Questions tagged [examples]
For questions about examples for some mathematical subject – usually for purposes of motivation and illustration.
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Examples of Financial Institutions that Compute Interest Atypically?
Are there examples of financial institutions that compound their interest more frequently than once-a-month? Are there examples of financial institutions that consider continually compounded interest ...
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"Real life" examples of limits of functions at finite points
This is more specific than this similar question on math.SE, since I'm not satisfied with the answers there.
Question:
Can you provide an interesting, natural and simple example of some physical/...
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Seeking References on Deterministic and Stochastic Phenomena Suitable for High School Students
Can anyone recommend good and didactic references that delve into the dualism between deterministic and stochastic phenomena? Ideally, I'm seeking materials that provide a conceptual explanation along ...
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What evidence is there in the literature that lessons geared towards dyslexic student help non-dyslexic students?
Dyslexic students sometimes benefit from informal analogies to things in the world which the student can see with their eyes, and/or touch with their hands.
Tentatively, we can conjecture that ...
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Are these explanations of variance and covariance intuitive?
When tutoring, I try to simplify concepts. I came up with these examples to explain the intention behind variance and covariance. Could you please help me find conceptual, pedagogical or mathematical ...
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Are there any fun toy applications of representation and character theory for finite groups to physics?
Representation theory has very deep ties with physics, leading to incredibly profound and admittedly cool results such as the classification of particles in the Standard Model via mass and spin by ...
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Applications of Triangle Inequality for high-school students?
The Triangle Inequality ($|x+y|\leq|x|+|y|$) is useful later on in the student's math education (e.g. in proving results about limits).
But for the high-school student, are there any useful and ...
user18187
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Proof by Contradiction vs. Proof of Negation
In constructive mathematics we make a distinction between "proof of negation" and "proof by contradiction". You can read a great account of the difference in this blog post of ...
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Favorite linear programming (not integer) examples?
I am wondering what examples you like to give when introducing linear programming, where the examples are not clearly better suited as integer linear programs. I would like a few examples where we can ...
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How well can students learn abstract concepts through concrete examples?
In my own personal experience in teaching linear algebra, where many students encounter abstract ideas for the first time, I find that most students have trouble consolidating observations from ...
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Real-world applications of taxicab metric
The taxicab metric can be used to measure distances in idealized gridded cities. However, usually this serves only as a fun exercise for students.
I'm looking for engaging (as non-technical as ...
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Concrete vectors spaces without an obvious basis or many "obvious" bases?
I am teaching a class on linear algebra to sophomore and junior science majors, and am having some trouble illustrating the difference between $\mathbb{R}^n$ and an n-dimensional vector space. The ...
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Good Examples of Equations Derived from Elementary Calculus
I'm collecting additional enrichment content for my calculus students. I'm looking for examples of equations that are used in various fields, but which can be derived at least somewhat ...
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What is the best way to introduce Laplace transforms on an Engineering Mathematics course?
Are there any practical applications of Laplace transform? I would not use Laplace transforms to solve first, second-order ordinary differential equations as it is much easier by other methods even if ...
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Abstract math, examples and understanding or visualising
After reading some papers about special kinds of algebras and rings like Gorenstein rings, Dickson algebras, Cayley-Dickson construction, i want to ask do examples of general abstract objects in math ...
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Probability — analytical results instead of simulations
After students learn how to use probabilistic simulations, what strategies can one use to encourage them to understand analytical results anyway? For example, I'm struggling to find a compelling ...
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Looking for good examples/explanations of maximum likelihood estimators for discrete random variables
The title basically says it all. I need to prepare material for a whole classroom of elementary statistics students, so if anyone wants to help me out in the name of math education, that'd be great!
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Motivating example for sequences, sums and limits in high school
I currently work as a substitute teacher at a local high school and the topic in one of the classes is sequences, series and limits. Because I always disliked learning about a topic without having ...
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Big list of "interesting" abstract vector spaces
When introducing an abstraction it is important (in my opinion) to have a wide variety of examples of this abstraction.
Since finite dimensional real vector spaces are classified up to isomorphism by ...
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An introductory example for Taylor series (12th grade)
I (a student) am doing a presentation on Taylor series in my class (12th grade, in Germany if this is relevant). I am looking for a good example where you can see when Taylor series might be useful. ...
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Example of why proof by exhaustion is inelegant
There's a nice example of why people dislike proof by exhaustion on the Wikipedia page. The problem statement is "prove that all years in which the Modern Olympics are held are divisible by 4&...
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Showing applications of calculus to intro students
So I'm wrapping up my second year teaching high school calculus, and my first as an AP course. In addition to review, I'd like to end the year by giving the students a taste of the kinds of real-...
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Pros/Cons of using a single story in multiple examples to demonstrate different points
Judea Pearl, in his book "Probabilistic reasoning in intelligent systems" uses a handful of stories over and over again, each time to demonstrate a different point. (His "Alarm" ...
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Relationships amusingly difficult to graph
Long ago, when I was the student, I encountered a bunch of stories that we were asked to illustrate with graphs. I seem to remember that it was a set of around 10 examples. One involved some two ...
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Do you avoid examples or test questions that showcase an algorithmic plug'n'chug approach?
If we accept that there's not much learning from doing the "same" questions, like find the derivative of $x^2$, and $x^3$, and $x^4$ due to the algorithmic way of how it's done, then what ...
user13544
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What are some famous problems, which are not difficult to understand, for senior high school students
I hope I am asking my question in the right forum.
