusing me, none of the examples given in lecture notes have this kind of example. I tried doing it and I got
when
and
when
, which I don't think is right..
Instead of looking at the function as a whole, let's break it up like so:
Okay, so now we know that for g(x), when x>-1, we have the graph y=x+1. When x<-1, we have the graph y=-x-1. Now, let's put that into the first function and see what we get:
And that's your piecewise function (although you should write it with the super-cool fancy curly brackets. ;) )
Post by: simba on August 10, 2014, 03:41:09 pm
Post by: kinslayer on August 10, 2014, 03:50:20 pm
Post by: emchun on August 10, 2014, 11:16:27 pm
You're right - a piecewise function is also called a hybrid function!
Instead of looking at the function as a whole, let's break it up like so:
Okay, so now we know that for g(x), when x>-1, we have the graph y=x+1. When x<-1, we have the graph y=-x-1. Now, let's put that into the first function and see what we get:
And that's your piecewise function (although you should write it with the super-cool fancy curly brackets. ;) )
I get it now! Thank you so much~
Post by: Chazef on August 12, 2014, 01:44:31 pm
Post by: e^1 on August 12, 2014, 04:20:47 pm
Realise that when you apply limit laws and continuity theorems, you get the indeterminate form 0/0. So you can use L'Hopital's rule to find the limit from there.
Post by: keltingmeith on August 13, 2014, 05:18:34 pm
Hey guys, this is for the MTH2010 assignment, so I'd rather not have the answer given to me. However, I'm a little unsure as to my reasoning.
I need to show that
So, since delta in this case represents the radius of a circle closing in at (0, 1), I substituted that into the bottom, giving
Back to this again.
I tried putting it into polar form, and it didn't work... Then I tried it again, and it did work after I had a better understanding of what I was doing. Now, I'm fine with all of my steps, except for my very first one.
Basically, my reasoning here is that since we're closing in on the point (0,1), I want to centre my coordinate system at (0,1). So, instead of doing your usual polar conversion of x=blah and y=similar blah, I've let x=blah and y-1=similar blah.
At first this seemed perfectly fine to me, but then a 4th year saw it, didn't realise what I was doing, and said it was all wrong... Then after explaining it, he got extremely confused and wasn't sure what was happening. So, I thought I'd ask here if what I'm doing is all right.
Post by: kinslayer on August 15, 2014, 09:42:57 pm
I didn't switch to polar coordinates so I haven't tried, but I'm sure you could also do it just as easily without translating first.
Post by: keltingmeith on August 15, 2014, 10:17:14 pm
Should see some of the methods for it, though - I've seen some really weird stuff to solve this. Best part is, that all the methods are right, thus the fifty different relations for delta and epsilon should be right. This assignment has taught me that delta-epsilon proofs are thoroughly stupid, hahah.
Post by: simba on August 16, 2014, 11:11:25 am
Post by: keltingmeith on August 16, 2014, 11:19:48 am
I ended up separating the limit into two separate limits and it was much easier from there!! although my answer was delta=sqrt(epsilon), which is different to kinslayer's but oh well haha!I have legit seen about 5 different answers, all with praise from 3rd year pure maths guys. I honestly don't think there's one right answer to this anymore, unless someone wants to say otherwise, hahah.
Post by: BigAl on August 16, 2014, 02:55:48 pm
Post by: keltingmeith on August 28, 2014, 09:37:37 am
Basically, we need to find a value of C to suit the above statement - or, in the words of the question, "obtain an upper bound on the distance between the mean and the mode". We're working with a binomial distribution.
So, what I've got so far:
This is where I run into problems. See, C should depend on p, but not on n, and I'm not sure how to get rid of r and thus n. I know that
EDIT: E-mailed my tutor, he said that I don't have a problem as
Post by: TrueTears on August 30, 2014, 03:28:30 am
Post by: keltingmeith on August 30, 2014, 11:08:38 am
from the man himself.
I did find that, thought it was pretty cool to so easily find Kais through a google search. Skipped it because I assumed that since it said median I wouldn't find any help in there - already submitted the work anyway, managed to figure something out (with a lot of help from kinslayer, thank you!). Thanks though, TT, I'll definitely give it a read now that my plate's cleared of that assignment.
