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Can undergraduate math courses be taught at a high school level? [closed]
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up vote
1
down vote
favorite
Can these be taught at a high school level?
multivariable calculus
linear algebra
abstract algebra
real analysis
complex analysis
(non-measure theoretic) probability theory
Maybe even other more math courses.
secondary-education
edited Aug 29 at 6:59
Community♦
1
asked Aug 28 at 21:21
Lenny
1656
closed as unclear what you're asking by Xander Henderson, Tommi Brander, inéquation, Andrew Sanfratello, mweiss Aug 30 at 14:07
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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show 3 more comments
up vote
1
down vote
favorite
Can these be taught at a high school level?
multivariable calculus
linear algebra
abstract algebra
real analysis
complex analysis
(non-measure theoretic) probability theory
Maybe even other more math courses.
secondary-education
edited Aug 29 at 6:59
Community♦
1
asked Aug 28 at 21:21
Lenny
1656
closed as unclear what you're asking by Xander Henderson, Tommi Brander, inéquation, Andrew Sanfratello, mweiss Aug 30 at 14:07
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
3
Yes. In fact, these should be required for graduation :)
– James S. Cook
Aug 29 at 0:59
9
What's the situation and goal here? Do you actually have a class's worth of students who are interested? A single student who wants a tutor? Idle speculation?
– Adam
Aug 29 at 1:08
6
Virtually anything can be taught at school level if you simplify the material enough. What constitutes knowing a particular subject is a more important question to ask. Also, note that teaching a basic version could negatively impact students if they take a fuller course later, as students have been shown to do worse on material they think they already know.
– Jessica B
Aug 29 at 5:48
3
In high school I took AP Calculus AB/BC, which covered single-variable calculus and the like, and a higher-level IB course that touched on some early aspects of linear algebra. Those were equivalent to first-year undergraduate math courses at the university I did my undergrad.
– JAB
Aug 29 at 6:15
1
In India the ncert (national council of educational research and training) has provided a syllabus in which they suggest topics of upto differential equations for highschool, but keep in mind that India is a country where sciences and math are highly stressed as important and thus would have different standards to other countries which may have a more holistic approach to education.
– casualcoder
Aug 29 at 7:35
 |Â
show 3 more comments
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Can these be taught at a high school level?
multivariable calculus
linear algebra
abstract algebra
real analysis
complex analysis
(non-measure theoretic) probability theory
Maybe even other more math courses.
secondary-education
edited Aug 29 at 6:59
Community♦
1
asked Aug 28 at 21:21
Lenny
1656
Can these be taught at a high school level?
multivariable calculus
linear algebra
abstract algebra
real analysis
complex analysis
(non-measure theoretic) probability theory
Maybe even other more math courses.
secondary-education
edited Aug 29 at 6:59
Community♦
1
asked Aug 28 at 21:21
Lenny
1656
edited Aug 29 at 6:59
Community♦
1
edited Aug 29 at 6:59
Community♦
1
edited Aug 29 at 6:59
Community♦
1
1
asked Aug 28 at 21:21
Lenny
1656
asked Aug 28 at 21:21
Lenny
1656
asked Aug 28 at 21:21
Lenny
1656
1656
closed as unclear what you're asking by Xander Henderson, Tommi Brander, inéquation, Andrew Sanfratello, mweiss Aug 30 at 14:07
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Xander Henderson, Tommi Brander, inéquation, Andrew Sanfratello, mweiss Aug 30 at 14:07
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
3
Yes. In fact, these should be required for graduation :)
– James S. Cook
Aug 29 at 0:59
9
What's the situation and goal here? Do you actually have a class's worth of students who are interested? A single student who wants a tutor? Idle speculation?
– Adam
Aug 29 at 1:08
6
Virtually anything can be taught at school level if you simplify the material enough. What constitutes knowing a particular subject is a more important question to ask. Also, note that teaching a basic version could negatively impact students if they take a fuller course later, as students have been shown to do worse on material they think they already know.
