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Questions tagged [exercises]

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Is there a risk that using the same name for analogous premises in different systems of set theory will confuse students? [closed]

It is conventional to use lowercase variable letters in ZFC, so that if we want to formulate an axiom asserting the existence of unordered pairs in ZFC, we write: $$\forall h \forall k \exists m \...
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3answers
134 views

What kind of problem do you learn most from (hard problems or easy problems)?

I am curious if it is true that one can learn more from hard problems, or from easy problems. I heard that we all learn a lot more from doing harder problems, because we have to learn all of the ...
8
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2answers
121 views

Exercise database

edit: Thanks for all your answers so far. I have decided to develop my own solution, both because it is fun and I can then form it exactly as I want to. Once I am done (which might take some time, ...
8
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4answers
285 views

Solutions to exercises

I am teaching the exercise sessions for a 3rd year algebra course (intro to field theory, Galois theory and Algebraic geometry). The format of the course is as follows: for every 2 hour lecture by the ...
5
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2answers
239 views

Unconstrained/Constrained optimization real life example

I am in charge of some practice lesson for Calculus II. I have to show how to apply the theory for unconstrained optimization (mainly Hessian analysis) and constrained optimization (Lagrange ...
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2answers
206 views

Where to find good exercises for term operations?

I'm searching for exercises for practising operations with terms. They should involve working with decimal numbers and fractions (ideally one should convert decimal numbers to simple fractions like ...
7
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4answers
451 views

Students understand during course but can't solve exam

I am teaching a math class where the students, most of them, tell me that they can understand the materials given by me during the course. I test them during the course too and they seem to get it. ...
6
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0answers
94 views

Questions similar to Wason Selection Task

The Wason Selection Task (described by Pete Clark here) is a great problem for getting students to grapple with all of the intricacies of logical implication. I will be teaching a discrete ...
4
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3answers
245 views

Could you recommend a book for studying calculus 1?

I would like to practice a large quantity of exercises from limit calculation, derivatives, sequences and series and finaly integrals.
3
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3answers
165 views

Are there any good exercises on point-slope form of a linear equation by itself?

Let's say we're running a basic algebra course and we're committed to showing proofs of everything we reasonably can. The development of equations of lines seems most straightforward in this sequence: ...
17
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8answers
786 views

Good Examples of Questions to have Students Ponder Over Without Paper

A few times now I've found myself in a situation where I want to give a precalculus-level undergraduate student something to think about that's kinda fun and that's well outside of their coursework. ...
8
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3answers
244 views

Is proof-based exercise-oriented math course without solution an effective way to teach pure math?

In recent years I have seen several courses in pure math in the undergrad level (year 2, 3, 4) such as real analysis and topology where the entire course consists of: notes written during the lecture ...
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2answers
299 views

Importance of exercises for learning mathematics

For me it seem to be obvious that exercises and exercise courses are important for undergraduates to learn mathematics and skills like finding a proof or writing it down. Was there any research ...
9
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3answers
403 views

How many problems do we have to do as undergraduate mathematicians in order to learn a subject?

I'm wondering how many problems are needed in order to learn a subject, let's say Calculus of Several Variables. We know that the professors often assign us a list of problems to solve as homework, ...
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0answers
62 views

How many problems do we have to do as undergraduate mathematicians in order to learn a subject? [duplicate]

I'm wondering how many problems are needed in order to learn a subject, let's say Calculus of Several Variables. We know that the professors often assign us a list of problems to solve as homework, ...
7
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1answer
344 views

Is there a repository with K-12 math exercises and problems written in LaTeX (English or Spanish)?

I've been searching for a repository or a database with math problems (K-12 levels) written in LaTeX, but with no luck. Neither in Spanish (my student's language) ...
10
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1answer
167 views

Software to organize and track your exercises

I am math teacher in secondary school and I have a few thousands of mathematical exercises in many Microsoft Word files. I tried to organize them in folders and keep track of new exercises to update ...
12
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0answers
213 views

Exercises to go with Simon's “Representations of finite and compact groups”

I am teaching an independent-reading course from Simon's "Representations of finite and compact groups". I chose this book based on fond memories from a previous reading course in which I had ...
4
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1answer
336 views

Abandon all hope, ye who enter my office!

The sentence in the title is inspired by a sentence on the gate of hell in Dante Alighieri's masterwork Divine Comedy (Part I: Inferno). I usually write it on my office door after exams when I think ...