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Questions tagged [logic]

The tag has no usage guidance.

11
votes
2answers
202 views

“Always/Sometimes/Never” vs. “True/False” questions for mathematical reasoning

Has anyone performed a study on the differences between student interpretations of these words? Background: When I taught high school geometry and later undergraduate precalculus, I noticed that ...
2
votes
1answer
117 views

What does “Four selected students are not born in the same months” mean?

I am teaching on probability. I found a question that seems to be ambiguous as follows. Four students are randomly chosen from a place. Assuming the birthdays of people are equally likely to occur ...
6
votes
2answers
200 views

Teaching logic through “high school algebra”?

I am going to be teaching a discrete math class in the fall. One of the major goals of the course is a solid understanding of the basics of logic: the precise meanings of "and", "or", "not", "implies"...
2
votes
2answers
169 views

Resources for Teaching Logic to Primary School Children?

What are some books or other resources for teaching primary school children logic?
15
votes
3answers
199 views

How to teach students the value of concrete counterexamples?

I teach exercise sessions for a Linear Algebra course for 1st semester students in Europe. Students have to prepare some exercises at home. In class, I call on students to present their solutions. ...
0
votes
1answer
135 views

What does math teach students who won't need university-level math, that Logic can't?

Sources: 1 by Tim Gowers. 2 by Marcus du Sautoy. 3 by Richard Muller. This question involves only those who won't need university-level math, and accepts that pre-calculus, probability & ...
-6
votes
4answers
292 views

How to write an individual real number? [closed]

I just read an interesting book: "Classical and nonclassical logics", Princeton Univ. Press (2005) by Eric Schechter. On p. 208 he writes: Also for simplicity of notation, we have chosen an ...
10
votes
5answers
1k views

Book request: teaching proving and reasoning at an American university

I am a European postdoc who recently teaching at a large public university in the United States. I will have to teach a course for undergraduate students that introduces them to proving and reasoning ...
16
votes
6answers
533 views

Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?

I am teaching Calculus I and will be teaching it again. To me, the $\varepsilon$-$\delta$ definition of limit is one of the key ideas of Calculus; learning calculus without learning $\varepsilon$-$\...
6
votes
2answers
189 views

Names for laws involving implication and/or exponentiation

The following are all logical equivalences $p \wedge q \Rightarrow r \;=\; p \Rightarrow (q \Rightarrow r)$ $p \Rightarrow q \wedge r \;=\; (p \Rightarrow q) \wedge (p \Rightarrow r)$ $p \vee q \...
8
votes
1answer
171 views

Where can I find a set of these 'logic' blocks?

(It will be difficult to answer this question without 'advertising' for a retailer, but I've searched for these several times in the past few years, to no avail.) In Math From Three To Seven (The ...
3
votes
2answers
198 views

Mathematics Branches and Foundation

Hi I hope every one is fine , I am an Electrical Engineer. I asked before about real and complex analysis because I am interested in Signal Processing also I am interested in coding theory and ...
4
votes
3answers
232 views

“The following are equivalent”

What do you say to the following way of teaching "if" and "the following are equivalent"? Has somebody ever taught it like this? An implication A -> B can be viewed as asserting that B is at least as ...
9
votes
4answers
554 views

Why are proofs by contradiction counterintuitive?

And how to make them intuitive? We are tasked to prove $P \implies Q$. So we assume $P$ and are trying to prove $Q$. We assume not-$Q$ ($\neg Q$) and derive a contradiction, establishing $Q$. There ...
1
vote
3answers
89 views

Determining sets to show sufficiency of a condition?

$p \to q$ that means (among others) $p$ is a sufficient condition for $q$. To show the sufficiency, I teach my study by determining the set for $p$, the set for $q$ first and comparing their ...
1
vote
1answer
74 views

Logic and arguing [closed]

When I was in school I studied mathematical logic and proofs, thinking on how to prove stuff on my own as practice. This can be useful to be able to influence others visa logical, undeceitful thought....
10
votes
4answers
6k views

Is it possible to improve logical thinking and problem solving abilities?

I'm from Italy and I'm 13 years old. I'm good in Math and I'm good in languages (I know Italian, English and Russian and I think I'm good at them). I'm a programmer and I know HTML, CSS, JS and Python....
17
votes
5answers
542 views

What is a variable?

There are two kinds of answers I'm looking for: What do students think a variable is? What do YOU, the teacher, think a variable is? I'm also interested in why you think a variable is what you think ...
8
votes
1answer
210 views

Educational styles for writing proofs

Can someone please point to research papers that analyze different ways of expressing informal proofs from an educational point of view? I am particularly interested in proofs by induction but I would ...
10
votes
3answers
4k views

What does maths teach you that logic does not?

