The review sheet for the final exam has been posted under Classroom Resources / Exam Reviews. I will distribute a hard copy of the review questions in class. As always, let me know in person, by email, or here on the OpenLab if you have any questions.

I found the Video created by Vi Hart is fascinating, beacause it make me feel that factoring is way more interesting than what I knew before. She found the pattern of factoring by drawing the stars. Which is very unlike with the way how other teachers introduce pattren of factoring to their students. I loved the out come of the last few drawings.

This video that created by Vi Hart is about how to explore the mysteries of flexagation., by use strips of paper. I found it if very fascinating, you strip and tape it nicely into a twisty – flody loop. and you can flip the Hexaflexagons again and again.

This Video is called Pi Day is Round, I found this is very interesting beacuse I remember that on the day 3/14/15,My hight school math teacher told our class the today is Pi day, but no one queation that if we round the Pi it wil 3.1416, not 3.1415.

Part 2.(Video One)

I am very glad that I got the chance to watch this videos created by Vi Hart, after I watched these videos I was shocked by Lady who create the videos. They show you many very intersting things that related to math, but you will naver see this things in taxt book or learn them in class. In addition, This Videos also shows that math is related to verything in our daliy life. It also convinced me that Math is not just a course, it is a independent world that has it own system and language. However,I think that I did not understant about her Videos was: what was the reason she speak so quickly in her very videos? I had to watch the video three or four time to get understant the concept of the video.

Part 3.

Many student give up math, because they belive that math class is one of most boring class, and it is also very hard. I have been ask many people about what is you favorite class and wich class you hate the most. I found one thing about math is very interesting, many people see math as thery their favorite calss or the class they hete the most. So I come up a conclution that people who understant the math will love math but people who don’t unserstant the math will think it is a very boring class. So as a math teacher, it is important that you can show your student the side of math that is interesting. But it is not a essey thing do to, beacuse, math is not like other courses, you can tell a intersting story about it or do a fancy expaeriment. I believe that Vi Hart showed us a very good way to teach your student math, just like the Video one.

Written work, due Tuesday, November 29th, in class:
Section 11.0 p178: 3,4
Sec 11.2 p187: 1,2,7 – In addition, complete Example 11.8 at the top of p182. WeBWorK – Assignment 6, due Tuesday, November 29th, at end of day. OpenLab – none

Project Deadlines:
Final Draft of paper due in class on Thursday, 12/1.

I forgot to get either of your contact information. So I figured I’d make a post and hope you guys (including Prof. Reitz) see this. If you have any comments or criticism, lay ’em on me. This is an inital draft so it’s not complete, currently juggling three essays T.T

Written work, due Tuesday, November 29th, in class:
Section 11.0 p178: 3,4
Sec 11.2 p187: 1,2,7 – In addition, complete Example 11.8 at the top of p182. WeBWorK – Assignment 6, due Tuesday, November 29th, at end of day. OpenLab – none

Project – First draft of group paper due in class this Thursday, 11/17.
Final Draft of paper due in class on Thursday, 12/1.
Group Presentations on Thursday, 12/1 and Tuesday, 12/6.

The review sheet for Exam #3, taking place next Tuesday 11/22, is posted under Classroom Resources / Exam Reviews. As always, if you have any questions or notice any errors please let me know (by email, in person, or here on the OpenLab).

This video shows the relation of simple doodling to demonstrate and compare the relationship between the Fibonacci sequence and real life.

This video demonstrates the use of symmetry and its reflection in order to create a pattern shaped as a braid. The use of this type of pattern may be used to produce a sound braid shape such that when notes are added to it there will be harmony. Mathematically speaking this sound braid is considered a an object exsting on a two-dimensional plane with space time.

This video gives details on the different types of infinity and impresses on the difference between countable infinity and uncountable infinity.

Part 2. My favorite video of the three is the Doodling in Math video. The video was eyeopening for me because I never knew how much of a connection a sequence can be related to real life. I loved the use of a pineapple and a pine cone, which already are two amazing things, the video left me wanting to know much more about the Fibonacchi sequence. I learned that in fact a pine cone of any shape still follows the order of the Fibonacchi sequence. One question I have is there a way to show that the pine cone’s leaves on the top reflects or follows the sequence as well?

Part 3. Thia video has inspired me to be creative when I teach math in the future. I believe videos like this or even examples related to this, could have helped me get a stronger foundation of math because it might have kept my attention a little but longer than the more traditional way of teaching where a teacher gives direction and leave the student to apply the concepts to solve problems. One may ask, is this way of teaching math? I declare that it is indeed math and this type of teaching may prove highly relevant in teaching students at any grade level, and it is done in a way that will help a student remember and apply it to other forms of sequences and patterns. There is a big connection between this video about the Fibonacchi sequence and the reading Lockhart’s Lament, because Lockhart professes that there is a need to teach students in a way in which they get a full understanding of the meaning of things instead of memorizing a formula. The example he used with a box whose space is shared by a triangle and using the triangle as part of the rectangle is a very useful way to show students why the formula of the area of a triangle works in turn helping them understand that the imagination is what helps you understand the notion. The author states that something as simple as drawing a straight line connecting to points on the rectangle gives a drawing more meaning. Accordingly, Vi Hart shows that she has the same sentiments by having a video where she explains the sequence but takes her time to demonstrate what a sequence meant and proved it in various ways using a pine cone and a pineapple giving the sequence more meaning. The use of real life examples is a effective way of teaching, I find that students may pay more attention and they will most likely remember what was taught without using memorization.