Post by: Orb on September 01, 2014, 07:00:41 pm
I had a look throughout the website but it doesn't specify:
-in detail what it's about
-what courses it contributes to
Could anyone please help me on this? Thanks in advance!
Post by: IndefatigableLover on September 01, 2014, 07:28:54 pm
Has anyone done MTH1040 as a subject? (extension maths for Year 12s)Have you had a look at this by any chance hamo94? It details what courses it contributes to: http://www.monash.edu/extension/study-options/mathematics.html
I had a look throughout the website but it doesn't specify:
-in detail what it's about
-what courses it contributes to
Could anyone please help me on this? Thanks in advance!
Quote
Credit arrangements
Students who successfully complete MTH1040 and subsequently gain a place in the Bachelor of Science (or associated degrees) will receive credit for a first-year sequence in Mathematics allowing them to proceed to second-year studies in Mathematics.
Students who successfully complete MTH1040 and subsequently gain a place in an engineering degree may receive credit for either one or both of these units depending on the course structure and their VCE preparation in entering the course. The Faculty of Engineering recommends that interested students should contact the course adviser prior to enrolment for more information.
Degrees from other faculties may also allow credit for first-year Mathematics.
Information on this page is correct as at 23 July,2014
I could ask my friend who's done it since there's quite a few of them who actually do this subject however you're definitely missing out on one of the best lecturers in the business (being Burkard LOL [he's fantastic]) since you'll be doing it at your school I presume?
I'll chuck this here too in case you need it for later on: http://futurestudents.unimelb.edu.au/admissions/credit_calculator
Post by: keltingmeith on September 01, 2014, 07:38:06 pm
Has anyone done MTH1040 as a subject? (extension maths for Year 12s)
I had a look throughout the website but it doesn't specify:
-in detail what it's about
-what courses it contributes to
Could anyone please help me on this? Thanks in advance!
MTH1040 is basically identical to MTH1030, except it's extended by a semester (this is what Burkard told us last semester, and I've heard from people who did MTH1040 in previous years). There are lots of reviews for this subject in the subject review thread, so go read up on MTH1030 (MTH1035 is also similar, so you can check out those reviews as well).
MTH1040 will contribute to the BSc and all double degrees containing it - however, you should be able to count it towards a normal BEng, and I'd assume there's units in the BComm that this could count towards as well. Basically, there are things in MTH1030/1040 you have to know to do Engineering and Commerce, but some of it is quite pure that the Eng/Comm people don't need, and so they basically get the same subject, but watered down for relevance sake. (can confirm for ENG1091(possibly wrong unit name), not for BComm though)
Post by: emchun on September 06, 2014, 02:45:02 am
I need help with these two questions. I keep trying to do them but I don't know where I am going.
True or False?
True or False? If
I understand that for it to be even it has to be
Post by: kinslayer on September 06, 2014, 11:17:48 am
True or False?then
. The answer is false but I have no idea what to do to prove that.
This is true for some functions, but not others. If
True or False? Ifis an even function, then
is even for any function
What you have done is correct. It doesn't matter whether f is even or odd since the value of g (which is even) is the same whether or not x>0 or x<0.
Since g is even, f(g(-x)) = f(g(x)) which means f(g(x)) is even.
Post by: emchun on September 08, 2014, 09:04:53 am
This is true for some functions, but not others. Ifthen it is true, for example, but if
then it is not true since for example
.
What you have done is correct. It doesn't matter whether f is even or odd since the value of g (which is even) is the same whether or not x>0 or x<0.
Since g is even, f(g(-x)) = f(g(x)) which means f(g(x)) is even.
Thank you for you help!
I've also done a differentiation question but I'm not sure if it's right. It would be great if someone can help check!
d/dx[(cos(x))^(1/x)] = -sin(x)cos(x)/x
Sorry for not using LaTeX, I couldn't work out how to use it for this one, it came out weirdly when I tried.
Post by: Kanon on September 08, 2014, 01:24:25 pm
Thank you for you help!
I've also done a differentiation question but I'm not sure if it's right. It would be great if someone can help check!
d/dx[(cos(x))^(1/x)] = -sin(x)cos(x)/x
Sorry for not using LaTeX, I couldn't work out how to use it for this one, it came out weirdly when I tried.
