Your grades have been submitted to CUNYFirst, and a detailed breakdown of your grades (including your score on the the final exam) has been posted to the GRADES page on the OpenLab. Send me an email if you have forgotten the password.

Happy holidays to all, and the very best of luck in your future work.

Just a heads up – I will be submitting grades by the deadline (12/27), but will likely not be able to get them in earlier as I had planned (unfortunately my family has been sick this week). Once I have submitted grades in CUNYFIRST, I will also post detailed info here on the OpenLab.

This assignment is the final deliverable for your project (worth 10 points). It is an individual, not a group, assignment and should be submitted by email, not on the OpenLab.

The Semester Project consisted of a number of related activities and assignments – before you begin writing, please take a look at the list and click each of the links to remind yourself of all the parts of the project.

Assignment (Due before your final exam – Tuesday, December 20th). SUBMIT BY EMAIL, NOT ON THE OPENLAB. This is your chance to reflect on the Semester Project, and to describe your contributions to the major group activities. Please respond to all of the following.

Part 1 (200 words minimum). Write one or two paragraphs reflecting on the Semester Project, from the initial assignment (“OpenLab #5: Bridges and Walking Tours“) through to the final presentations. You can use the following questions to guide your writing if you wish (or you can respond in whatever way you wish):

What was your overall impression of the project? What did you enjoy the most? Least?

Do you feel that the project enhanced your experience of the class? Was the project related to the course material?

How did you feel during the process? What was the best moment? The worst?

Was the project scaffolded appropriately? Did you need more or different support for any of the assignments? Do you have any suggestions for making the project more effective?

Part 2. Describe your personal contributions to the final two major group assignments, the group paper and the group presentation. Do you think that you were an equal contributor in your group? Be as specific as you can.

Assignment (due Thursday, December 15). Imagine that you are invited to speak on the first day of MAT 2071, to give advice to entering students. Write at least three sentences responding to at least one of the following, describing what you would tell them.

What do you wish that you had been told at the start of this class, to help you succeed?

Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.

What is the most important prior knowledge (not taught in the class) that you need in order to succeed? Why is it important?

Extra Credit. Respond to someone else’s comment. Do you agree? disagree? Have anything to add?

Written work: The following problems are SUGGESTED for practice (they could be on the final!), but will NOT be collected. Sec 12.5 p214: 2, 6
Sec 12.6 p216: 1, 2
Sec 13.1 p222: 1, 4, 5 WeBWorK – none OpenLab – OpenLab #8: Advice for the future, Due Thursday 12/15. Project Reflection – Due before the final exam, Tuesday 12/20.

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.

Consider LF, the logical framework used to define UTT (unified theory of dependent types). The next two quotes are from here. LF is a simple type system with terms of the following forms: $$\textbf {Type}, El(A), (x:K)K', [x:K]k', f(k),$$ where the free occurences of variable $x$ in $K'$ and $k'$ are bound by the binding […]

Let $A$ and $B$ be arbitrary sets and consider the following two statements: \begin{gather} (x\in A)\Rightarrow (x\in B)\\ (x\in A)\Leftrightarrow (x\in B) \end{gather} These two statements are usually worded as follows: If $x$ belongs to $A$, then $x$ belongs to $B$” “$x$ belongs to $A$ if and only if $x$ belongs to $B$”. My questions […]

In the Peano arithmetic wikipedia article, a figure is shown on why the axiom of induction is necessary, without it, the set of whole dominos would be a valid representation of N In Robinson arithmetic, we have the axiom y=0 ∨ ∃x (Sx = y) instead. I don't see how this axiom prevent that situation, […]

I'm currently reading some notes on AECs (here), and just wanted to make sure I understand the argument in Corollary 12.8, for I'm still getting used to generalized Ehrenfeucht-Mostowski models in AECs. As far as I understand, EM blueprints/templates $\Phi$ keep track of the quantifier-free sentences some indiscernible satisfies (that is, a single $n$-type for […]

I am preparing to take an entrance exam for a university in my country, which will happen soon. As part of my preparation, I have been practicing with some sample math tests provided by the university. However, I recently came across a math problem that I could not understand at all. This is the exercise: […]

I'm new to logic theory and i'm stuck with the understanding of decidability of a logical system. As far as I understand, the decidability of a logical system is related to the existence of an effective (in terms of time) procedure to tell whether a given formula can be proved by using the "instruments" of […]

I work relative to a fixed first-order language $L$. As usual I call those formulas which do not contain free variables sentences. There are several derivation systems for first-order logic. For example, in Goldrei's Propositional and Predicate Calculus a derivation of $\psi$ relative to a set $Ax$ of sentences is a list of formulas $\phi_1,....,\phi_n$ […]

A set is limit computable, or $\Delta^0_2$, if its characteristic function is equal to $\lim_{s\rightarrow\infty}g(x,s)$ for some total computable function $g$. And given a computable ordinal $\alpha$ and a path $P$ through Kleene's $O$, a set is $\alpha$-c.e. if its characteristic function is equal to $\lim_{s\rightarrow\infty}g(x,s)$ for some total computable function $g$ such that there […]

Context The System CL In section 6.3 of Topoi, Robert Goldblatt describes a Hilbert-style deductive calculus (the only inference law is modus ponens) for the propositional logic of a language with the primitive logical connective symbols $\\{\neg, \wedge, \vee, \rightarrow\\}$, which he calls CL, with following axiom schemata: $\alpha\rightarrow(\alpha\wedge\alpha)$ $(\alpha\wedge\beta)\rightarrow(\beta\wedge\alpha)$ $(\alpha\rightarrow\beta)\rightarrow((\alpha\wedge\gamma)\rightarrow(\beta\wedge\gamma))$ $((\alpha\rightarrow\beta)\wedge(\beta\rightarrow\gamma))\rightarrow(\alpha\rightarrow\gamma)$ $\beta\rightarrow(\alpha\rightarrow\beta)$ $(\alpha\wedge(\alpha\rightarrow\beta))\rightarrow\beta$ $\alpha\rightarrow(\alpha\vee\beta)$ […]

Robinson arithmetic (Q) is weaker than PA. We know that any theory that interpret Robinson arithmetic will be incomplete as well. It seems Robinson found his axioms noting what was necessary to conclude the incompleteness proof. But what if there is some very strange axiom system we don't really think that is connected to arithmetic, […]

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