What college classes cover hypercubes and topology?

In summary, there are various college classes that could include the learning of tesseracts, such as advanced calculus, differential geometry, and topology of manifolds. The only class where tesseracts were explicitly mentioned was an advanced group theory class. However, some calculus textbooks also discuss hyperspheres and cubes. While these topics may seem like pure mathematical exercises, they have real-world applications, particularly in the context of triple integrals.
  • #1
Andrewjh07
8
0
Have been reading up on tesseracts lately and I was wondering what class in college if any include the learning of these. Was thinking it would be a physics class of some sort but at the same time it could be a math class too.
 
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  • #2
Higher dimensional geometry or just a standard advanced geometry class.
 
  • #3
We were studying hypervolumes and stuff in calc 3, actually.
 
  • #4
Hmmm, this depends really. A lot of math classes will give you the tools to handle hypercubes, but they will rarely ever mention it.
Some classes that could be useful are:
- advanced calculus
- differential geometry (for hyperspheres and stuff)
- topology of manifolds, algebraic topology

The only class where hypercubes and stuff were explicitely mentioned and studied was a class called "advanced group theory". The idea there was to describe a certain n-dimensional shape by studying its reflection group. The theory then moves on to Coxeter diagrams and the like. It's extremely interesting, but I don't know if that is what you're looking for?

What kind of study do you want to do on hypercubes?
 
  • #5
Hhmm, I don't remember doing hyper-stuff in Calc 3, its been awhile since I took it. Ill have to look around for that book and see if anything is inside that is of value. All of these classes sound like high 300-400 level math classes, so unfortunately I wouldn't ever be able to take unless I tried to double major in math. I only got up to Lin. Algebra. :frown:
 
  • #6
Some calculus textbook will include some discussions on hypersphere, cube etc. I get the impression that they are pure mathematical exercise with no real world applications.
 
  • #7
We touched on them in Discrete Math.
 
  • #8
kingkong11 said:
Some calculus textbook will include some discussions on hypersphere, cube etc. I get the impression that they are pure mathematical exercise with no real world applications.

Maybe y'all are talking about something else (I get that distinct impression in this thread), but any time you have a triple integral, it can be described in terms of a four-dimensional geometric object, or a hyperobject. These have loads of applications.
 
  • #9
micromass said:
- topology of manifolds, algebraic topology
Definitely topology :)
 

1. What is a hypercube?

A hypercube is a geometric shape that exists in higher dimensions, similar to how a cube exists in three dimensions. It is also known as a tesseract and is made up of eight cubes connected by their faces.

2. How are hypercubes used in a college class?

Hypercubes are used in various mathematical and scientific fields, such as geometry, topology, and computer science. They are often used as a visual representation of higher dimensional concepts and can help students better understand these abstract concepts.

3. What are some real-world applications of hypercubes?

Hypercubes have been used in the design of computer algorithms, data compression techniques, and even in the study of the human brain. They can also be found in the design of certain buildings and sculptures.

4. How do you calculate the volume of a hypercube?

The formula for calculating the volume of a hypercube is V = s^n, where s is the length of one side and n is the number of dimensions. For example, the volume of a 4-dimensional hypercube with a side length of 5 units would be 5^4 = 625 units cubed.

5. Can you visualize a hypercube?

It can be difficult for our brains to imagine objects in more than three dimensions, but there are various techniques and computer simulations that can help us visualize hypercubes. One common method is using projections or "shadows" of the hypercube onto a lower-dimensional space.

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