– Jessica B
Aug 29 at 5:48
3
In high school I took AP Calculus AB/BC, which covered single-variable calculus and the like, and a higher-level IB course that touched on some early aspects of linear algebra. Those were equivalent to first-year undergraduate math courses at the university I did my undergrad.
– JAB
Aug 29 at 6:15
1
In India the ncert (national council of educational research and training) has provided a syllabus in which they suggest topics of upto differential equations for highschool, but keep in mind that India is a country where sciences and math are highly stressed as important and thus would have different standards to other countries which may have a more holistic approach to education.
– casualcoder
Aug 29 at 7:35
 |Â
show 3 more comments
3
Yes. In fact, these should be required for graduation :)
– James S. Cook
Aug 29 at 0:59
9
What's the situation and goal here? Do you actually have a class's worth of students who are interested? A single student who wants a tutor? Idle speculation?
– Adam
Aug 29 at 1:08
6
Virtually anything can be taught at school level if you simplify the material enough. What constitutes knowing a particular subject is a more important question to ask. Also, note that teaching a basic version could negatively impact students if they take a fuller course later, as students have been shown to do worse on material they think they already know.
– Jessica B
Aug 29 at 5:48
3
In high school I took AP Calculus AB/BC, which covered single-variable calculus and the like, and a higher-level IB course that touched on some early aspects of linear algebra. Those were equivalent to first-year undergraduate math courses at the university I did my undergrad.
– JAB
Aug 29 at 6:15
1
In India the ncert (national council of educational research and training) has provided a syllabus in which they suggest topics of upto differential equations for highschool, but keep in mind that India is a country where sciences and math are highly stressed as important and thus would have different standards to other countries which may have a more holistic approach to education.
– casualcoder
Aug 29 at 7:35
3
3
Yes. In fact, these should be required for graduation :)
– James S. Cook
Aug 29 at 0:59
Yes. In fact, these should be required for graduation :)
– James S. Cook
Aug 29 at 0:59
9
9
What's the situation and goal here? Do you actually have a class's worth of students who are interested? A single student who wants a tutor? Idle speculation?
– Adam
Aug 29 at 1:08
What's the situation and goal here? Do you actually have a class's worth of students who are interested? A single student who wants a tutor? Idle speculation?
– Adam
Aug 29 at 1:08
6
6
Virtually anything can be taught at school level if you simplify the material enough. What constitutes knowing a particular subject is a more important question to ask. Also, note that teaching a basic version could negatively impact students if they take a fuller course later, as students have been shown to do worse on material they think they already know.
– Jessica B
Aug 29 at 5:48
Virtually anything can be taught at school level if you simplify the material enough. What constitutes knowing a particular subject is a more important question to ask. Also, note that teaching a basic version could negatively impact students if they take a fuller course later, as students have been shown to do worse on material they think they already know.
– Jessica B
Aug 29 at 5:48
3
3
In high school I took AP Calculus AB/BC, which covered single-variable calculus and the like, and a higher-level IB course that touched on some early aspects of linear algebra. Those were equivalent to first-year undergraduate math courses at the university I did my undergrad.
– JAB
Aug 29 at 6:15
In high school I took AP Calculus AB/BC, which covered single-variable calculus and the like, and a higher-level IB course that touched on some early aspects of linear algebra. Those were equivalent to first-year undergraduate math courses at the university I did my undergrad.
– JAB
Aug 29 at 6:15
1
1
In India the ncert (national council of educational research and training) has provided a syllabus in which they suggest topics of upto differential equations for highschool, but keep in mind that India is a country where sciences and math are highly stressed as important and thus would have different standards to other countries which may have a more holistic approach to education.
– casualcoder
Aug 29 at 7:35
In India the ncert (national council of educational research and training) has provided a syllabus in which they suggest topics of upto differential equations for highschool, but keep in mind that India is a country where sciences and math are highly stressed as important and thus would have different standards to other countries which may have a more holistic approach to education.
