What can I teach to non-maths major undergraduates in a $10$ minutes session?
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I will be giving a $10$ minutes teaching session and my audience consists of five to six possibly non-maths major first year undergraduates in Asia.
I am free to choose any topic for the session as long as it can be understood within $10$ minutes.
I would like to teach something that will interest almost everyone. For example, we use online transaction everyday so it might be of interest to everyone to understand underlying mechanism, that is, encryption and decryption.
However, to understand it, one needs to understand linear congruences, which I think some of my audience might not have it.
Question: What topics in Mathematics will be of interest to every undergraduate, including non-Maths major?
As I need to write teaching aim and learning outcomes as well, the topic cannot be a puzzle like Knights and Knaves as I am not able to suggest possible learning outcomes in solving the puzzles.
I thought of teaching optimisation calculus in one variable without any constraint. However, I am afraid that I may spend too much time in explaining what is a first and second derivative.
reference-request education
asked Sep 1 at 5:44
Idonknow
3,115642108
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up vote
3
down vote
favorite
I will be giving a $10$ minutes teaching session and my audience consists of five to six possibly non-maths major first year undergraduates in Asia.
I am free to choose any topic for the session as long as it can be understood within $10$ minutes.
I would like to teach something that will interest almost everyone. For example, we use online transaction everyday so it might be of interest to everyone to understand underlying mechanism, that is, encryption and decryption.
However, to understand it, one needs to understand linear congruences, which I think some of my audience might not have it.
Question: What topics in Mathematics will be of interest to every undergraduate, including non-Maths major?
As I need to write teaching aim and learning outcomes as well, the topic cannot be a puzzle like Knights and Knaves as I am not able to suggest possible learning outcomes in solving the puzzles.
I thought of teaching optimisation calculus in one variable without any constraint. However, I am afraid that I may spend too much time in explaining what is a first and second derivative.
reference-request education
asked Sep 1 at 5:44
Idonknow
3,115642108
1
This thread on MathOverflow might be useful: How To Present Mathematics To Non-Mathematicians [in 10 Minutes]? Some examples from the top answers: infinite ordinals, the Euler characteristic, Fermat's two squares theorem, Ramsey numbers. Though I guess these are examples of things non-maths majors may find interesting, rather than things they may find useful (like your idea of optimization).
– Rahul
Sep 1 at 6:49
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I will be giving a $10$ minutes teaching session and my audience consists of five to six possibly non-maths major first year undergraduates in Asia.
I am free to choose any topic for the session as long as it can be understood within $10$ minutes.
I would like to teach something that will interest almost everyone. For example, we use online transaction everyday so it might be of interest to everyone to understand underlying mechanism, that is, encryption and decryption.
However, to understand it, one needs to understand linear congruences, which I think some of my audience might not have it.
Question: What topics in Mathematics will be of interest to every undergraduate, including non-Maths major?
As I need to write teaching aim and learning outcomes as well, the topic cannot be a puzzle like Knights and Knaves as I am not able to suggest possible learning outcomes in solving the puzzles.
I thought of teaching optimisation calculus in one variable without any constraint. However, I am afraid that I may spend too much time in explaining what is a first and second derivative.
reference-request education
asked Sep 1 at 5:44
Idonknow
3,115642108
I will be giving a $10$ minutes teaching session and my audience consists of five to six possibly non-maths major first year undergraduates in Asia.
I am free to choose any topic for the session as long as it can be understood within $10$ minutes.
I would like to teach something that will interest almost everyone. For example, we use online transaction everyday so it might be of interest to everyone to understand underlying mechanism, that is, encryption and decryption.
However, to understand it, one needs to understand linear congruences, which I think some of my audience might not have it.
Question: What topics in Mathematics will be of interest to every undergraduate, including non-Maths major?
As I need to write teaching aim and learning outcomes as well, the topic cannot be a puzzle like Knights and Knaves as I am not able to suggest possible learning outcomes in solving the puzzles.
