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. Â 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). Â Once I have submitted grades in CUNYFIRST, I will also post detailed info here on the OpenLab.

ThisÂ assignment is the final deliverable for your project (worth 10 points). Â It is an individual, not a group, assignment and should beÂ submittedÂ 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 Â of all the parts of the project.

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

Part 1 (200 words minimum). Â 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. Â 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? Â WhatÂ did you enjoy the most? Least?

Do you feel that the project enhancedÂ your experience of the class? Â 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?Â Did you need more or different support for any of the assignments?Â Do you have any suggestions for making the projectÂ more effective?

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

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

What do you wish that you had beenÂ 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 importantÂ prior knowledgeÂ (not taught in the class) that you need in order to succeed? Â Why is it important?

Extra Credit.Â Respond to someone else’s comment. Â 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 –Â none OpenLab –Â 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. Â I will distribute a hard copy of the review questions in class. Â 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, Â you strip and tape it nicely into a twisty – flody loop. Â 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? Â 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 Â 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. Â I believe that Vi Hart showed us a very good way to teach your student math, just like the Video one.

When proving implications, I always thought to prove it true I need to reach the same conclusion given in the implication. I encountered this problem (pg 56) that asked to prove "for all $x\in\mathbb R$, if $x^2 - 7x + 10 \ge 0$ and $x > 3$, then $x \ge 4$." To which the proof […]

In my lectures, we define an Henkin set for a theory $T$ as a set $H$ of enunciates in a signature $L$ that is: Deductively closed for $T$: if $T \vdash A_1,...,A_n \Rightarrow B$ and $A_1,...,A_n \in H $, then $ B \in H$; Rich: if $\exists xB \in H$, then it exists a ground […]

Why should a math student understand logic before understanding and doing proofs? Why is it necessary? It's true that the formal language of logic is useful, but, for example, where's the practical use of truth tables or inference rules? When proving mathematical statements, one typically uses proof methods like direct or induction. And most proofs […]

Let $T$ be a sound, r.e. theory containing elementary arithmetic. Fix a $T$-proof predicate $\mathrm{Proof}_T(x,y)$. Let $\phi(x)$ be such that, for all $n$, $T\vdash\phi(n)$; $\forall x\,\phi(x)$ is true but $T$ does not prove it. Define $f(n)$ as the minimal length of the $T$-proof of $\phi(n)$ (i.e. $f(n)$ is the minimal $m$ such that $\mathrm{Proof}_T(m,\ulcorner\phi(n)\urcorner)$). Suppose […]

I'm trying to prove that a set of clauses are unsatisfiable using resolution and unification, however, I am unsure about a step I made during my calculation. Here is the set of clauses I am working with: {{p(a,f(x)),Â¬q(x,f(a))}, {Â¬p(y,y),r(a,y)}, {Â¬p(x,y),Â¬r(x,f(a)}, {p(x,f(y)),Â¬q(f(y),x)}, {q(x,x)}} The first thing I did was substitute f(x) for z and f(y) for […]

The subsystem of second order arithmetic $\textbf{RCA}_0$ is understood as the relative computability. In another word, if there exists a non-computable function $f$, $\textbf{RCA}_0$ can prove all functions $g$ exists where $g \leq_T f$. However, the axioms of $\textbf{RCA}_0$ can not prove the existence of $f$. One of the explanations is we can view $f$ […]

I've seen from various sources that NBG can be written with finitely many axioms. But I've been struggling for a while to find a list of these axioms, every list I can find uses an axiom of schema in one form or another. Example nlab uses a schema for Class comprehension. My question is what […]

The axiom of replacement says, loosely speaking, something like "if a set surjects onto a class, that class is also a set." If we modify this as follows: If a class injects into a set, that class is also a set. If a class is in bijection with a set, that class is also a […]

This might be an elementary question, and I apologize for that. I've been dabbling in ordinal analysis / proof theory for a few days, back when I read W. Buchholz, â€śA new system of proof-theoretic ordinal functionsâ€ť. Then, I read up on ordinal analysis itself on Wikipedia. There, it states that: The proof-theoretic ordinal $n$ […]

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