– casualcoder
Aug 29 at 7:35
 |Â
show 3 more comments
6 Answers
6
active
oldest
votes
up vote
1
down vote
accepted
In Spain, some linear algebra is taught in high school and is examined on the exams required to enter the university. Topics taught include matrices, determinants, solvability of and solving linear systems of equations, and Euclidean geometry of lines and planes in the plane and three space. Basic probability is also taught, focusing on the binomial and normal distributions. One variable calculus is taught in more detail, and notions such as continuity and differentiability are included.
One might ask how much students really learn. The answer is that most of this material has to be retaught, albeit rapidly, in the first few weeks of the university.
In the US, with the great flexibility of its otherwise generally undemanding school system, advanced students often find a way to learn multivariable calculus, linear algebra, and more. The limiting factor is often the availability of an instructor competent to teach these things.
answered Aug 29 at 12:14
Dan Fox
1,516510
This is very similar to france. The problem is students just learn the techniques without understanding any theory.
– inéquation
Aug 30 at 15:07
add a comment |Â
up vote
6
down vote
Why not? As long as the students have the appropriate prerequisites and aptitude, go for it. Our local private/boarding school regularly offers one of multivariate, linear algebra, or discrete math to the seniors. A lot of these kids take precalculus freshman year and are looking for more once they complete second semester calculus.
answered Aug 28 at 22:50
Aeryk
3,613630
add a comment |Â
up vote
5
down vote
This paper discusses Linear Algebra as an elective ("Mathematics III") for science
high-school students in South Korea.
Choe, Young Han. "Teaching Linear Algebra to High School Students." Research in Mathematical Education 8 (2004).
PDF download.
So certainly Linear Algebra can be and has been taught at the high-school level.
answered Aug 28 at 23:20
Joseph O'Rourke
14.2k33177
add a comment |Â
up vote
4
down vote
Well, in India some of the topics you mentioned above are already being taught at high school level, infact they are necessary for students who want to become future engineers. You can check out the JEE-MAINS syllabus India(earlier known as IIT-JEE).
Edit:
link to syllabus - look at page 23 for required topics for mathematics
edited Aug 29 at 17:53
casualcoder
1032
answered Aug 29 at 6:24
Divyansh
411
3
Welcome to matheducators.se. The answer would be improved by adding a link to the syllabus.
– Tommi Brander
Aug 29 at 6:58
add a comment |Â
up vote
3
down vote
In the UK, some students take A-Level Further Mathematics, which covers bits of linear algebra (determinants, solving and interpreting systems of 3 linear equations, possibly also eigenvalues and eigenvectors and diagonalizing matrices) and some simple first and second order ODEs.
It also gives students the option to study some elementary group theory (the definition of a group, basic examples, and Lagrange's Theorem) and elementary number theory (Euclidean algorithm, modular arithmetic, solving congruence equations).
One syllabus can be found here.
answered Aug 29 at 11:50
rbird
31829
add a comment |Â
up vote
2
down vote
If you want to teach more advanced courses and have sufficient students, I would advise 3rd semester calc, or ODEs. The reason is these are all "no regrets" moves from the student point of view. Pretty much any hard science, math or engineering will require them.
Abstract algebra is only required for math students which is a tiny tiny percentage of your class population (with undeclared major high school students). Just because they are good or advanced in math do not assume they will become math majors. Common sense and personal experience and statistic should show that most will go into engineering or chemistry or physics or the like.
Linear algebra is not a bad choice either, especially if it is one with emphasis on matrices and calculation (not proofs). For one thing, it is an easier course than 3rd sem calc or ODEs. (Perhaps important for kids who already feel they are essentially doing an elective.) It won't be as central for engineers or physicists (most don't have a semester requirement, just pick up a little in midst of engine math class). But it will be more central and required for comp sci students.
Maybe do the LA because of the easiness and serving the future comp sci students. It won't hurt the engineers either. Plus it will appeal to you more. At least it is algebra even if not abstract.
answered Aug 30 at 11:28
guest
2974
Elementary differential geometry seems very good.
– inéquation
Aug 30 at 15:10
I took linear algebra, it was easily my favorite course. However, I was sad that when it was over and we didn't get to cover the 'interesting' subjects such as normal forms and orthogonal basis as much.
