Math HL IA topic

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Hi guys, I'm about to submit my IA idea for math and I just want a few pieces of advice choosing one.

Currently, I'm very much interested in cryptography and machine learning which are the topics that I want to do my Math IA on, are these viable ideas? Earlier when I talked to my teacher, he said that writing about the Global Positioning System (GPS) would be a great idea, but I'd much prefer the other two topics. What should I do to ensure that I get a high grade while doing something that I actually enjoy?

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In my opinion (as a Math HL student who also wrote his EE in math) I think the most important thing is for you to choose a topic that you're interested in. It's much easier to show personal engagement that way and when writing a conclusion you can talk about why it's relevant and why you think it's interesting. If you're not interested it's hard to talk about that. If you're interested in cryptography and machine learning you should definitely do that. I cannot stress how important it is to be passionate about the topic you're exploring.

I actually did my Math IA on celestial navigation, which is basically GPS. I found it to be interesting but if you're not interested I can imagine it would be difficult to pursue this topic. (I ended up using simultaneous plane equations and polar coordinates )

Cryptography has connections to discrete mathematics (especially prime numbers), one of the Math HL options. Perhaps that is something you could look into if you're interested in writing about this topic? The math is definitely within the scope of Math HL...

Best of luck with your IA!

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Thank you so much for your reply Kaito! I'm so sorry what I meant were cryptocurrency and the blockchain technology instead of cryptography, I did look into cryptography though (e.g. the RSA cryptosystem, symmetric encryption,...) and proposed that idea to my maths teacher, however, he said that the mathematics was too simple for a Math IA and would score rather poorly on Criterion E. I was thinking of machine learning, in particular, neural networks and deep learning, but I don't know if this is a viable option for the IA.

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1 minute ago, deanbrok said:

Thank you so much for your reply Kaito! I'm so sorry what I meant were cryptocurrency and the blockchain technology instead of cryptography, I did look into cryptography though (e.g. the RSA cryptosystem, symmetric encryption,...) and proposed that idea to my maths teacher, however, he said that the mathematics was too simple for a Math IA and would score rather poorly on Criterion E. I was thinking of machine learning, in particular, neural networks and deep learning, but I don't know if this is a viable option for the IA.

To be honest, I have no idea how either cryptography or blockchain technology works so I can't give you any advice on that. However, I recommend that you find a way to clearly link the mathematics behind your topic to part of the Math HL syllabus (or one of the options). If you are able to clearly identify the link and present it there shouldn't be any problem.

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Ok, thank you for the advice!

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Just now, deanbrok said:

Ok, thank you for the advice!

No problem!

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• 3 years later...
On 4/13/2018 at 3:40 AM, Kaito said:

In my opinion (as a Math HL student who also wrote his EE in math) I think the most important thing is for you to choose a topic that you're interested in. It's much easier to show personal engagement that way and when writing a conclusion you can talk about why it's relevant and why you think it's interesting. If you're not interested it's hard to talk about that. If you're interested in cryptography and machine learning you should definitely do that. I cannot stress how important it is to be passionate about the topic you're exploring.

I actually did my Math IA on celestial navigation, which is basically GPS. I found it to be interesting but if you're not interested I can imagine it would be difficult to pursue this topic. (I ended up using simultaneous plane equations and polar coordinates )

Cryptography has connections to discrete mathematics (especially prime numbers), one of the Math HL options. Perhaps that is something you could look into if you're interested in writing about this topic? The math is definitely within the scope of Math HL...

Best of luck with your IA!

Hi, I am currently thinking of Math HL IA ideas and GPS sounds really interesting to me. Can you tell me more about what you did for your IA? Thank you!

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On 5/25/2021 at 11:43 AM, BonnieW said:

Hi, I am currently thinking of Math HL IA ideas and GPS sounds really interesting to me. Can you tell me more about what you did for your IA? Thank you!

I'd love to tell you more about the topic and my IA and I could even send a copy of it if the IBO and your school both allow it. If you want specific help with the topic feel free to message me and I can even provide some quick online tutoring on the topic if you would like. I'm going to look for my Math IA, I know I have it saved somewhere but it's been a couple of years so I don't remember everything. Here's what I remember.

