# Taking PDE or abstract algebra

• quasar987
In summary: I think being required to take a PDE course is a good thing. It makes you really understand the underlying math and how it applies to physics.
quasar987
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In my uni I am forced to make a painful choice btw taking PDE or abstract algebra. I will take algebra, but I'd like to know what I will be missing?

What is being taught in this class exactly? (BESIDES HOW TO SOLVE A PDE BY SEPARATION OF VARIABLES )

what is pde

I think it depends on what your academic/career goals are. In a Partial Differential Equations class, you'll probably cover Laplace Transforms and Fourier Series in addition to separation of variables. At least that's what I remember from that class.

Isn't abstract algebra something you could self-study?

I think Jamesrc is right. We covered both Laplace and Fourier and separation of variables. We concentrated on a lot of applications in my PDE class (wave equation, heat equation, membrane vibrations etc...).

"Equation of the first order and secod order, caracteristic and classification, elliptic equations : laplace & poisson. wave equation, heat equation. Introduction to distributions and Green functions."

How important are Green functions and distributions and what is an elliptic equation?

Overall this looks like easily self-studiable stuff (contrary to the dense and fundamental group theory! I tried to self-study it last summer bu it was rough without the guidance of a prof.)P.S. PDE=Partial Differential Equations

A course in PDE's is more important to the education of a physicist than a course in abstract algebra. Almost every equation you solve as a physicist can be solved using those techniques. Unless you are going to be a mathematical physicist, you shouldn't need abstract algebra.

FredGarvin said:
I think Jamesrc is right. We covered both Laplace and Fourier and separation of variables. We concentrated on a lot of applications in my PDE class (wave equation, heat equation, membrane vibrations etc...).

You had to take PDE at LTU? It is not required anymore.

Fourier analysis is usually a big part of a PDE course. I'm suprised a PDE course isn't required for the Physics degree, or at least strongly recommended.

god that's all it takes to get a physics near you? i am required to take both those courses, plus another course dealing with method of characterisics and more advanced DE's... ugh

Daverz said:
Fourier analysis is usually a big part of a PDE course. I'm suprised a PDE course isn't required for the Physics degree, or at least strongly recommended.

We we have a course called "Applied analysis" instead, where we see Fourier series, Fourier integrals, Sturm-Liouville theory and special functions at the level of a real analysis class.

## 1. What is PDE?

PDE stands for Partial Differential Equations. It is a branch of mathematics that deals with equations involving multiple variables and their partial derivatives. PDEs are used to model various phenomena in physics, engineering, and other fields.

## 2. What is abstract algebra?

Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. These structures are defined by a set of elements and operations, and abstract algebra focuses on their properties and relationships.

## 3. How are PDE and abstract algebra related?

PDE and abstract algebra are both areas of mathematics that involve the study of equations and their solutions. In particular, PDEs can be solved using techniques from abstract algebra, such as group theory and linear algebra.

## 4. Why is taking PDE or abstract algebra important?

Both PDE and abstract algebra are fundamental areas of mathematics that have applications in various fields such as physics, engineering, and computer science. They also help develop critical thinking and problem-solving skills that are useful in many areas of life.

## 5. Is PDE or abstract algebra more difficult?

This is subjective and depends on individual strengths and interests. Some may find PDE more challenging due to its use of advanced calculus and differential equations, while others may struggle with the abstract concepts in algebra. It is best to try both and see which one suits your strengths and interests better.

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