– Lenny
Aug 30 at 17:41
add a comment |Â
6 Answers
6
active
oldest
votes
6 Answers
6
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
In Spain, some linear algebra is taught in high school and is examined on the exams required to enter the university. Topics taught include matrices, determinants, solvability of and solving linear systems of equations, and Euclidean geometry of lines and planes in the plane and three space. Basic probability is also taught, focusing on the binomial and normal distributions. One variable calculus is taught in more detail, and notions such as continuity and differentiability are included.
One might ask how much students really learn. The answer is that most of this material has to be retaught, albeit rapidly, in the first few weeks of the university.
In the US, with the great flexibility of its otherwise generally undemanding school system, advanced students often find a way to learn multivariable calculus, linear algebra, and more. The limiting factor is often the availability of an instructor competent to teach these things.
answered Aug 29 at 12:14
Dan Fox
1,516510
This is very similar to france. The problem is students just learn the techniques without understanding any theory.
– inéquation
Aug 30 at 15:07
add a comment |Â
up vote
1
down vote
accepted
In Spain, some linear algebra is taught in high school and is examined on the exams required to enter the university. Topics taught include matrices, determinants, solvability of and solving linear systems of equations, and Euclidean geometry of lines and planes in the plane and three space. Basic probability is also taught, focusing on the binomial and normal distributions. One variable calculus is taught in more detail, and notions such as continuity and differentiability are included.
One might ask how much students really learn. The answer is that most of this material has to be retaught, albeit rapidly, in the first few weeks of the university.
In the US, with the great flexibility of its otherwise generally undemanding school system, advanced students often find a way to learn multivariable calculus, linear algebra, and more. The limiting factor is often the availability of an instructor competent to teach these things.
answered Aug 29 at 12:14
Dan Fox
1,516510
This is very similar to france. The problem is students just learn the techniques without understanding any theory.
– inéquation
Aug 30 at 15:07
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
In Spain, some linear algebra is taught in high school and is examined on the exams required to enter the university. Topics taught include matrices, determinants, solvability of and solving linear systems of equations, and Euclidean geometry of lines and planes in the plane and three space. Basic probability is also taught, focusing on the binomial and normal distributions. One variable calculus is taught in more detail, and notions such as continuity and differentiability are included.
One might ask how much students really learn. The answer is that most of this material has to be retaught, albeit rapidly, in the first few weeks of the university.
In the US, with the great flexibility of its otherwise generally undemanding school system, advanced students often find a way to learn multivariable calculus, linear algebra, and more. The limiting factor is often the availability of an instructor competent to teach these things.
answered Aug 29 at 12:14
Dan Fox
1,516510
In Spain, some linear algebra is taught in high school and is examined on the exams required to enter the university. Topics taught include matrices, determinants, solvability of and solving linear systems of equations, and Euclidean geometry of lines and planes in the plane and three space. Basic probability is also taught, focusing on the binomial and normal distributions. One variable calculus is taught in more detail, and notions such as continuity and differentiability are included.
One might ask how much students really learn. The answer is that most of this material has to be retaught, albeit rapidly, in the first few weeks of the university.
In the US, with the great flexibility of its otherwise generally undemanding school system, advanced students often find a way to learn multivariable calculus, linear algebra, and more. The limiting factor is often the availability of an instructor competent to teach these things.
answered Aug 29 at 12:14
Dan Fox
1,516510
answered Aug 29 at 12:14
Dan Fox
1,516510
answered Aug 29 at 12:14
Dan Fox
1,516510
answered Aug 29 at 12:14
Dan Fox
1,516510
1,516510
This is very similar to france. The problem is students just learn the techniques without understanding any theory.
– inéquation
Aug 30 at 15:07
add a comment |Â
This is very similar to france. The problem is students just learn the techniques without understanding any theory.
– inéquation
Aug 30 at 15:07
This is very similar to france. The problem is students just learn the techniques without understanding any theory.
– inéquation
Aug 30 at 15:07
This is very similar to france. The problem is students just learn the techniques without understanding any theory.
