Number theory or intro to topology for comp sci/math

In summary, the individual is considering which course to take between intro to topology and number theory, with interests in computational complexity, physics engines, graphics engines, and other related topics. While number theory may be useful for encryption and security, topology is seen as a course that every math major should take for general knowledge, although it may not directly relate to scientific computing.
  • #1
Deneir
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I'm pursuing dual degrees in mathematics and computer science with a concentration in scientific computing and am trying to decide whether I should take intro to topology or number theory.

Interests in no order are computational complexity, P=NP?, physics engines, graphics engines, geometry, linear algebra, computational science, medical robotics, algorithms, etc. I've already taken or am planning to take any related courses. Any advice on which course might be more pertinent?
 
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  • #2
Number theory MIGHT be useful to you in encryption and security. But there are no guarantees, it depends on the course.

I feel, however, that every math major should take topology. It's one of the courses you should know for "general culture". I don't think it will be useful to scientific computing though.
 

1. What is number theory?

Number theory is a branch of mathematics that deals with the properties and relationships of numbers. It involves studying patterns and structures in numbers, as well as solving problems related to primes, divisibility, and modular arithmetic.

2. How is number theory related to computer science?

Number theory is closely related to computer science as it provides the foundation for many algorithms and cryptographic techniques used in computer security and data encryption. It also plays a role in coding theory and error-correcting codes.

3. What is topology in mathematics?

Topology is a branch of mathematics that studies the properties of spaces that are preserved under continuous deformations, such as stretching and bending. It involves studying the concepts of continuity, connectedness, and compactness.

4. How is topology relevant to computer science?

Topology has many applications in computer science, particularly in the field of data analysis and machine learning. It is used to study and analyze complex data sets, such as networks and graphs, by identifying patterns and relationships between different data points.

5. What are some real-world applications of number theory and topology?

Number theory and topology have many practical applications in fields such as cryptography, coding theory, computer security, data analysis, and machine learning. They are also used in various engineering and scientific fields, such as physics, chemistry, and biology, to model and analyze complex systems and structures.

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