I thought of teaching optimisation calculus in one variable without any constraint. However, I am afraid that I may spend too much time in explaining what is a first and second derivative.
reference-request education
reference-request education
asked Sep 1 at 5:44
Idonknow
3,115642108
asked Sep 1 at 5:44
Idonknow
3,115642108
asked Sep 1 at 5:44
Idonknow
3,115642108
asked Sep 1 at 5:44
Idonknow
3,115642108
asked Sep 1 at 5:44
Idonknow
3,115642108
3,115642108
1
This thread on MathOverflow might be useful: How To Present Mathematics To Non-Mathematicians [in 10 Minutes]? Some examples from the top answers: infinite ordinals, the Euler characteristic, Fermat's two squares theorem, Ramsey numbers. Though I guess these are examples of things non-maths majors may find interesting, rather than things they may find useful (like your idea of optimization).
– Rahul
Sep 1 at 6:49
add a comment |Â
1
This thread on MathOverflow might be useful: How To Present Mathematics To Non-Mathematicians [in 10 Minutes]? Some examples from the top answers: infinite ordinals, the Euler characteristic, Fermat's two squares theorem, Ramsey numbers. Though I guess these are examples of things non-maths majors may find interesting, rather than things they may find useful (like your idea of optimization).
– Rahul
Sep 1 at 6:49
1
1
This thread on MathOverflow might be useful: How To Present Mathematics To Non-Mathematicians [in 10 Minutes]? Some examples from the top answers: infinite ordinals, the Euler characteristic, Fermat's two squares theorem, Ramsey numbers. Though I guess these are examples of things non-maths majors may find interesting, rather than things they may find useful (like your idea of optimization).
– Rahul
Sep 1 at 6:49
This thread on MathOverflow might be useful: How To Present Mathematics To Non-Mathematicians [in 10 Minutes]? Some examples from the top answers: infinite ordinals, the Euler characteristic, Fermat's two squares theorem, Ramsey numbers. Though I guess these are examples of things non-maths majors may find interesting, rather than things they may find useful (like your idea of optimization).
– Rahul
Sep 1 at 6:49
add a comment |Â
1 Answer
1
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up vote
2
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In ten minutes you can't do too much. I would try to explain something puzzling - like why 1 = .9999....
A related idea might be on the difference between a countably infinite set vs. the power of the continuum. Cantor's diagonalization is easy to comprehend and provides a compelling - but curious - result.
answered Sep 1 at 6:02
eSurfsnake
2949
I think a potential question from students would be why do we care about Cantor diagonalization and continuum hypothesis...
– Idonknow
Sep 1 at 6:11
2
It's a simple idea to grasp but one most non-mathematical people have never grappled with: are there different types of infinity? The Cantor diag makes a concrete demonstration that is constructive.
– eSurfsnake
Sep 1 at 6:51
I just did some googling on hand another worry, that is, does infinity even exist in our world? If it does not exist, why do we study it?
– Idonknow
Sep 1 at 12:01
It is an extension of the real numbers: R' = R + $-infty, infty$
– eSurfsnake
2 days ago
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
In ten minutes you can't do too much. I would try to explain something puzzling - like why 1 = .9999....
A related idea might be on the difference between a countably infinite set vs. the power of the continuum. Cantor's diagonalization is easy to comprehend and provides a compelling - but curious - result.
answered Sep 1 at 6:02
eSurfsnake
2949
I think a potential question from students would be why do we care about Cantor diagonalization and continuum hypothesis...
– Idonknow
Sep 1 at 6:11
2
It's a simple idea to grasp but one most non-mathematical people have never grappled with: are there different types of infinity? The Cantor diag makes a concrete demonstration that is constructive.
– eSurfsnake
Sep 1 at 6:51
I just did some googling on hand another worry, that is, does infinity even exist in our world? If it does not exist, why do we study it?
– Idonknow
Sep 1 at 12:01
It is an extension of the real numbers: R' = R + $-infty, infty$
– eSurfsnake
2 days ago
add a comment |Â
up vote
2
down vote
In ten minutes you can't do too much. I would try to explain something puzzling - like why 1 = .9999....
A related idea might be on the difference between a countably infinite set vs. the power of the continuum. Cantor's diagonalization is easy to comprehend and provides a compelling - but curious - result.
answered Sep 1 at 6:02
eSurfsnake
2949
I think a potential question from students would be why do we care about Cantor diagonalization and continuum hypothesis...