Basically the way navigation works is you have 3 celestial objects, usually stars or in the case of GPS, satellites, and you are able to measure angles and find your position based on your distance to the projection of 3 different points on the Earth, assumed to be a perfect sphere.

I don't think this vector projection was covered in Math HL in IB and the syllabus has probably changed anyway since I graduated so I'm going to explain vector projection briefly. You can think of it as a shadow. An example of vector projection used in both Math SL and Math HL would be projecting a vector onto the x axis using cos(θ) and y axis using sin(θ). You can take a 3D object and its shadow on the ground is a projection of that 3D object onto a 2D surface. Similarly, you need to project the position of a star in longitude and latitude onto the Earth, a sphere. This point is defined such that if you were at that point and looked straight up you would be directly underneath the star. You can draw a line from the center of the earth to the star and this point is the intersection of that imaginary line and the surface of the Earth.

You start by measuring the altitude of a star. If I recall correctly that is the angle between the horizon and the star. This is not the same as height, it is an angle. You can look up the positions of stars in longitude and latitude at any time and date in specific books containing such data. When you measure the altitude and know the star's position on Earth, you can calculate your distance to that point on the sphere, using longitude and latitude. (Technically it's the projection of the star onto the Earth's surface but saying "the star's position on Earth" is easier and more intuitive).

Once again, we are dealing with angles and not straight lines since the Earth is a sphere. You need to do this with three stars and your end result will (hopefully) consist of 3 circles defined by the stars' positions on Earth (measured using 2 angles, longitude and latitude) and your distance to the stars (an angle derived from the altitude). Your position is the point where all 3 of these circles intersect. It's worth mentioning that these aren't regular circles, they are circles projected onto the surface of a sphere, measure in angles from the center. You can represent these circular projections in several ways including polar coordinates and planes.

Things can get difficult here depending on your approach and I don't remember exactly how I did it but you can take a plane and have it intersect a sphere. The points of intersection form a circle, much like the circles you would get from these calculations. This means that each circular projection that you use to measure distance from a star's position on Earth can be represented as a plane intersecting a sphere at an angle. You can model your circles as planes and solve them simultaneously using linear algebra. Alternatively you can look into using polar coordinates, you can probably skip the radius though so you would just need to represent the three circles using a few angles.

This last part can be a bit tricky and the exact method you use isn't important as long as you can represent these projected circles as equations and solve them simultaneously.

I'll try to provide a better answer once I've reread my IA. Feel free to contact me with any questions you may have.

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5 hours ago, Kaito said:

I'd love to tell you more about the topic and my IA and I could even send a copy of it if the IBO and your school both allow it. If you want specific help with the topic feel free to message me and I can even provide some quick online tutoring on the topic if you would like. I'm going to look for my Math IA, I know I have it saved somewhere but it's been a couple of years so I don't remember everything. Here's what I remember.

Basically the way navigation works is you have 3 celestial objects, usually stars or in the case of GPS, satellites, and you are able to measure angles and find your position based on your distance to the projection of 3 different points on the Earth, assumed to be a perfect sphere.

I don't think this vector projection was covered in Math HL in IB and the syllabus has probably changed anyway since I graduated so I'm going to explain vector projection briefly. You can think of it as a shadow. An example of vector projection used in both Math SL and Math HL would be projecting a vector onto the x axis using cos(θ) and y axis using sin(θ). You can take a 3D object and its shadow on the ground is a projection of that 3D object onto a 2D surface. Similarly, you need to project the position of a star in longitude and latitude onto the Earth, a sphere. This point is defined such that if you were at that point and looked straight up you would be directly underneath the star. You can draw a line from the center of the earth to the star and this point is the intersection of that imaginary line and the surface of the Earth.

You start by measuring the altitude of a star. If I recall correctly that is the angle between the horizon and the star. This is not the same as height, it is an angle. You can look up the positions of stars in longitude and latitude at any time and date in specific books containing such data. When you measure the altitude and know the star's position on Earth, you can calculate your distance to that point on the sphere, using longitude and latitude. (Technically it's the projection of the star onto the Earth's surface but saying "the star's position on Earth" is easier and more intuitive).