– inéquation
Aug 30 at 15:07
add a comment |Â
up vote
6
down vote
Why not? As long as the students have the appropriate prerequisites and aptitude, go for it. Our local private/boarding school regularly offers one of multivariate, linear algebra, or discrete math to the seniors. A lot of these kids take precalculus freshman year and are looking for more once they complete second semester calculus.
answered Aug 28 at 22:50
Aeryk
3,613630
add a comment |Â
up vote
6
down vote
Why not? As long as the students have the appropriate prerequisites and aptitude, go for it. Our local private/boarding school regularly offers one of multivariate, linear algebra, or discrete math to the seniors. A lot of these kids take precalculus freshman year and are looking for more once they complete second semester calculus.
answered Aug 28 at 22:50
Aeryk
3,613630
add a comment |Â
up vote
6
down vote
up vote
6
down vote
Why not? As long as the students have the appropriate prerequisites and aptitude, go for it. Our local private/boarding school regularly offers one of multivariate, linear algebra, or discrete math to the seniors. A lot of these kids take precalculus freshman year and are looking for more once they complete second semester calculus.
answered Aug 28 at 22:50
Aeryk
3,613630
Why not? As long as the students have the appropriate prerequisites and aptitude, go for it. Our local private/boarding school regularly offers one of multivariate, linear algebra, or discrete math to the seniors. A lot of these kids take precalculus freshman year and are looking for more once they complete second semester calculus.
answered Aug 28 at 22:50
Aeryk
3,613630
answered Aug 28 at 22:50
Aeryk
3,613630
answered Aug 28 at 22:50
Aeryk
3,613630
answered Aug 28 at 22:50
Aeryk
3,613630
3,613630
add a comment |Â
add a comment |Â
up vote
5
down vote
This paper discusses Linear Algebra as an elective ("Mathematics III") for science
high-school students in South Korea.
Choe, Young Han. "Teaching Linear Algebra to High School Students." Research in Mathematical Education 8 (2004).
PDF download.
So certainly Linear Algebra can be and has been taught at the high-school level.
answered Aug 28 at 23:20
Joseph O'Rourke
14.2k33177
add a comment |Â
up vote
5
down vote
This paper discusses Linear Algebra as an elective ("Mathematics III") for science
high-school students in South Korea.
Choe, Young Han. "Teaching Linear Algebra to High School Students." Research in Mathematical Education 8 (2004).
PDF download.
So certainly Linear Algebra can be and has been taught at the high-school level.
answered Aug 28 at 23:20
Joseph O'Rourke
14.2k33177
add a comment |Â
up vote
5
down vote
up vote
5
down vote
This paper discusses Linear Algebra as an elective ("Mathematics III") for science
high-school students in South Korea.
Choe, Young Han. "Teaching Linear Algebra to High School Students." Research in Mathematical Education 8 (2004).
PDF download.
So certainly Linear Algebra can be and has been taught at the high-school level.
answered Aug 28 at 23:20
Joseph O'Rourke
14.2k33177
This paper discusses Linear Algebra as an elective ("Mathematics III") for science
high-school students in South Korea.
Choe, Young Han. "Teaching Linear Algebra to High School Students." Research in Mathematical Education 8 (2004).
PDF download.
So certainly Linear Algebra can be and has been taught at the high-school level.
answered Aug 28 at 23:20
Joseph O'Rourke
14.2k33177
answered Aug 28 at 23:20
Joseph O'Rourke
14.2k33177
answered Aug 28 at 23:20
Joseph O'Rourke
14.2k33177
answered Aug 28 at 23:20
Joseph O'Rourke
14.2k33177
14.2k33177
add a comment |Â
add a comment |Â
up vote
4
down vote
Well, in India some of the topics you mentioned above are already being taught at high school level, infact they are necessary for students who want to become future engineers. You can check out the JEE-MAINS syllabus India(earlier known as IIT-JEE).
Edit:
link to syllabus - look at page 23 for required topics for mathematics
edited Aug 29 at 17:53
casualcoder
1032
answered Aug 29 at 6:24
Divyansh
411
3
Welcome to matheducators.se. The answer would be improved by adding a link to the syllabus.