– Idonknow
Sep 1 at 6:11
2
It's a simple idea to grasp but one most non-mathematical people have never grappled with: are there different types of infinity? The Cantor diag makes a concrete demonstration that is constructive.
– eSurfsnake
Sep 1 at 6:51
I just did some googling on hand another worry, that is, does infinity even exist in our world? If it does not exist, why do we study it?
– Idonknow
Sep 1 at 12:01
It is an extension of the real numbers: R' = R + $-infty, infty$
– eSurfsnake
2 days ago
add a comment |Â
up vote
2
down vote
up vote
2
down vote
In ten minutes you can't do too much. I would try to explain something puzzling - like why 1 = .9999....
A related idea might be on the difference between a countably infinite set vs. the power of the continuum. Cantor's diagonalization is easy to comprehend and provides a compelling - but curious - result.
answered Sep 1 at 6:02
eSurfsnake
2949
In ten minutes you can't do too much. I would try to explain something puzzling - like why 1 = .9999....
A related idea might be on the difference between a countably infinite set vs. the power of the continuum. Cantor's diagonalization is easy to comprehend and provides a compelling - but curious - result.
answered Sep 1 at 6:02
eSurfsnake
2949
answered Sep 1 at 6:02
eSurfsnake
2949
answered Sep 1 at 6:02
eSurfsnake
2949
answered Sep 1 at 6:02
eSurfsnake
2949
2949
I think a potential question from students would be why do we care about Cantor diagonalization and continuum hypothesis...
– Idonknow
Sep 1 at 6:11
2
It's a simple idea to grasp but one most non-mathematical people have never grappled with: are there different types of infinity? The Cantor diag makes a concrete demonstration that is constructive.
– eSurfsnake
Sep 1 at 6:51
I just did some googling on hand another worry, that is, does infinity even exist in our world? If it does not exist, why do we study it?
– Idonknow
Sep 1 at 12:01
It is an extension of the real numbers: R' = R + $-infty, infty$
– eSurfsnake
2 days ago
add a comment |Â
I think a potential question from students would be why do we care about Cantor diagonalization and continuum hypothesis...
– Idonknow
Sep 1 at 6:11
2
It's a simple idea to grasp but one most non-mathematical people have never grappled with: are there different types of infinity? The Cantor diag makes a concrete demonstration that is constructive.
– eSurfsnake
Sep 1 at 6:51
I just did some googling on hand another worry, that is, does infinity even exist in our world? If it does not exist, why do we study it?
– Idonknow
Sep 1 at 12:01
It is an extension of the real numbers: R' = R + $-infty, infty$
– eSurfsnake
2 days ago
I think a potential question from students would be why do we care about Cantor diagonalization and continuum hypothesis...
– Idonknow
Sep 1 at 6:11
I think a potential question from students would be why do we care about Cantor diagonalization and continuum hypothesis...
– Idonknow
Sep 1 at 6:11
2
2
It's a simple idea to grasp but one most non-mathematical people have never grappled with: are there different types of infinity? The Cantor diag makes a concrete demonstration that is constructive.
– eSurfsnake
Sep 1 at 6:51
It's a simple idea to grasp but one most non-mathematical people have never grappled with: are there different types of infinity? The Cantor diag makes a concrete demonstration that is constructive.
– eSurfsnake
Sep 1 at 6:51
I just did some googling on hand another worry, that is, does infinity even exist in our world? If it does not exist, why do we study it?
– Idonknow
Sep 1 at 12:01
I just did some googling on hand another worry, that is, does infinity even exist in our world? If it does not exist, why do we study it?
– Idonknow
Sep 1 at 12:01
It is an extension of the real numbers: R' = R + $-infty, infty$
– eSurfsnake
2 days ago
It is an extension of the real numbers: R' = R + $-infty, infty$
– eSurfsnake
2 days ago
add a comment |Â
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1
This thread on MathOverflow might be useful: How To Present Mathematics To Non-Mathematicians [in 10 Minutes]? Some examples from the top answers: infinite ordinals, the Euler characteristic, Fermat's two squares theorem, Ramsey numbers. Though I guess these are examples of things non-maths majors may find interesting, rather than things they may find useful (like your idea of optimization).
– Rahul
Sep 1 at 6:49