If I'm not sure what I did is correct when doing a derivation or something requiring few steps is I just chuck it into wolfram alpha.
https://www.wolframalpha.com/input/?i=derive+cos%28x%29%5E%281%2Fx%29
It'll show you if the interpretation it has is correct and if it is correct or not.
FTAO: Anyone that has done MTH1030, for the mid semester test should I really worry about theory? Or could I get away with just knowing how to solve things? :)
Post by: kinslayer on September 08, 2014, 03:32:36 pm
If you are still worried, you can ask Simon and he will tell you pretty much exactly what is on it.
Post by: keltingmeith on September 14, 2014, 05:26:15 pm
Can any of you think of any reasons as to why a maths minor would be any less useful than any other minor?
Post by: donkson on September 14, 2014, 05:37:10 pm
of course it isexactly, not really sure what the argument against it would be.
Post by: keltingmeith on October 03, 2014, 10:50:43 am
Has this been talked about in MTH2015 by John at all? Because while I'm not doing 2015, I am very intrigued and curious to do 2025. It doesn't say that 2015 or 2010 is a pre-req at all, so I'm assuming they should be fine with me doing 2025 regardless of my doing 2010 instead this semester.
Post by: Phy124 on October 03, 2014, 08:07:48 pm
I just noticed that Monash is offering a new unit - MTH2025, which appears to be like MTH2015 but for the linear algebra unit.Fuck. That.
I am very intrigued and curious to do 2025.
Post by: simba on October 04, 2014, 12:18:41 pm
Fuck. That.
Amen.
Post by: keltingmeith on October 04, 2014, 12:36:55 pm
There's gotta be someone here who still believes in the advanced maths units.
Post by: BigAl on October 04, 2014, 02:35:45 pm
:<
There's gotta be someone here who still believes in the advanced maths units.
you'll give up as soon as you see the lecturer proving
Post by: nerdgasm on October 05, 2014, 01:51:19 am
A peer summarised this feeling quite well - MTH2021 is classified as an 'applied' unit, but is taught more in the style of a 'pure' unit. What does that mean? Well, firstly, part of the course deals with more general and abstract concepts relating to matrices and vectors. A lot of people said that trying to get through 'general vector spaces' was when the hate first started. The whole concept of matrices and vectors had basically become abstracted to something so vague and general that it was hard to conceptualise what our minds were grappling with now.
What kinds of properties did these 'general vectors' have? Well, it turns out this is where the counterintuitive proofs came in - essentially proving stuff that appears to be intuitive. Why do we do this? So we KNOW that we are justified in manipulating these objects as our intuition suggests. This is a quality that is more associated with pure maths - we want full rigour; we want to build up a general mathematical framework from the most basic of axioms, and we most certainly want proof! However, I think that for most students studying MTH2021, it is not the process (proving intuitive properties) that is of greatest importance, but rather the end result (knowing that you can use those properties). As a result, attempting to place these bits of pure maths in the unit probably resulted in an inhomogeneous blend that just made things worse for pretty much everyone.
When it was time for assessments, it was mostly the computational and procedural aspects of this unit that ended up being tested. The simpler proofs that ended up being questions did not contribute too much to the overall final mark.
With all this in mind, perhaps MTH2025 is meant to be for those who enjoy engaging in purer, more abstract-styled maths. How will it be different to MTH2021? I reckon the lectures will be the same, but the weekly tutes will probably have some additional stuff on there. That, and/or the assessment questions will probably have more proof-based material. I guess time will tell. It looks like MTH2021 is still going to contain those purer aspects in its design, so I guess things aren't really going to change there.
With regard to the 'advanced' maths units as a whole, I personally think that while it can be fun to extend your learning and delve deeper, the time needed to understand the material (keeping in mind how much of it is assessable) really has to be considered. Taking the advanced units also means less tute time to discuss the bits of the 'standard' unit that may prove challenging. My overall opinion of these units is that if you're the kind of student these programs target, you'll probably have *some* fun being exposed to new concepts and learning extensions/background to the stuff you do in the normal classes. But at the same time, if you do the regular unit, I'd say you're definitely not missing out on all that much.
If you're still undecided on advanced units - I say give it a go; most course coordinators are more than happy to 'transfer' you back to the regular unit after a couple of weeks if you decide this isn't for you, no harm done. But I reckon it takes a bit of commitment (or masochism) to persist beyond that, so perhaps if you're still uncertain, erring on the side of caution might be prudent.