– Tommi Brander
Aug 29 at 6:58
add a comment |Â
up vote
4
down vote
Well, in India some of the topics you mentioned above are already being taught at high school level, infact they are necessary for students who want to become future engineers. You can check out the JEE-MAINS syllabus India(earlier known as IIT-JEE).
Edit:
link to syllabus - look at page 23 for required topics for mathematics
edited Aug 29 at 17:53
casualcoder
1032
answered Aug 29 at 6:24
Divyansh
411
3
Welcome to matheducators.se. The answer would be improved by adding a link to the syllabus.
– Tommi Brander
Aug 29 at 6:58
add a comment |Â
up vote
4
down vote
up vote
4
down vote
Well, in India some of the topics you mentioned above are already being taught at high school level, infact they are necessary for students who want to become future engineers. You can check out the JEE-MAINS syllabus India(earlier known as IIT-JEE).
Edit:
link to syllabus - look at page 23 for required topics for mathematics
edited Aug 29 at 17:53
casualcoder
1032
answered Aug 29 at 6:24
Divyansh
411
Well, in India some of the topics you mentioned above are already being taught at high school level, infact they are necessary for students who want to become future engineers. You can check out the JEE-MAINS syllabus India(earlier known as IIT-JEE).
Edit:
link to syllabus - look at page 23 for required topics for mathematics
edited Aug 29 at 17:53
casualcoder
1032
answered Aug 29 at 6:24
Divyansh
411
edited Aug 29 at 17:53
casualcoder
1032
edited Aug 29 at 17:53
casualcoder
1032
edited Aug 29 at 17:53
casualcoder
1032
1032
answered Aug 29 at 6:24
Divyansh
411
answered Aug 29 at 6:24
Divyansh
411
answered Aug 29 at 6:24
Divyansh
411
411
3
Welcome to matheducators.se. The answer would be improved by adding a link to the syllabus.
– Tommi Brander
Aug 29 at 6:58
add a comment |Â
3
Welcome to matheducators.se. The answer would be improved by adding a link to the syllabus.
– Tommi Brander
Aug 29 at 6:58
3
3
Welcome to matheducators.se. The answer would be improved by adding a link to the syllabus.
– Tommi Brander
Aug 29 at 6:58
Welcome to matheducators.se. The answer would be improved by adding a link to the syllabus.
– Tommi Brander
Aug 29 at 6:58
add a comment |Â
up vote
3
down vote
In the UK, some students take A-Level Further Mathematics, which covers bits of linear algebra (determinants, solving and interpreting systems of 3 linear equations, possibly also eigenvalues and eigenvectors and diagonalizing matrices) and some simple first and second order ODEs.
It also gives students the option to study some elementary group theory (the definition of a group, basic examples, and Lagrange's Theorem) and elementary number theory (Euclidean algorithm, modular arithmetic, solving congruence equations).
One syllabus can be found here.
answered Aug 29 at 11:50
rbird
31829
add a comment |Â
up vote
3
down vote
In the UK, some students take A-Level Further Mathematics, which covers bits of linear algebra (determinants, solving and interpreting systems of 3 linear equations, possibly also eigenvalues and eigenvectors and diagonalizing matrices) and some simple first and second order ODEs.
It also gives students the option to study some elementary group theory (the definition of a group, basic examples, and Lagrange's Theorem) and elementary number theory (Euclidean algorithm, modular arithmetic, solving congruence equations).
One syllabus can be found here.
answered Aug 29 at 11:50
rbird
31829
add a comment |Â
up vote
3
down vote
up vote
3
down vote
In the UK, some students take A-Level Further Mathematics, which covers bits of linear algebra (determinants, solving and interpreting systems of 3 linear equations, possibly also eigenvalues and eigenvectors and diagonalizing matrices) and some simple first and second order ODEs.
It also gives students the option to study some elementary group theory (the definition of a group, basic examples, and Lagrange's Theorem) and elementary number theory (Euclidean algorithm, modular arithmetic, solving congruence equations).