Doodling in Math Class: Stars
This video involves the concept of factoring using stars. The stars total points are factored and you are able to create 1 dimensional stars with those factors.

Doodling in Math: Sick Number Games
This video is about turning numbers in specific triangles and creating patterns that would make it easy to guess the numbers that would follow.

Rhapsody on the Proof of Pi=4
This video involves breaking down a square with perimeter 4 into even smaller ones until you almost get the shape of a circle. Other shapes were used and were broken down until they became almost straight lines.

Part 2
The video I chose to discuss is Doodling in Math Class: Stars which explains how you can make factors of star points useful. It was the first video I watched so it completely intrigued me at first glance. The quick drawing with precision and accuracy made the presentation that was displayed appear visually entertaining. When I then looked at what was being said I became even more intrigued since it showed at first how stars can be easily made by using 2 of the same shapes. These shapes included a triangle, which came first, then a square and finally a hexagon. Then she went into factoring these stars and made 1 dimensional stars that correlated to the factors. It was like making factoring, which she said was barely discussed, into a more enlightening scope than a formal one.

Part 3
This video reflects to my math teaching since it can help to make people think outside of the box. Factoring might be simple but there is never a fun way to teach it. By creating stars and then factoring them then factoring can lead children to see the fun in math. People usually remember entertaining teachings but tend to forget the boring ones. It can even lead you to start your own ideas since one perspective can lead to many others. By looking at this video I was able to broaden my understanding of star points where they can be made using regular shapes instead of having to draw every single point one by one. This sort of correlates to Lockharts Lament since this sort of teaching of factoring would make children think and to not see things with a formal approach but a creative one. By doing this, it might spark creativity in them as well making them real mathematicians instead of just the copy and paste ones.

Let BExpr be the variety of all boolean expressions that are defined by the following grammar: I have two recursive functions numbinexprs and numexprs. numbinexprs returns the number of binary subformulas when given a boolean expression, and numexprs returns the number of subformulas. I am supposed to prove the following statement by structural induction: numbinexprs(b) […]

I got the following definition: $F$ and $G$ are propositional formulas, which are called resemblant, or in symbols $F \asymp G$, if there exists at least one allocation, such that $\beta(F) = \beta(G)$. Now, while the definition is easy, I would like to find out if $\asymp$ is reflexive, transitive and symmetric, but I do […]

The problem: Define the recursive function numexprs that returns the number of part expressions when given an arithmetic expression. Note that even bool is a part expression.(Individual parentheses are not counted as part expressions.) Evaluate your function on the expression below, and verify that it returns the expected value of 8. I don't understand how […]

Assume a first-order context. Let $\mathrm{tran}(x)$ denote that $x$ is transitive: $$\mathrm{tran}(x) \leftrightarrow (\forall y \in x) (\forall z \in y) (z \in x)$$ Let $\mathrm{suptran}(x)$ denote that $x$ is supertransitive: $$\mathrm{suptran}(x) \leftrightarrow (\forall y \in x) (\forall z \subseteq y) (z \in x)$$ Consider the following axiom schemas of reflection: \begin{align} & \phi \to […]

Consider the graph coloring problem. Below is a graph and we want to color the nodes using one of the three colors Red, Green, or Blue. The constraint is that the two neighboring nodes cannot have the same color. See the graph here (a) Specify the variables, domains of each variable, and the constraint network. […]

Let $\mathsf{SOL_{abs}}$ be the "forcing-absolute" fragment of second-order logic - that is, the set of second-order formulas $\varphi$ such that for every (set) forcing $\mathbb{P}$ and every (set-sized) structure $\mathfrak{A}$ we have $$\mathfrak{A}\models\varphi\quad\iff\quad\Vdash_\mathbb{P}(\mathfrak{A}\models\varphi).$$ Note that this is in fact definable since the second-order theory of a structure in $V_\kappa$ is calculated, uniformly, in $V_{\kappa+1}$; by […]

Let $A$ be a formula, $x$ a variable, $t$ a term and $\Gamma$ a set of formulas. If $\Gamma\vdash A$ and $x$ is not a free variable of some open assumption, then $\Gamma\vdash A\to\forall_xA$ and $\vdash \forall_xA\to A[x:=t]$ by the natural deduction rules. Thus, $\Gamma\vdash A[x:=t]$. However, I was just told that $$\tag{1}\text{If }\vdash A\text{, […]

I am having a hard time finding the correct solution for the following problem, right now. "New trade agreement means Dollar and Yuan will rise and fall together" How should I express this statement mathematically? Given that: D: the Dollar is strong, Y: the Yuan is strong T:New US-China trade agreement is signed Which one […]

Let $A$, $B$ be formulas and $x$ a variable. It seems like the formula \begin{equation}\tag{1} (A\to B)\to\forall_xA\to\forall_xB \end{equation} can only be derived (using the natural deduction rules) if $x$ is not a free variable of $A\to B$. However, based on my intuition, I expected that $(1)$ is derivable for all formulas and variables. Maybe a […]

Let C = ∩{A | A is ({A1}, {ξ→})-inductive}. Show that any element of C is a tautology or tautologically equivalent to A1. By definition of an inductive set, I know that A1 must be a subset of C by virtue of the ξ→ function. And I know that to prove any element of C […]

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