Linear Algebra vs. Analysis: Which Should I Study First?

In summary, the conversation is about self-studying math and the question of whether to start with linear algebra or mathematical analysis. The speaker recommends having a strong foundation in linear algebra before attempting analysis and suggests studying Shilov's Elementary Real and Complex Analysis, Rosenlicht's Introduction to Analysis, or Apostol's Mathematical Analysis for analysis. The conversation also mentions that linear algebra is a big part of real analysis and is beneficial for getting used to rigorous mathematics.
  • #1
cordyceps
50
0
Hey guys,

I want to self-study some math this year. Would you recommend linear algebra or mathematical analysis first, or does it even make a difference? (If analysis, which text would you recommend? Shilov's Elementary Real and Complex Analysis, Rosenlicht's Introduction to Analysis, or Apostol's Mathematical Analysis?) Thanks a bunch.[/I]
 
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  • #2
Any real study of analysis requires a fair bit of linear algebra.
 
  • #3
What he means is have linear algebra down cold before you attempt to do analysis. Linear algebra is a big part of real analysis, especially once you deal with mutlivariables. Also, getting used to rigorous mathematics is best accomplished by studying linear algebra.
 
  • #4
Alright. I'll start working on LA then. Thanks a lot.
 
  • #5
thats like asking which is better, lafite roTHSCHILD OR LATour. those are all superb.
 

1. What is the difference between linear algebra and analysis?

Linear algebra is a branch of mathematics that deals with systems of linear equations and their properties. It involves the study of vectors, matrices, and linear transformations. Analysis, on the other hand, is a branch of mathematics that deals with limits, continuity, derivatives, and integrals. It is used to study functions and their properties.

2. Why is linear algebra important in science?

Linear algebra is important in science because it provides a framework for solving complex systems of equations. It is used in various fields such as physics, engineering, computer science, and economics to model and analyze real-world problems. Additionally, many machine learning and data analysis techniques rely on linear algebra.

3. What are some real-life applications of linear algebra?

Linear algebra has many real-life applications, including image and signal processing, cryptography, network analysis, and optimization problems. It is also used in computer graphics and animation, as well as in solving systems of equations in physics and engineering.

4. How does analysis help in understanding functions?

Analysis helps in understanding functions by studying their properties such as continuity, differentiability, and integrability. These concepts allow us to analyze the behavior of functions and make predictions about their values. Analysis also provides tools for approximating functions and finding their extrema.

5. Can linear algebra and analysis be used together?

Yes, linear algebra and analysis can be used together to solve problems in a variety of fields. For example, in physics, linear algebra is used to represent physical systems, while analysis is used to study their behavior. In optimization problems, linear algebra is used to model the problem, and analysis is used to find the optimal solution. Many other scientific applications also combine the use of linear algebra and analysis.

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