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Adventures in FOM | a day in the life of a FOM student at SMCMa day in the life of a FOM student at SMCM
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a day in the life of a FOM student at SMCM
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March | 2013 | Adventures in FOM
https://cdmachlin.wordpress.com/2013/03
A day in the life of a FOM student at SMCM. Monthly Archives: March 2013. March 29, 2013. Practice Proof by Induction. Prove: for all t. For our base case, we will show this is true at t=1. 1 2, so this holds at t=1. For the induction step, we assume that our statement is true at t=k, so, we know that k 2 k. We must show that it is true for t=k 1, which means k 1 2 k 1. This means 1 k. Adding k to each side, we see that 1 k 2k. Looking at k 2 k, if we multiply both sides by 2 we get 2k 2 k 2. F(x)=f(y) =...
FOM Hunt = Complete! | Adventures in FOM
https://cdmachlin.wordpress.com/2013/04/25/fom-hunt-complete
A day in the life of a FOM student at SMCM. April 25, 2013. FOM Hunt = Complete! Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). You are commenting using your WordPress.com account. ( Log Out. You are commenting using your Twitter account. ( Log Out. You are commenting using your Facebook account. ( Log Out. You are commenting using your Google account. ( Log Out. Notify me of new comments via email.
Proof of Uncountability | Adventures in FOM
https://cdmachlin.wordpress.com/2013/04/16/proof-of-uncountability
A day in the life of a FOM student at SMCM. April 16, 2013. Prove that the interval (0,1) is uncountable. If something is uncountable, that means there does not exist a bijective function f:. 0,1) We will prove this by contradiction, so assume that there does exist such a function. So, f:. 0,1) is bijective. This means we can use f to list out all the real numbers in (0,1). We will say a. F(n) We can write each a. In decimal form. f(1)=a. 11526, and a. Leave a Reply Cancel reply. Enter your comment here.
February | 2013 | Adventures in FOM
https://cdmachlin.wordpress.com/2013/02
A day in the life of a FOM student at SMCM. Monthly Archives: February 2013. February 27, 2013. GYHD 3.2 #2,3,4. 2 Suppose either A or B is the empty set. What does that mean about possible functions from A to B? If so, what are they like? 3 Prove in detail that the function f:. Given by the equation f(x)=2x 3-5 is surjective. The definition of surjective is (. A)(f(y)=x). Let b. B We need to show that there is some a. A such that f(a)=b. A=( 5 b)/2) 1/3. F( (5 b)/2) 1/3) = 2( 5 b)/2)-5 = b. 2 if ( a,b).
January | 2013 | Adventures in FOM
https://cdmachlin.wordpress.com/2013/01
A day in the life of a FOM student at SMCM. Monthly Archives: January 2013. January 30, 2013. Conditional Sentences and Ch. 1.3. A conditional sentence is a statement in the form of “if , then ”. The “if” part of the sentence is referred to as the hypothesis, while the “then” part is called the conclusion. If the hypothesis occurs, so does the conclusion. Pretty basic, right? If I am a wizard, then I will buy you a house. Other important things to note from chapter 1.3:. January 30, 2013. Here are just s...
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mathematicalypse.wordpress.com
Examples of Differentiable Manifolds | Casey Douglas
https://mathematicalypse.wordpress.com/2015/05/22/examples-of-differentiable-manifolds
Armageddon serious about maff. Examples of Differentiable Manifolds. May 22, 2015. June 2, 2015. Dedicates a fair amount of its zero-th chapter to examples of (real) differentiable manifolds. I wanted to add a few more examples, in addition to repeating some of those already mentioned. First, of course, are the Euclidean spaces,. Each of these can be covered by the single open set. Is the identity function. However, it should be noted that there are. And this can be generalized to the spaces. With a simi...
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Pre-Calc Review Problems | Casey Douglas
https://mathematicalypse.wordpress.com/2014/07/15/pre-calc-review-problems
Armageddon serious about maff. July 15, 2014. July 15, 2014. 1 Expand the product. Are variables representing unknown real numbers. 2 Here is an expression involving the variable. A) Is the expression. Equal to the original one? Why or why not? B) Is the expression. Equal to the original one? Why or why not? C) Is the expression. Equal to the original one? Why or why not? D) Is the expression. Equal to the original one? Why or why not? E) Are there any numbers that we are not allowed to plug in for.
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Quotient Manifolds | Casey Douglas
https://mathematicalypse.wordpress.com/2015/05/27/quotient-manifolds
Armageddon serious about maff. May 27, 2015. July 15, 2015. Quotient spaces are fundamental objects of study in mathematics, but they nonetheless feel strange or unclear the first few (dozen? Equivalence Relations and Quotient Spaces. Be a set equipped with an equivalence relation. Note that we needn’t impose any additional structure on. For what follows —. Is not assumed to be a group, a ring, a manifold, a vector space, or even a topological space, its just a set. The. The three defining properties.
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Tangent Vectors (Part I) | Casey Douglas
https://mathematicalypse.wordpress.com/2015/07/17/tangent-vectors-part-i
Armageddon serious about maff. Tangent Vectors (Part I). July 17, 2015. July 21, 2015. As discussed in our differential geometry course, a vector field,. On a differentiable manifold,. Is a correspondence that associates to each point. Is the velocity vector. This definition works perfectly fine when. Is an abstract manifold, though, we do not know how to differentiate the outputs of a curve. Even if we use the charts and local. Is a function with domain. This function is obtained from a curve. And we ha...
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Blog | Casey Douglas | Armageddon serious about maff
https://mathematicalypse.wordpress.com/mathematicalypse/blog
Armageddon serious about maff. October 27, 2016. The set of all points. Forms a sphere-like object called an ellipsoid centered at the point. A picture of this surface is shown below). Find the points on this ellipsoid that are closest to and farthest away from the point the origin. Find the equation for the tangent plane to the surface determined by. Find the maximum and minimum values of. Over all points in the region of space. Find the linear approximation of the function. At the point $latex (0, 1)4.
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More Great Math Quotes | Casey Douglas
https://mathematicalypse.wordpress.com/2013/01/28/more-great-math-quotes
Armageddon serious about maff. More Great Math Quotes. January 28, 2013. January 30, 2013. These are taken from various FOM students. 8220;Math was here before we were here to describe it.” – Cyrus. 8220;… the marks that dictate a mathematicians train of thought are far from meaningless … math is a necessary field of learning because it describes and proves why the physical world works the way it does.” – Kyle. 8221; – Cara. 8220;If x is an element of the null set, then this blog will be the best....
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Adventures in FOM | a day in the life of a FOM student at SMCM
A day in the life of a FOM student at SMCM. April 25, 2013. FOM Hunt = Complete! April 23, 2013. Also, it turns out that that confusing paradox that dealt with “the set of integers definable in 12 words or less” has a name! It’s called the Berry Paradox. And here I just thought that it was some weird, convoluted example that Casey made up. April 21, 2013. On that related note, the semester’s almost over. Just one more week of classes! April 18, 2013. April 16, 2013. So, it turns out that the set of sets ...
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