# Questions tagged [logic]

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40 questions
218 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 ...
120 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 ...
211 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"...
254 views

### Resources for Teaching Logic to Primary School Children?

What are some books or other resources for teaching primary school children logic?
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### 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. ...
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 & ...
306 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 ...
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 ...
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### 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 ...
212 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 ...
239 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 ...
556 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 ...
90 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 ...
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### 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....
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....
545 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 ...
211 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 ...
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 ...
737 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 ...
163 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 ...
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 ...
462 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 ...
119 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 ...
523 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 "...
370 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 ...
235 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 ...
635 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 ...
557 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 ...
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 ...
503 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. ...
620 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 ...
448 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 ...
373 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 ...
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 ...
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### 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 ...
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 ...