Post by: keltingmeith on October 05, 2014, 07:27:44 pm
I had heard all that about 2021 - maybe the advanced unit is to try and limit some of the rigor in the regular unit, as much as present more pure material for those who want it?
Either way, it seems like I should possibly send Tim an e-mail about it (it says he's the coordinator for both, I'd have thought they'd get someone new for 2025), and see if he has any early comments on the new unit.
Post by: keltingmeith on October 07, 2014, 08:25:22 pm
So, while trying to apply for a second year research project, I found out they've changed some of the pure units. Topology has been moved to second semester, and renamed "Functional Analysis", and to fix the moving-semesters they've also moved Diff Geo to first semester.
Also, if anyone cares, the Double Major in Mathematics and Mathematical Statistics is now just an Extended Major in Mathematical Statistics (because really, adding in the extra "mathematics" part is just a tad ridiculous, hahah)
Post by: BigAl on October 12, 2014, 12:00:37 am
Post by: Fraxyz on December 19, 2014, 03:00:41 pm
Post by: keltingmeith on December 19, 2014, 09:53:14 pm
Has anyone here done MTH3241? I've done a fair few of stochastic processes subjects already and was looking for a relatively easier subject to add to my econometrics honours. How would it compare to say, ETC3420 or MTH3251?
You probably won't find too many people who have done the unit that will notice this post - however, TrueTears will definitely be able to give you an answer.
I do have one friend who did both MTH3251 and MTH3241, and he said that he found MTH3241 to be a lot easier (in fact, he failed MTH3251, but did fairly well in MTH3241).
Post by: innerproduct on December 24, 2014, 11:31:38 am
Hmm, this new 'advanced' linear algebra unit is certainly an interesting idea - but I wonder about its motivation.
One somewhat unique target audience for this may be students who took the University of Melbourne Extension Maths in Year 12 (roughly equivalent to Accelerated Maths I at Melb Uni). Accelerated Maths I is supposed to encompass linear algebra but, traditionally, extension students who go to Monash are given credit for MTH1030 instead. This makes MTH2021 easy because they've done ~50% of it before. (For the other ~50%, MTH2021 goes into heaps of applications, including a large section on coding and even venturing as far out as economics and traffic systems. It also delves deeper into other concepts like complex vector spaces.)
UPDATE FOR THE PURE GUYS~
So, while trying to apply for a second year research project, I found out they've changed some of the pure units. Topology has been moved to second semester, and renamed "Functional Analysis", and to fix the moving-semesters they've also moved Diff Geo to first semester.
Thanks for pointing that out! It would have taken me a while to figure that out on my own. (Incidentally, this also sends my plans for next year into slight disarray.)
Post by: keltingmeith on December 24, 2014, 11:40:02 am
One somewhat unique target audience for this may be students who took the University of Melbourne Extension Maths in Year 12 (roughly equivalent to Accelerated Maths I at Melb Uni). Accelerated Maths I is supposed to encompass linear algebra but, traditionally, extension students who go to Monash are given credit for MTH1030 instead. This makes MTH2021 easy because they've done ~50% of it before. (For the other ~50%, MTH2021 goes into heaps of applications, including a large section on coding and even venturing as far out as economics and traffic systems. It also delves deeper into other concepts like complex vector spaces.)
Except I'm looking through the handbook now, and it looks like what's done in advanced mathematics is only slightly more than the amount of linear algebra in MTH1030. I personally think the motivation is simply the same as that behind MTH1035, or MTH2015 - let's teach the students more cool things about maths, just for the sake of it. Who knows - they may venture to do this for all of the common maths units (only other one I can think of MTH2032, though...) for the same reason.
Post by: Shad on December 25, 2014, 07:40:19 pm
Please PM me, looking for lecture notes and problem sets.
Cheers :)
and merry christmas and happy new year !!
Post by: tigerlivie on December 28, 2014, 08:09:01 pm
Doing MAT1830 at Monash next semester and I found this really old upload of the lecture notes and questions.
See: http://www.slideshare.net/CameronBanks/mat1830-notes2014
I know it's a long shot, but does anyone know if these are the current lecture notes or if there are any available problem sets from last semester?
If not I have a couple of questions from the PDF above - are there any threads/subforums on AN that I can get help?
Cheers buddies!