Once again, we are dealing with angles and not straight lines since the Earth is a sphere. You need to do this with three stars and your end result will (hopefully) consist of 3 circles defined by the stars' positions on Earth (measured using 2 angles, longitude and latitude) and your distance to the stars (an angle derived from the altitude). Your position is the point where all 3 of these circles intersect. It's worth mentioning that these aren't regular circles, they are circles projected onto the surface of a sphere, measure in angles from the center. You can represent these circular projections in several ways including polar coordinates and planes.

Things can get difficult here depending on your approach and I don't remember exactly how I did it but you can take a plane and have it intersect a sphere. The points of intersection form a circle, much like the circles you would get from these calculations. This means that each circular projection that you use to measure distance from a star's position on Earth can be represented as a plane intersecting a sphere at an angle. You can model your circles as planes and solve them simultaneously using linear algebra. Alternatively you can look into using polar coordinates, you can probably skip the radius though so you would just need to represent the three circles using a few angles.

This last part can be a bit tricky and the exact method you use isn't important as long as you can represent these projected circles as equations and solve them simultaneously.

I'll try to provide a better answer once I've reread my IA. Feel free to contact me with any questions you may have.

Thank you so much! I really appreciate the information though it does seem pretty complicated 😂. Would you mind if I ask what you scored on your final IA?

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• 3 weeks later...
On 5/27/2021 at 3:22 AM, BonnieW said:

Thank you so much! I really appreciate the information though it does seem pretty complicated 😂. Would you mind if I ask what you scored on your final IA?

Hey, sorry for the slow reply, I've been busy and almost forgot to reply. I don't actually know what I got on my Math IA but on my EE in math I got an A.

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53 minutes ago, Kaito said:

Hey, sorry for the slow reply, I've been busy and almost forgot to reply. I don't actually know what I got on my Math IA but on my EE in math I got an A.

By the way, I found my Math IA about celestial navigation so if anyone wants to read it just send me a message with an e-mail or some other preferred method of file transfer and I'll send a copy.

In case anyone was wondering, the elegantly worded IB-style title is:

Mathematics Exploration – How can celestial navigation be mathematically modeled to find one’s location on Earth when time and the position of celestial bodies are known?

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• 1 month later...
On 5/27/2021 at 4:13 AM, Kaito said:

I'd love to tell you more about the topic and my IA and I could even send a copy of it if the IBO and your school both allow it. If you want specific help with the topic feel free to message me and I can even provide some quick online tutoring on the topic if you would like. I'm going to look for my Math IA, I know I have it saved somewhere but it's been a couple of years so I don't remember everything. Here's what I remember.

Basically the way navigation works is you have 3 celestial objects, usually stars or in the case of GPS, satellites, and you are able to measure angles and find your position based on your distance to the projection of 3 different points on the Earth, assumed to be a perfect sphere.

I don't think this vector projection was covered in Math HL in IB and the syllabus has probably changed anyway since I graduated so I'm going to explain vector projection briefly. You can think of it as a shadow. An example of vector projection used in both Math SL and Math HL would be projecting a vector onto the x axis using cos(θ) and y axis using sin(θ). You can take a 3D object and its shadow on the ground is a projection of that 3D object onto a 2D surface. Similarly, you need to project the position of a star in longitude and latitude onto the Earth, a sphere. This point is defined such that if you were at that point and looked straight up you would be directly underneath the star. You can draw a line from the center of the earth to the star and this point is the intersection of that imaginary line and the surface of the Earth.

You start by measuring the altitude of a star. If I recall correctly that is the angle between the horizon and the star. This is not the same as height, it is an angle. You can look up the positions of stars in longitude and latitude at any time and date in specific books containing such data. When you measure the altitude and know the star's position on Earth, you can calculate your distance to that point on the sphere, using longitude and latitude. (Technically it's the projection of the star onto the Earth's surface but saying "the star's position on Earth" is easier and more intuitive).

Once again, we are dealing with angles and not straight lines since the Earth is a sphere. You need to do this with three stars and your end result will (hopefully) consist of 3 circles defined by the stars' positions on Earth (measured using 2 angles, longitude and latitude) and your distance to the stars (an angle derived from the altitude). Your position is the point where all 3 of these circles intersect. It's worth mentioning that these aren't regular circles, they are circles projected onto the surface of a sphere, measure in angles from the center. You can represent these circular projections in several ways including polar coordinates and planes.

