Week 3 Assignments
Written work – None
WeBWorK – Start on WeBWorK 3, (it will not be due until Tuesday, 9/25 at midnight).
OpenLab – OpenLab #3, due Tuesday, 9/20 (at start of class).
NOTE: Next week Tuesday 9/18 there are no classes.
Page 5 of 5
This assignment is due Thursday, September 13, at the start of class.
Assignment. Choose ONE of the following two topics. Write a reply to this post, responding to the topic. Begin by telling us which topic you chose. (1-2 paragraphs).
Topics.
- Sometimes people can recognize a time when their opinion of math dramatically changed either for the better or the worse. If such a time happened to you, tell us about it.
- Choose an experience you had in which you suddenly understood a math concept (it could be any kind of math, from elementary school up through college). Describe what happened. Do you think you could explain it to others in a way that they could have the same flash of understanding?
Extra Credit. For extra credit, write a response to one of your classmates’ comments. Do you feel the same, or different? Did you learn anything? Did you get any ideas about teaching, or about learning?
Why are we doing this, anyway? We are following two ideas that have come up already in class — things that may not seem related to learning math, but research shows that engaging in these activities can dramatically increase the amount that you learn, and change the way you learn it. The first is writing – something not typically associated with mathematics. When you express your ideas in words, it forces you to think them through very carefully, detail by detail. A great way to check and see if you really understand something is to try to explain it to someone else, either out loud or in writing. Example: if you know how to add fractions, try teaching it someone who doesn’t know how. The second is called metacognition, or “thinking about thinking.” This happens when you think about what was going on in your head while you were working on a problem or trying to learn a new idea. What train of thought did you follow? Where did you get stuck, and what did you do next? What were you feeling at the time? and so on. Combining writing and metacognition can be a tremendously powerful tool in identifying the ways we learn best and the ways we make mistakes, and learning to improve. However, like any skill, it takes practice. That’s why we’re getting started by writing a little about our past experiences with mathematics.
Week 2 Assignments
Because we do not have class on Tuesday, September 11th, all assignments will be due on Thursday, September 13th, this week.
Written work – Sec 1.8 p.28: 3, 5, 6, 8, Due Thursday, September 13th, at the start of class.
NOTE: On this assignment, odd problems are worth 3 points, even problems worth 5 points.
WeBWorK – Assignment #2, dueThursday, September 13th, at midnight.
OpenLab – OpenLab #2, dueThursday, September 13th, at the start of class.
WeBWorK is accessible from on and off campus (anywhere you have access to the internet). Your first WeBWorK assignment is due on Tuesday, September 4th, at midnight, and will cover the material from the second day of class. Here’s what you have to do:
Assignment. To get started , you must complete the following three steps.
Step 1. Log in to WeBWorK here: http://mathww.citytech.cuny.edu/webwork2/MAT2071-F18-Reitz. I have created Usernames and Passwords for each student registered for my class.
Username. Your username for WeBWorK consists of your first initial plus your last name, all lowercase (for example, John Smith would have username ‘jsmith’).
Password. Your temporary password is the same as your username (if your username is ‘jsmith’, your password is currently ‘jsmith’).
Step 2. Change your password and update your email address. To do this, select “Password/Email” from the main menu on the left. Use whatever email address you like (I suggest using one that you check often).
Step 3. Complete the first assignment, titled Assignment1-Sec1.2-1.3. Click on an assignment on the main screen to get started.
If you have any trouble – either with logging in, or with completing the assignment, post a comment here or send me an email and I will get back to you.
WeBWorK Tips:
- Click on a problem to see the details (the list of problems appears in the menu on the left). Enter an answer and hit “Submit Answers”. Don’t worry, if you get it wrong you can try it again.
- You can work on the problems in any order you wish. You can do some problems now, and come back and do the rest another day (your work will be saved, as long as you submit your answers).
- If you want to print out a copy of the assignment, click on the assignment name in the main menu on the left, and then click the link in the main screen area that reads “Download a hardcopy of this homework set.”
Hi everyone,
Your first homework assignment consists of some problems from the book, as well as a WeBWorK assignment – these are due on Tuesday (written work must be handed in in class, WeBWorK must be completed online by the end of the day). Your first OpenLab Assignment is due next Thursday, September 6.
Welcome back,
Prof. Reitz
Week 1 Assignments
Written work due Tuesday September 4th – Sec 1.1 p.7: 1, 12, 19, 26, 29, 35
NOTE: On this assignment, odd problems are worth 2 points and even problems worth 4 points.
WeBWorK – WeBWorK 1, due Tuesday September 4th at midnight
OpenLab – Register for the OpenLab and join this course (instructions provided in a separate post). “OpenLab #1: Advice from the Past” due Thursday, September 6.
For the past several years I have taught this same course in the Fall semester. At the end of each course, I give my students the following assignment:
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 … describing what you would tell them.
To see the assignment and the students’ responses, follow this link for Fall 2017 and this link for Fall 2016.
Your assignment, due at the beginning of class on Thursday, September 6th, is to:
- Read through ALL the responses (there are 25 of them altogether).
- Write a reply to this post (1 paragraph) responding to all of the following:
- What advice seemed most relevant to you personally? Why? (you can copy/paste a short statement, or put it in your own words)
- Based on this advice, what changes can you make right now to help you succeed in this course?
Extra Credit. For extra credit, write a response to one of your classmates’ comments. Do you have any advice? Be kind.
This course is MAT 2071, Introduction to Proofs and Logic, taking place in the Fall 2018 semester with Professor Reitz. We will be using this website in a variety of ways this semester – as a central location for information about the course (assignments, review sheets, policies, and so on), a place to write about the work we are doing, to ask and answer questions, to post examples of our work, and to talk about logic, proofs, mathematics, reality and so on.