One syllabus can be found here.
answered Aug 29 at 11:50
rbird
31829
In the UK, some students take A-Level Further Mathematics, which covers bits of linear algebra (determinants, solving and interpreting systems of 3 linear equations, possibly also eigenvalues and eigenvectors and diagonalizing matrices) and some simple first and second order ODEs.
It also gives students the option to study some elementary group theory (the definition of a group, basic examples, and Lagrange's Theorem) and elementary number theory (Euclidean algorithm, modular arithmetic, solving congruence equations).
One syllabus can be found here.
answered Aug 29 at 11:50
rbird
31829
answered Aug 29 at 11:50
rbird
31829
answered Aug 29 at 11:50
rbird
31829
answered Aug 29 at 11:50
rbird
31829
31829
add a comment |Â
add a comment |Â
up vote
2
down vote
If you want to teach more advanced courses and have sufficient students, I would advise 3rd semester calc, or ODEs. The reason is these are all "no regrets" moves from the student point of view. Pretty much any hard science, math or engineering will require them.
Abstract algebra is only required for math students which is a tiny tiny percentage of your class population (with undeclared major high school students). Just because they are good or advanced in math do not assume they will become math majors. Common sense and personal experience and statistic should show that most will go into engineering or chemistry or physics or the like.
Linear algebra is not a bad choice either, especially if it is one with emphasis on matrices and calculation (not proofs). For one thing, it is an easier course than 3rd sem calc or ODEs. (Perhaps important for kids who already feel they are essentially doing an elective.) It won't be as central for engineers or physicists (most don't have a semester requirement, just pick up a little in midst of engine math class). But it will be more central and required for comp sci students.
Maybe do the LA because of the easiness and serving the future comp sci students. It won't hurt the engineers either. Plus it will appeal to you more. At least it is algebra even if not abstract.
answered Aug 30 at 11:28
guest
2974
Elementary differential geometry seems very good.
– inéquation
Aug 30 at 15:10
I took linear algebra, it was easily my favorite course. However, I was sad that when it was over and we didn't get to cover the 'interesting' subjects such as normal forms and orthogonal basis as much.
– Lenny
Aug 30 at 17:41
add a comment |Â
up vote
2
down vote
If you want to teach more advanced courses and have sufficient students, I would advise 3rd semester calc, or ODEs. The reason is these are all "no regrets" moves from the student point of view. Pretty much any hard science, math or engineering will require them.
Abstract algebra is only required for math students which is a tiny tiny percentage of your class population (with undeclared major high school students). Just because they are good or advanced in math do not assume they will become math majors. Common sense and personal experience and statistic should show that most will go into engineering or chemistry or physics or the like.
Linear algebra is not a bad choice either, especially if it is one with emphasis on matrices and calculation (not proofs). For one thing, it is an easier course than 3rd sem calc or ODEs. (Perhaps important for kids who already feel they are essentially doing an elective.) It won't be as central for engineers or physicists (most don't have a semester requirement, just pick up a little in midst of engine math class). But it will be more central and required for comp sci students.
Maybe do the LA because of the easiness and serving the future comp sci students. It won't hurt the engineers either. Plus it will appeal to you more. At least it is algebra even if not abstract.
answered Aug 30 at 11:28
guest
2974
Elementary differential geometry seems very good.
– inéquation
Aug 30 at 15:10
I took linear algebra, it was easily my favorite course. However, I was sad that when it was over and we didn't get to cover the 'interesting' subjects such as normal forms and orthogonal basis as much.
– Lenny
Aug 30 at 17:41
add a comment |Â
up vote
2
down vote
up vote
2
down vote
If you want to teach more advanced courses and have sufficient students, I would advise 3rd semester calc, or ODEs. The reason is these are all "no regrets" moves from the student point of view. Pretty much any hard science, math or engineering will require them.
Abstract algebra is only required for math students which is a tiny tiny percentage of your class population (with undeclared major high school students). Just because they are good or advanced in math do not assume they will become math majors. Common sense and personal experience and statistic should show that most will go into engineering or chemistry or physics or the like.