Things can get difficult here depending on your approach and I don't remember exactly how I did it but you can take a plane and have it intersect a sphere. The points of intersection form a circle, much like the circles you would get from these calculations. This means that each circular projection that you use to measure distance from a star's position on Earth can be represented as a plane intersecting a sphere at an angle. You can model your circles as planes and solve them simultaneously using linear algebra. Alternatively you can look into using polar coordinates, you can probably skip the radius though so you would just need to represent the three circles using a few angles.

This last part can be a bit tricky and the exact method you use isn't important as long as you can represent these projected circles as equations and solve them simultaneously.

I'll try to provide a better answer once I've reread my IA. Feel free to contact me with any questions you may have.

can I hv a copy of your work pls? I will probably do similar topics as yours and I want a reference. thank you so much!

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5 hours ago, Alannaud said:

can I hv a copy of your work pls? I will probably do similar topics as yours and I want a reference. thank you so much!

Sure, if you send me a message including your e-mail I can send you a copy of my math IA and answer any questions you may have.

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• 3 weeks later...
On 8/8/2021 at 11:39 PM, Kaito said:

Sure, if you send me a message including your e-mail I can send you a copy of my math IA and answer any questions you may have.

Can I also have a copy of your work? Similar to Alannaud, I wanted a reference because I am really puzzled as to what I am supposed to do. Thank you in advance!

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On 8/24/2021 at 1:44 PM, tjpj970 said:

Can I also have a copy of your work? Similar to Alannaud, I wanted a reference because I am really puzzled as to what I am supposed to do. Thank you in advance!

Sure! If you don't mind, can you send me a private message with your e-mail address so I can send you a copy?

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6 hours ago, Kaito said:

Sure! If you don't mind, can you send me a private message with your e-mail address so I can send you a copy?

Hi! Can I also have a copy?? I'm interested in similar topics :)) thank you

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6 hours ago, jujd0839 said:

Hi! Can I also have a copy?? I'm interested in similar topics :)) thank you

Sure, I can't post my Math IA here but if you message me with your e-mail address I can send you a copy there.

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On 8/27/2021 at 4:32 PM, Kaito said:

Sure, I can't post my Math IA here but if you message me with your e-mail address I can send you a copy there.

HI!! can I have a copy? I sent a message.  thank you!!

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• 2 months later...
On 5/27/2021 at 8:13 AM, Kaito said:

I'd love to tell you more about the topic and my IA and I could even send a copy of it if the IBO and your school both allow it. If you want specific help with the topic feel free to message me and I can even provide some quick online tutoring on the topic if you would like. I'm going to look for my Math IA, I know I have it saved somewhere but it's been a couple of years so I don't remember everything. Here's what I remember.

Basically the way navigation works is you have 3 celestial objects, usually stars or in the case of GPS, satellites, and you are able to measure angles and find your position based on your distance to the projection of 3 different points on the Earth, assumed to be a perfect sphere.

I don't think this vector projection was covered in Math HL in IB and the syllabus has probably changed anyway since I graduated so I'm going to explain vector projection briefly. You can think of it as a shadow. An example of vector projection used in both Math SL and Math HL would be projecting a vector onto the x axis using cos(θ) and y axis using sin(θ). You can take a 3D object and its shadow on the ground is a projection of that 3D object onto a 2D surface. Similarly, you need to project the position of a star in longitude and latitude onto the Earth, a sphere. This point is defined such that if you were at that point and looked straight up you would be directly underneath the star. You can draw a line from the center of the earth to the star and this point is the intersection of that imaginary line and the surface of the Earth.

You start by measuring the altitude of a star. If I recall correctly that is the angle between the horizon and the star. This is not the same as height, it is an angle. You can look up the positions of stars in longitude and latitude at any time and date in specific books containing such data. When you measure the altitude and know the star's position on Earth, you can calculate your distance to that point on the sphere, using longitude and latitude. (Technically it's the projection of the star onto the Earth's surface but saying "the star's position on Earth" is easier and more intuitive).