Post by: Phy124 on December 29, 2014, 02:44:47 am
Hey all,Those are actually the most recent notes for this unit, from 2014 semester 1 (it only runs in semester 1).
Doing MAT1830 at Monash next semester and I found this really old upload of the lecture notes and questions.
See: http://www.slideshare.net/CameronBanks/mat1830-notes2014
I know it's a long shot, but does anyone know if these are the current lecture notes or if there are any available problem sets from last semester?
If not I have a couple of questions from the PDF above - are there any threads/subforums on AN that I can get help?I did this unit in semester 1 this year but I'm pretty sure all the MAT1830 stuff I had was on my harddrive that became corrupt and hence I lost it all. If you're keen to look at some problem sets you could probably shoot Daniel Horsley (Coordinator/lecturer for the unit) an email and ask if you could have a look at them, since he was a pretty chill guy.
Cheers buddies!
If you require any assistance with any of the content in this unit feel free to post in this thread about it - I'm sure a few of us remember enough of the content to help you! :)
Post by: tigerlivie on January 02, 2015, 01:54:08 pm
If you can switch your brain back to a year ago, I am a bit confused by the questions from 4.2:
Quote
Let p be the preposition "I carry an umbrella" and let q be the preposition "It is raining." Write the following prepositions in symbols, using p, q,and
.
- I carry an umbrella, because it is raining.
- I carry an umbrella, hence it is raining.
- It is raining, hence I carry an umbrella.
- I don't carry an umbrella unless it is raining.
- It is raining, because I carry an umbrella.
- It is raining, because I don't carry an umbrella.
- It rains only if I don't carry an umbrella.
- I carry an umbrella only if it rains.
I have given it a go, but because you're limited in the symbols you can use (I assume?) a lot of them are the same. Am I missing something?
Here are my attempts:
| 1. | I carry an umbrella, because it is raining. | Not sure. causation, so how do you demonstrate a 'because' using the permitted symbols? |
| 2. | I carry an umbrella, hence it is raining. | |
| 3. | It is raining, hence I carry an umbrella. | |
| 4. | I don't carry an umbrella unless it is raining. | |
| 5. | It is raining, because I carry an umbrella. | See 1 |
| 6. | It is raining, because I don't carry an umbrella. | See 1 |
| 7. | It rains only if I don't carry an umbrella. | |
| 8. | I carry an umbrella only if it rains. |
You can probably tell from my answers that I have no idea what I'm doing.jpg.
Any help would be appreciated, I assure you!
Post by: Phy124 on January 04, 2015, 01:06:39 am
Thanks Phy124 you're a champ. I didn't know it only ran semester one so that's a relief! I'll definitely send Horsley an email. It's hard to know what lecturers are like until you meet them, but if you say he's 8) then I'll trust you. ;)Well it's been a while and I didn't spend too much time learning this stuff so I don't think I'll be able to teach you but I believe the following is correct:
If you can switch your brain back to a year ago, I am a bit confused by the questions from 4.2:
I have given it a go, but because you're limited in the symbols you can use (I assume?) a lot of them are the same. Am I missing something?
Here are my attempts:
1. I carry an umbrella, because it is raining. Not sure.
causation, so how do you demonstrate a 'because'
using the permitted symbols?2. I carry an umbrella, hence it is raining. 3. It is raining, hence I carry an umbrella. 4. I don't carry an umbrella unless it is raining. 5. It is raining, because I carry an umbrella. See 1 6. It is raining, because I don't carry an umbrella. See 1 7. It rains only if I don't carry an umbrella. This one really seems like it needs
...
8. I carry an umbrella only if it rains.
You can probably tell from my answers that I have no idea what I'm doing.jpg.
Any help would be appreciated, I assure you!
1. "I carry an umbrella, because it is raining" = "It is raining, hence I carry an umbrella" =
5. "It is raining, because I carry an umbrella" = "I carry an umbrella, hence it is raining" =
6. "It is raining, because I don't carry an umbrella" = "I don't carry an umbrella, hence it is raining" =
Your 2, 3, 4 and 8 also look right, but I'm a little bit suss on 7 buuutttt yeah can't remember soz (using some of those predicate logic rules it could well be the same thing I am interpreting it as). Either way Daniel will cover the examples in greater depth in the lectures and add in a few more of his own, so I wouldn't worry too much. Good that you're keen, though!