Recent Changes

{MHF4UExamRevAns.doc}
{finalreview.doc}
AWNSERS
I do hope you all know how to extract .zip files, if not(or if your a heretic and use macs) Let me know and i will reupload it in a different way
{Mathexam.zip}

{MHF4UExamRevAns.doc}
{finalreview.doc}
{Sample Exam Communication Problems.doc}
AWNSERS
different way
{Mathexam.zip}

Creating An Account:
1. You’ll get an email saying you’ve been invited to join the wikispace by gillianeevans. Click on the link indicated to join the wikispace.
an account.
a. Please keep your username appropriate and as close to your actual name as possible – everyone will be able to see it, including me.
your email.
c. DO NOT LOSE YOUR USERNAME AND PASSWORD. I cannot reset either of these.
Your Assignment: Posting Lesson Summaries
the lesson.
We do NOT have a traditional textbook for this course, so you will rely heavily on class notes, handouts and each other. You should add images, videos, and links to other sites to enrich the lesson and help your fellow classmates! You will be assigned a date to update the wiki.
Please post your lesson summaries on the correct unit page. On the left side bar click on your current unit (ex: Polynomial Functions), then press the "Edit" button in the top right corner. Add your lesson summary and press 'save' on the Editor tool bar. Please put your full name, descriptive title and the date of the lesson.

Final Exam
SABRINA's Cool Math Thingy
Liam Cool Math Thingy (Chaos Theory)

Chaos Theory
Most people have heard of the butterfly effect. That is, a butterfly that flaps its wings in Brazil eventually causes a tornado in Texas. This is essentially, an easily understood analogy to the Chaos Theory. It is basically the general term for the branch of mathematics that studies complex dynamic systems (things changing relative time). Chaos Theory can describe many complex systems in our world including weather, movement of celestial bodies, population growth, Brownian Motion (random movement of molecules), turbulent flow, and even plate tectonics and the stock market.
Formally, it consists of 2 basic parts which state that:
No matter how complex a system is, it must rely upon some fundamental order that defines it.
Very small changes to the initial conditions of a system can cause very dramatic and complex behaviours.
Which basically mean that everything is the way it is because of the buildup of many small changes and changing just one of these contributors fractionally would result in dramatic differences. It also is quite frustrating because it states that every system has a reason and thus formulas that could explain it, but that those formulas are so complex that they would be almost impossible to determine.
Chaos is a very recent concept in mathematics which was developed in the 1960s although not all thought up by one person. The name Chaos, however was first used by Jim Yorke, a mathematical from Maryland, US. Before the idea of chaos theory existed, mathematicians thought that dynamic systems that displayed behaviours that were not periodic, forever increasing or forever approaching a fixed point were completely random and unsolvable.
One of the first recorded observations of chaos was by meteorologist, Edward Lorenz in 1961. He was running a weather simulator on a computer and decided to take a shortcut by starting the simulation halfway and using the data that he had copied earlier. He was baffled when the results came out completely different than the first time the simulation was run and he later figured out it was because he had copied the data to 3 decimal places and the computer stored up to 6 decimal places. Such a dramatic change from changes in the thousandth place clearly demonstrate that the weather does depend completely on the initial conditions of the world but also that no modern computer or measuring system could predict it at all accurately because it would not be precise enough.
To learn more watch:
http://www.youtube.com/watch?v=JnlkKdDXk-I&feature=related
or visit:
http://www.imho.com/grae/chaos/chaos.html
http://whatis.techtarget.com/definition/0,,sid9_gci759332,00.html

Teamwork Tuesdays!
Final Exam
SABRINA's Cool Math Thingy

Millennium Prize Problems
The year 2000 brought about a whirlwind of changes and chaos. Not only was it the subject of the Y2K concerns (the fears that the computers would not be able to properly switch from 1999 to 2000 due to the rollover from 99 to 00), but it was designated as the International Year For The Culture Of Peace (by United Nations) and the World Mathematics Year.
In order to celebrate mathematics in the New Year, the Clay Mathematics Institution of Cambridge (CMI) established seven prize problems, known as the Millennium Prize Problems. The prize problems were chosen by the founding Scientific Advisory Board (SAB) of CMI and they were announced at a meeting in Paris, held on May 24, 2000. The Board of Directors at CMI has actually set aside 7 million dollars for prize funds, and to whoever can be the first to solve (prove the statement true or false) a problem will receive a million dollars. The seven problems are:
1. P versus NP problem:
Suppose that solutions to a problem can be verified quickly. Then, can the solutions themselves also be computed quickly?
2. Hodge Conjecture:
Let X be a projective complex manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.
3. Poincaré Conjecture:
Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
4. Riemann Hypothesis:
The distribution of such prime numbers among all natural numbers does follow any regular pattern
5. Yang-Mills existence and mass gap
Proving that the quantum field theory underlying the Standard Model of particle physics, called Yang–Mills theory, satisfies the standard of rigor that characterizes contemporary mathematical physics, i.e. constructive quantum field theory. The winner must also prove that the mass of the smallest particle predicted by the theory be strictly positive, i.e., the theory must have a mass gap.
6. Navier-Stokes existence and smoothness
In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.
7. Birch and Swinnerton-Dyer conjecture
It is conjectured that the rank of the abelian group E(K) of points of E is the order of the zero of L(E, s) at s = 1, and the first non-zero coefficient in the Taylor expansion of L(E, s) at s = 1 is given by more refined arithmetic data attached to E over K.
As of January 2011, six problems remain unsolved. The one problem that has been solved is the Poincaré Conjecture, by Grigori Yakovlevich Perelman. It was announced on March 18, 2010 that he had met the criteria to receive the first Millennium Prize Problem award, but he turned it down because he believed that his contribution was no greater than that of Richard Hamilton, who first suggested a solution to the problem.
So I’ll leave you with that- there are six problems left, six million dollars left and six billion people in the world that can give it a shot. So go ahead, try one.
http://www.youtube.com/watch?v=9sfkw8IWkl0
A video about the Poicare Conjecture (the only problem that has been proven)

{finalreview.doc}
{Sample Exam Communication Problems.doc}
AWNSERS
I do hope you all know how to extract .zip files, if not(or if your a heretic and use macs) Let me know and i will reupload it in a different way
{Mathexam.zip}

Therefore:
f^-1 o g^-1 = [[(x-3)^0.5]+1]/2(f o g)^-1 = 2(x^2+3)-1x=2(y^2+3)-1x+1=2(y^2+3)[(x+1) -3]/2=y^2([(x+1 -3]/2)^0.5= (f o g)^-1Therefore f^-1 o g^-1 does not equal (f o g)^-1Given:f(x)=3x-1 g(x)=(x+1)/31. f(x) is the inverse of g(x)2. f o g = 3(x+1)/3 -1y=x 3. g o f = (3x-1)+1/3y=x4. No matter which way you composes these two functions they will always become y=xThis true for any two functions that are the inverses of each other - the round trip theorem----==------------------------Tuesday January 4thFiona D'ArcyGillian away- Free time to work on graphing calculator assignment (Due Wednesday January 12th)If you need a graphing calculator, you can download graphmatica online @http://www.graphmatica.com/
==Wikispaces is spazzing, it keeps mashing up our entries. It is determined to bring us together.
Friday January 7th=
Robert Piggott