Once again, we are dealing with angles and not straight lines since the Earth is a sphere. You need to do this with three stars and your end result will (hopefully) consist of 3 circles defined by the stars' positions on Earth (measured using 2 angles, longitude and latitude) and your distance to the stars (an angle derived from the altitude). Your position is the point where all 3 of these circles intersect. It's worth mentioning that these aren't regular circles, they are circles projected onto the surface of a sphere, measure in angles from the center. You can represent these circular projections in several ways including polar coordinates and planes.

Things can get difficult here depending on your approach and I don't remember exactly how I did it but you can take a plane and have it intersect a sphere. The points of intersection form a circle, much like the circles you would get from these calculations. This means that each circular projection that you use to measure distance from a star's position on Earth can be represented as a plane intersecting a sphere at an angle. You can model your circles as planes and solve them simultaneously using linear algebra. Alternatively you can look into using polar coordinates, you can probably skip the radius though so you would just need to represent the three circles using a few angles.

This last part can be a bit tricky and the exact method you use isn't important as long as you can represent these projected circles as equations and solve them simultaneously.

I'll try to provide a better answer once I've reread my IA. Feel free to contact me with any questions you may have.

Hey, I'm also quite interested in your IA, can you please sent it to me? I'll DM

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• 1 month later...
On 5/26/2021 at 2:13 PM, Kaito said:

I'd love to tell you more about the topic and my IA and I could even send a copy of it if the IBO and your school both allow it. If you want specific help with the topic feel free to message me and I can even provide some quick online tutoring on the topic if you would like. I'm going to look for my Math IA, I know I have it saved somewhere but it's been a couple of years so I don't remember everything. Here's what I remember.

Basically the way navigation works is you have 3 celestial objects, usually stars or in the case of GPS, satellites, and you are able to measure angles and find your position based on your distance to the projection of 3 different points on the Earth, assumed to be a perfect sphere.

I don't think this vector projection was covered in Math HL in IB and the syllabus has probably changed anyway since I graduated so I'm going to explain vector projection briefly. You can think of it as a shadow. An example of vector projection used in both Math SL and Math HL would be projecting a vector onto the x axis using cos(θ) and y axis using sin(θ). You can take a 3D object and its shadow on the ground is a projection of that 3D object onto a 2D surface. Similarly, you need to project the position of a star in longitude and latitude onto the Earth, a sphere. This point is defined such that if you were at that point and looked straight up you would be directly underneath the star. You can draw a line from the center of the earth to the star and this point is the intersection of that imaginary line and the surface of the Earth.

You start by measuring the altitude of a star. If I recall correctly that is the angle between the horizon and the star. This is not the same as height, it is an angle. You can look up the positions of stars in longitude and latitude at any time and date in specific books containing such data. When you measure the altitude and know the star's position on Earth, you can calculate your distance to that point on the sphere, using longitude and latitude. (Technically it's the projection of the star onto the Earth's surface but saying "the star's position on Earth" is easier and more intuitive).

Once again, we are dealing with angles and not straight lines since the Earth is a sphere. You need to do this with three stars and your end result will (hopefully) consist of 3 circles defined by the stars' positions on Earth (measured using 2 angles, longitude and latitude) and your distance to the stars (an angle derived from the altitude). Your position is the point where all 3 of these circles intersect. It's worth mentioning that these aren't regular circles, they are circles projected onto the surface of a sphere, measure in angles from the center. You can represent these circular projections in several ways including polar coordinates and planes.

Things can get difficult here depending on your approach and I don't remember exactly how I did it but you can take a plane and have it intersect a sphere. The points of intersection form a circle, much like the circles you would get from these calculations. This means that each circular projection that you use to measure distance from a star's position on Earth can be represented as a plane intersecting a sphere at an angle. You can model your circles as planes and solve them simultaneously using linear algebra. Alternatively you can look into using polar coordinates, you can probably skip the radius though so you would just need to represent the three circles using a few angles.

This last part can be a bit tricky and the exact method you use isn't important as long as you can represent these projected circles as equations and solve them simultaneously.

I'll try to provide a better answer once I've reread my IA. Feel free to contact me with any questions you may have.

Hi! If you do not mind could I plz have a copy of your IA ? It would be great to use it as a reference.

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