Getting Started
Anyone on the internet can look around the site and see what we are doing, and even leave a comment on one of the pages. However, only registered users can create new posts and participate in the discussion boards.
How do I register?
You will need to do two things:
- If you have not used the OpenLab before, you must first create an account. You will need access to your citytech email address for this. Detailed instructions for signing up on the OpenLab can be found here.
- Once you have created an account on the OpenLab, log in and then join this particular course, 2018 Fall – MAT 2071 Proofs and Logic – Reitz. To do this, first click the “Course Profile” link at the top left of this page (just under the picture). Then click the “Join Now” button, which should appear just underneath the picture there.
Problems with the OpenLab or with your CityTech email:
Please let me know if you run into any problems registering or joining our course (send me an email, jreitz@citytech.cuny.edu). I also wanted to give you two resources to help out in the process:
1. For problems with your citytech email account, contact the Student Computing Helpdesk, either in person, by phone, or by email:
Student Computing Helpdesk
Location: Library Building, First Floor (L-114)
Hours: TBD
Phone: 718.260.4900
E-mail: Studenthelpdesk@citytech.cuny.edu
Their website also contains tutorials and FAQ on common problems
2. For problems registering for the OpenLab, contact the OpenLab support team, either by email at openlab@citytech.cuny.edu, or by following this link.
Logic on Math StackExchange
- Do we distinguish between these uses of $"="$ in logic? July 16, 2024In the didactics of mathematics it is common (at least in the German literature) to distinguish these uses of "$=$": $(1)$ Identities: $(a+b)^2=a^2+2ab+b^2$ (we sometimes use $\equiv$) $(2)$ Bestimmungsgleichungen (literally: determination equation): $x^2-4x+1=0$ (we sometimes use $\overset{!}=$) $(3)$ Defining equations: $f'(x_0)=\lim\limits_{h\to 0}\frac{f(x_0+h)-f(x_0)}{h}$ (we sometimes use $:=$) Do we distinguish, on a logical basis, between these […]math_undergrad_questions
- Problem with Fitch : How to Eliminate ¬∃? July 16, 2024fitch problem: I've been working on a Fitch-style proof problem, and I've encountered a difficulty in a specific step (step 11). The problem restricts me to using Taut-Con rules from Con-Rules. Here’s where I’m stuck: I need to eliminate ¬∃ from ¬∃x ¬Cube(x), so I could use Disj.-Elimination, but every attempt I've made results in […]Bogdan Klinowitzki
- Proving that the set of sentences that are true using the symbols $+,<,=$ is the same over all ordered fields July 16, 2024I am interested in whether the set of formulas that one can prove true for a concrete ordered field using the symbols $+, 1 and every x there is y with n · y = x. G ≡ Q. G is o-minimal: all definable subsets of $G$ are finite unions of (possibly degenerate) intervals The […]user1868607
- A paradox like Russell's paradox is found in the proof of Godel's incompleteness theorem. Right or wrong? July 16, 2024The Gödel Incompleteness Theorem was a major discovery in modern logic that has consistently attracted the attention of scientific and philosophical circles. However, since the Gödel Incompleteness Theorem was put forward, the scientific and philosophical significance of its proof has been questioned; in particular, Wittgenstein regarded it as a certain logical paradox. In the proof […]Zhang Hong
- What strategies can I follow to find the counterexample of an invalid categorical reasoning? [closed] July 15, 2024I am taking the discrete mathematics course in Engineering and I am having problems with the reasoning exercises in the logic part. I have an extremely hard time finding suitable propositional functions and a universal set that invalidates the reasoning, for example with these two invalid reasonings: ∀x: [d(x) ⇒ c(x)]; ∃x: [-c(x) ∧ p(x)] […]Lucio Mazzini
- logic puzzle birth year July 15, 2024Suppose we have two people A and B. A died 129 years after B was born. At least one of A or B was alive for exactly 100 years. B died in 30 B.C. When was A born? This confused me. If B lived 100 years, B would be born in 130 BC and so […]james
- Prove $(B \implies (C \implies D)) \implies (C \implies (B \implies D))$ without the Deduction Theorem July 15, 2024I am reading "Introduction to Mathematical Logic" by Elliott Mendelson, and I am currently at the axiomization of propositional calculus. Mendelson presents the following three axioms (with modus ponens as the only rule of inference): $A1: B \implies (C \implies B)$ $A2: (B \implies (C \implies D)) \implies ((B \implies C) \implies (B \implies D))$ […]gestory2
- If sub-universe $S$ of lattice has congruence $\theta$, does the lattice have a congruence $\lambda = \theta \cap S^2$? [duplicate] July 15, 2024Let $(L, \lor , \land )$ be a lattice and $S$ a sub-universe of the lattice. A sub-universe of a lattice will be any subset of the lattice set that is non-empty and closed under $\land$ and $\lor$. Let $\theta$ a congruence of $(S, \lor_{S\times S}, \land_{S\times S})$. Is it true that there is a […]lafinur
- Is implication true if two statements are always the case? July 14, 2024I have a task that requires me to show that under a certain set of circumstances, a set has property A if and only if it has property B. I can show that under the given circumstances, the set always has property A. I can also show that it always has property B. Since these […]ormondo
- Examples of index set not Turing equivalent to the Halting Problem? July 14, 2024By definition, a set $I \subseteq \mathbb{N} $ is an index set if $\forall i,j ((i \in I \land \varphi_i = \varphi_j) \implies j \in I)$. Thanks to the Rice's Theorem, we know that, said $F$ a family of partial computable functions on the naturals, the set of their code $E = \{e \in \mathbb{N} […]NON
Recent Comments