I am trying to introduce some mathematical problems (Better to be famous in the math community) to a group of senior high school students with a ...
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Are there direct practical applications of differentiating natural logarithms?
The textbook I am using to teach Calculus I includes in the exercises of most chapters a number of interesting real-world applications of the concepts from that chapter. However, the chapter on the ...
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How can teachers warn students about common mistakes without causing the student to make the mistake?
For example, if you're teaching integration of $\int \frac{dx}{1+x^2}$, would you mention the common wrong answer of $\ln\left(1+x^2\right)+C$?
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For myself, I very rarely mention common mistakes ...
user13544
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Proof by contradiction - more than one case
I am looking for some examples of when proof by contradiction is used in a problem with more than one case.
In all the elementary examples, there are only two options (eg rational/irrational, ...
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Examples for "good" exponential growth versus linear growth
I am writing up a small text about (increasing) exponential functions versus linear functions. I want to make the point that it is not true that if an exponential is bigger than a linear function that ...
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Algorithmic thinking problems
In Norway we will have a new national mathematics curriculum for all ages including high school beginning august 2020. A fundamental change is the new focus on so called algorithmic thinking. In ...
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How to address opportunities for improvement with a teacher
My daughter’s 5th grade teacher gives some pretty impossible questions and I don’t think she understands the material she’s teaching.
For example, this question has no context from previous questions ...
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Introductory exercise for the addition of large natural numbers
I'm starting a repetition with my students in 5th grade after they learned in elementary school how to sum up larger natural numbers (also 5- to 6-digits) by writing down that calculation.
As ...
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The propagation of the wave equation in even versus odd dimension
I am about to teach a second year undergraduate class on applied differential equation (first time) and, while I won't have time to go into the details, I wanted to show my students the difference ...
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Examples for environmental topics in the context of terms or linear inequalities
I want to emphasize the aspect of environmental education in my math class. Now I'm reasoning whether to do that with linear inequalities or terms with two variables - these are our next topics. The ...
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Applied ODEs for Numerical Methods
I am looking for a list of ODEs to use as examples in the teaching of a numerical methods course for engineers.
I am looking for first and second order examples - the more applied (to engineering) ...
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Easy examples of correspondence between global and local, as preparation for Gauss's theorem and Stokes's theorem
I'm teaching freshman electricity and magnetism this semester, and as usual in this type of course, I will need to teach my students a lot of vector calculus before they see it in a math course. The ...
user507
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Examples of application problems of coordinate geometry in the complex plane?
I am currently writing some basic introductory texts to
complex numbers for third-year high school students (Denmark). My main goal is to introduce complex numbers as a practical tool that both ...
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Examples of solving for unknowns using equivalence relations that are not equality, inequality, or boolean truth?
In a book i'm writing, i want to introduce students to equations in slightly more general terms. Solving an equation with some unknown is just
one example of finding an object by fact that it is a ...
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Ideas for the introduction of the derivative?
I want to introduce to my class to the derivative, but I am still searching for a good, realistic context that isn't too hard to understand, without seeming to be contrived. Do you have an ideas for ...
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Real-life exceptions to PEMDAS?
What are some real-life exceptions to the PEMDAS rule?
I am looking for examples from "real" mathematical language --- conventions that are held in modern mathematics practice, such as those appearing ...
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Which examples should we mention when teaching the concept of derivatives?
I am teaching Calculus for non-maths major students. As far as I know, when we teach about derivatives, we should mention "the rate of change". There are some practical examples to motivate this ...
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Published papers for Intro Stat students to read
I am looking for studies and experiments in the literature that I can share with undergraduate students in an intro statistics course. I do not expect students to understand everything, and I plan to ...
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is it appropriate or beneficial to mention weird results in math?
Is it appropriate to mention weird/exciting results in math (or use as cautionary tales why one cannot apply mathematics naively) in say high school level?
Examples of these results include the ...
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A Markov chain demonstration that doesn't require computers
I have a large probability class and would like to do some memorable demonstrations of Markov chains for them. Does anyone have any recommendations for a "low-tech" demo that doesn't involve ...
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A good example to show group actions and Burnside's lemma
I want to make a presentation of Burnside's lemma outside of group theory, and more as the stand-alone combinatorial tool that it can also be. My plan right now is to make it into a 15-20 minute video,...
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What is a realistic situation that illustrates precisely what a p-value is?
Students in the basic statistics courses I teach often learn a little bit of probability and then learn hypothesis testing. The core concept that ties the course together is the p-value, but most ...
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Using discrete examples in the beginning of integration
In Germany, one usual example to start teaching about integrals is to look at a simple (piecewise constant or with constant slope) functions that make up a water flow vs. time diagram and ask about ...
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Examples (for beginners) of real functions which are not given by elementary formulae
Question: What are good examples of functions $f: \Bbb R \rightarrow \Bbb R$ (or $f: D \rightarrow \Bbb R$ with $D \subseteq \Bbb R$) which are not just given by "a formula" (or finitely many formulae ...
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Good real-life examples of transformations of function graphs
I am a graduate student teaching college algebra at a larger state school, and currently I'm covering transformations of graphs of function, i.e.:
Given the graph of a function $y =f(x)$, what do ...
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