<|im_start|>system
You are a helpful AI assistant.<|im_end|>
<|im_start|>user
What is the difference between linear algebra, discrete math and analysis? Explain it to me as if only went to highschool.<|im_end|>
<|im_start|>assistant
I will try to explain them at a high school level: 

Linear algebra: Focuses on studying linear equations and linear functions. It deals with linear relationships and linear transformations between vectors and matrices. The core ideas are about lines, planes and linear functions. The tools are vectors, matrices and linear equations. It's about linear patterns and changes.

Discrete math: Focuses on mathematical structures that are fundamentally discrete, like integers, graphs, statements/logic, etc. Rather than continuous quantities, it deals with distinct/separate objects. It covers topics like combinatorics, graph theory, number theory, proofs and logic. It's about counting, ordering and logical reasoning with distinct objects, choices or conditions.

Analysis: Focuses on the study of continuity, change and limits. It deals with concepts like convergence, differentiation and integration for functions with real variables. The core ideas revolve around rates of change and accumulation of quantities. The tools are limits, derivatives and integrals. It's about analyzing patterns of continuous change.

So in short, linear algebra deals with linear patterns, discrete math deals with discrete structures, and analysis deals with continuous change. They have different areas of focus and different core tools, but can also be related to each other in some ways. Let me know if you need more details!<|im_end|>
<|im_start|>user
so, is Analysis a generalization of the other two ?<|im_end|>
<|im_start|>assistant
Yes, you can think of it that way. Analysis is a more general field that encompasses the core ideas of linear algebra and discrete math, but also deals with other topics like calculus and real analysis. While linear algebra and discrete math focus on specific topics and tools, analysis looks at a broader range of topics and ideas.<|im_end|>
<|im_start|>user
I can see the real use of linear algebra and discrete math, but I haven't really understood how Analysis is applied. Could you give me examples or explain to me why it is so important?<|im_end|>
<|im_start|>assistant
Analysis is used extensively in fields like physics and engineering to describe the behaviour of mechanical systems. Take for example the position of an object moving through space, dependent on time. You can describe the velocity of the object as the derivative of the position with respect to time. Conversely, if you know the velocity of an object at all points in time, you can get the position up to a constant as the integral of velocity. 

These kinds of relationships allow scientists to describe physical systems as the sets of constraints applying to it. Analysis then helps to construct the functions that describe the behaviour of all parameters in this system. 

Historically, calculus was developed by Newton and Leibnitz to describe the motion of planets in the solar system as the consequence of the sun's gravity and their own affecting each other.<|im_end|>