[Source:] Having studied maths gives you a particular way of thinking through problems that Intro to Logic just doesn't. Will someone please explain and explicate the quote above? Please pardon me ...
19
votes
2answers
731 views

Can students tell the difference between the “definition if” and the “theorem if”?

The word "if" is used in two meanings in mathematics: Definition. A topological space is compact if every open cover has a finite subcover. Theorem. A topological space is compact if it is ...
12
votes
2answers
162 views

Words used in quantifier proofs

I'm creating a list of "gotcha words" that are often used in writing proofs (particularly quantifier proofs), but frequently in more than one possible way, and that beginners frequently misuse or ...
15
votes
2answers
380 views

Logic in symbols or words

Making precise logical statements is an important part of teaching and learning mathematics. There are many ways to write such statements, and let me divide them into two main types1: writing in ...
12
votes
2answers
454 views

What to teach in Set Theory & Logic Course

I will be teaching a third-year introductory course on Set Theory and Logic soon and was hoping to get advice from this community. I would rate my students' proof abilities as weak and was hoping to ...
5
votes
1answer
118 views

Logic/Mathematics problems for training

Where I live, there is this competition called the "Känguru Wettbewerb" (german), in English, that would be "Kangaroo Competition". This is a mathematics competition where the goal is to solve ...
12
votes
10answers
518 views

Entertaining examples of multiply quantified statements

I am teaching a discrete math course, and doing multiply quantified statements. All the book examples are sober and forgettable: Every real number has a reciprocal. For all triangles x [in a "...
6
votes
3answers
369 views

What is a good answer to the question “Which logic is better?”

In my undergraduate logic courses I introduce several types of logics to my students including propositional, first order, second order, intuitionistic and fuzzy logics and it usually happens that ...
10
votes
2answers
234 views

Distinction between problems (such as equations), and universal truths

How the distinction between problems (find/describe such values of x that… ) and universal truths (identities) is taught to secondary-school students and higher? Especially in English-speaking ...
17
votes
6answers
629 views

What is a number?

In a set theoretic point of view all mathematical objects are sets. We "call" some of them as numbers (e.g. sets in $\mathbb{N}$, $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, $Ord$, $Card$) but what is ...
8
votes
1answer
553 views

What goes wrong when students interchange “there exists” and “for all” randomly? How to fix this?

I think, it is a very common problem that some students have huge problems with definitions when there appears a quantification. Some examples: Of course the sequence is bounded, because every part ...
28
votes
13answers
6k views

What do you say to students who want to apply Banach-Tarski theorem in practice?

Once when I was talking about Banach-Traski theorem (paradox) I said: OK! This is Banach-Tarski's theorem which is against our intuition but provable from our intuitive axioms! It says you can ...
6
votes
2answers
496 views

Puzzles for Logic Courses featuring propositional logic and set theory?

Puzzles are interesting form of exercises. They help students to learn the teaching material in a funny way. Particularly in logic, puzzles could be very useful to show the complexity of the subject. ...
12
votes
3answers
616 views

Is there a program like ALEKS for mathematical logic?

ALEKS (http://www.aleks.com/) is a good way of learning procedural math, because it is very systematic and forces you to master the dependencies of a kind of problem before working on that kind of ...
11
votes
1answer
443 views

Ideological Teaching in Logic Courses

Logic and its sub-fields are closely related to philosophy. There is an undeniable mutual interaction between one's philosophical point of view and his/her approach in teaching mathematical logic. In ...
8
votes
1answer
370 views

Standard word for a formula that is always true

If it is known from context that variables $x$ and $y$ represent integers, an open Boolean formula such as $x \ge y \Rightarrow x+1 > y$ evaluates to true regardless of the value assigned to ...
17
votes
12answers
10k views

Real-World Applications of Logic

When introducing logic in a first semester university course, the examples I use are often quite artificial. One example: One of three kids (Annie, Bob, Chris) has broken a window. Annies says "it was ...
6
votes
1answer
133 views

Philosophical Subjects in Logic Courses

Many of the notions, methods and theorems of the mathematical logic and its different sub-fields like set theory, model theory, etc. are closely related to some philosophical background. I believe ...
19
votes
7answers
1k views

Notation Conflict between Teachers and Textbooks

In mathematics notation plays an important role in clarifying the subject. A bad notation could be confusing. Recently I use a logic textbook which has a very nice approach and content but an ...
38
votes
15answers
2k views

How to teach logical implication?

One of the challenges of undergraduate teaching is logical implication. The case by case definition, in particular, is quite disturbing for most students, that have trouble accepting "false implies ...
26
votes
8answers
1k views

Teaching logic with a proof assistant

I am thinking about teaching a university-level "introduction to proofs" class (mainly for math and CS majors) making use of a computer proof assistant like Coq. I feel like there is a lot of ...