Linear algebra is not a bad choice either, especially if it is one with emphasis on matrices and calculation (not proofs). For one thing, it is an easier course than 3rd sem calc or ODEs. (Perhaps important for kids who already feel they are essentially doing an elective.) It won't be as central for engineers or physicists (most don't have a semester requirement, just pick up a little in midst of engine math class). But it will be more central and required for comp sci students.
Maybe do the LA because of the easiness and serving the future comp sci students. It won't hurt the engineers either. Plus it will appeal to you more. At least it is algebra even if not abstract.
answered Aug 30 at 11:28
guest
2974
If you want to teach more advanced courses and have sufficient students, I would advise 3rd semester calc, or ODEs. The reason is these are all "no regrets" moves from the student point of view. Pretty much any hard science, math or engineering will require them.
Abstract algebra is only required for math students which is a tiny tiny percentage of your class population (with undeclared major high school students). Just because they are good or advanced in math do not assume they will become math majors. Common sense and personal experience and statistic should show that most will go into engineering or chemistry or physics or the like.
Linear algebra is not a bad choice either, especially if it is one with emphasis on matrices and calculation (not proofs). For one thing, it is an easier course than 3rd sem calc or ODEs. (Perhaps important for kids who already feel they are essentially doing an elective.) It won't be as central for engineers or physicists (most don't have a semester requirement, just pick up a little in midst of engine math class). But it will be more central and required for comp sci students.
Maybe do the LA because of the easiness and serving the future comp sci students. It won't hurt the engineers either. Plus it will appeal to you more. At least it is algebra even if not abstract.
answered Aug 30 at 11:28
guest
2974
answered Aug 30 at 11:28
guest
2974
answered Aug 30 at 11:28
guest
2974
answered Aug 30 at 11:28
guest
2974
2974
Elementary differential geometry seems very good.
– inéquation
Aug 30 at 15:10
I took linear algebra, it was easily my favorite course. However, I was sad that when it was over and we didn't get to cover the 'interesting' subjects such as normal forms and orthogonal basis as much.
– Lenny
Aug 30 at 17:41
add a comment |Â
Elementary differential geometry seems very good.
– inéquation
Aug 30 at 15:10
I took linear algebra, it was easily my favorite course. However, I was sad that when it was over and we didn't get to cover the 'interesting' subjects such as normal forms and orthogonal basis as much.
– Lenny
Aug 30 at 17:41
Elementary differential geometry seems very good.
– inéquation
Aug 30 at 15:10
Elementary differential geometry seems very good.
– inéquation
Aug 30 at 15:10
I took linear algebra, it was easily my favorite course. However, I was sad that when it was over and we didn't get to cover the 'interesting' subjects such as normal forms and orthogonal basis as much.
– Lenny
Aug 30 at 17:41
I took linear algebra, it was easily my favorite course. However, I was sad that when it was over and we didn't get to cover the 'interesting' subjects such as normal forms and orthogonal basis as much.
– Lenny
Aug 30 at 17:41
add a comment |Â
3
Yes. In fact, these should be required for graduation :)
– James S. Cook
Aug 29 at 0:59
9
What's the situation and goal here? Do you actually have a class's worth of students who are interested? A single student who wants a tutor? Idle speculation?
– Adam
Aug 29 at 1:08
6
Virtually anything can be taught at school level if you simplify the material enough. What constitutes knowing a particular subject is a more important question to ask. Also, note that teaching a basic version could negatively impact students if they take a fuller course later, as students have been shown to do worse on material they think they already know.
– Jessica B
Aug 29 at 5:48
3
In high school I took AP Calculus AB/BC, which covered single-variable calculus and the like, and a higher-level IB course that touched on some early aspects of linear algebra. Those were equivalent to first-year undergraduate math courses at the university I did my undergrad.
– JAB
Aug 29 at 6:15
1
In India the ncert (national council of educational research and training) has provided a syllabus in which they suggest topics of upto differential equations for highschool, but keep in mind that India is a country where sciences and math are highly stressed as important and thus would have different standards to other countries which may have a more holistic approach to education.
– casualcoder
Aug 29 at 7:35