# Differential Equations or Number Theory for Computer Science?

• sschmiggles
In summary, the conversation is about the speaker's upcoming course selection for the fall semester. They are considering taking either differential equations or number theory and are seeking advice on which would be more beneficial for their career, specifically in the field of scientific research. The speaker mentions their interest in computer science and their potential future job in a company that does scientific research. They also mention enjoying their current math class, Linear Algebra, and its practical applications. The other person in the conversation suggests differential equations as it is more useful for science, while acknowledging that number theory has applications in computer science, particularly in cryptography.
sschmiggles
I'm getting ready to register for classes for the fall. To make a long story short, I might have to take another math class to satisfy a degree requirement, rather than a computer science class.

I'm taking Linear Algebra right now. I enjoy it, and it seems to have a lot of practical applications.

Next semester, I have two options: differential equations or number theory. Which do you think would be a better choice for my career, in terms of building a knowledge base? I'd like to work for a company that does a lot of scientific research. I don't mind writing code for business or anything like that, but I'm really interested in science. Differential equations would strike me as more useful for science.

Number theory seems more like pure mathematics. On the other hand, that might help me understand a lot of computer science concepts better.

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I doubt either of them are going to matter very much past school but I would suggest diff. eq. since the first course on number theory is usually doing some useless things such as finding the number of solutions for $$x^3 + y^3 = z^3$$ and seeing if 23458623786487236483 is divisible by 9.

sschmiggles said:
Next semester, I have two options: differential equations or number theory. Which do you think would be a better choice for my career, in terms of building a knowledge base?
Number theory is pretty applicable to upper division computer science courses such as cryptography, or theoretical computer science.

I don't know much about diff. eq...still need to take it. As Math Warrior said, though, number theory has a fair number of computational applications--RSA public-key cryptography, integer factorization, primality testing.

As a scientist, my opinion would be to take differential equations. While number theory may have some applications in computer science, differential equations are widely used in various fields of science, including physics, engineering, and biology. They are essential for modeling and solving complex systems and can also be applied to computer science problems such as optimization and machine learning.

Furthermore, many companies that conduct scientific research value employees with a strong background in mathematics, particularly differential equations. It shows that you have the ability to think critically and solve complex problems, which are highly sought after skills in the scientific industry.

That being said, number theory can also be beneficial in understanding certain computer science concepts, particularly in the field of cryptography. It may also be useful in certain research projects, but for a more well-rounded and practical knowledge base, I would recommend differential equations.

Ultimately, the decision should be based on your personal interests and career goals. If you are more interested in pursuing a career in pure mathematics or theoretical computer science, then number theory may be the better choice for you. However, if you are interested in applying mathematics to real-world problems and working in scientific research, then differential equations would be the more practical option.

## 1. What is the difference between differential equations and number theory in computer science?

Differential equations deal with the relationships between variables and their rates of change, while number theory focuses on the properties of numbers and their relationships. In computer science, differential equations are often used to model dynamic systems, while number theory is used for cryptography and data encryption.

## 2. How are differential equations and number theory used in computer science?

Differential equations are used to model and analyze complex systems such as weather patterns, population dynamics, and physical processes. Number theory is used in cryptography and data encryption to ensure secure communication and protect sensitive information.

## 3. Can you give an example of how differential equations are used in computer science?

One example is the use of differential equations in machine learning algorithms. These equations are used to model and predict patterns in data, allowing computers to learn and make decisions based on the data.

## 4. How does number theory apply to computer science?

Number theory is an important part of computer science, particularly in the field of cryptography. It is used to develop algorithms for data encryption and decryption, as well as to test the security of these algorithms.

## 5. Are differential equations and number theory difficult to understand for non-mathematicians?

Like any other mathematical concept, differential equations and number theory can be challenging for non-mathematicians. However, with proper explanation and understanding, anyone can grasp the basic concepts and their applications in computer science.

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