Number theory or intro to topology for comp sci/math

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SUMMARY

The discussion centers on the decision between taking an introductory course in topology versus number theory for a dual degree in mathematics and computer science, particularly with a focus on scientific computing. Participants highlight that number theory is relevant for encryption and security, while topology is considered essential for a well-rounded mathematical education. However, topology may not directly contribute to scientific computing applications. Ultimately, the choice depends on the individual's career goals and interests in computational complexity and algorithms.

PREREQUISITES
  • Understanding of computational complexity and P=NP? concepts
  • Familiarity with encryption and security principles
  • Basic knowledge of topology and its significance in mathematics
  • Awareness of scientific computing applications and related coursework
NEXT STEPS
  • Research the applications of number theory in encryption algorithms
  • Explore the fundamentals of topology and its relevance in mathematics
  • Investigate the implications of P=NP? in computational theory
  • Examine the role of topology in advanced computational science
USEFUL FOR

Students pursuing dual degrees in mathematics and computer science, particularly those interested in scientific computing, encryption, and foundational mathematical concepts.

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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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.
 

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