I think I have a weak formal education in mathematics

In summary, the conversation discusses the concept of restrictions on variables in equations and functions. The first equation includes an inequality that explicitly gives the domain of the function, while the second equation has an implied restriction. The conversation also touches on the importance of having a solid understanding of mathematics and asks for book recommendations to improve this understanding.
  • #1
xorg
15
0
For example:
$$ y^{2} = 25- x^{2} $$
$$ y = \sqrt{25- x^{2}} , -5\leq x\leq 5 $$

This part: $$ , -5\leq x\leq 5 $$

What is the name of this?If it were a function, it would be the domain. And for equations, and resolutions of equations, what is the name?

Other example, the equation:
xy = 1

It would restriction X ∈ ℝ
However, if x ≠ 0 then
y =1/x, x ≠ 0

But then returning to the above equation,
xy = 1, It seems that it would have to have the same restriction x ≠ 0 and not X ∈ ℝ In order to have consistency.

What is the purpose of this topic?
I showed some examples of how I do not have a solid background. I'm not convinced of what I am doing. And I'm not sure how to improve it, but I really want.

Can anyone recommend books to form a solid foundation in mathematics, to feel peaceful with, for example, above questions?
 
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  • #2
xorg said:
For example:
$$ y^{2} = 25- x^{2} $$
$$ y = \sqrt{25- x^{2}} , -5\leq x\leq 5 $$

This part: $$ , -5\leq x\leq 5 $$

What is the name of this?If it were a function, it would be the domain. And for equations, and resolutions of equations, what is the name?
The inequality indicates a restriction on the values of x. If you view y as being a function of x, the inequality explicitly gives the domain. Whether the inequality is present or not, the domain of the function is still ##-5 \le x \le 5##.
Note that the second equation about is not equivalent to the first equation - their graphs are different.
xorg said:
Other example, the equation:
xorg said:
xy = 1

It would restriction X ∈ ℝ
However, if x ≠ 0 then
y =1/x, x ≠ 0

But then returning to the above equation,
xy = 1, It seems that it would have to have the same restriction x ≠ 0 and not X ∈ ℝ In order to have consistency.
The graphs of the equation xy = 1 and y = 1/x are identical. For the equation xy = 1 there is an implied restriction that x cannot equal 0.
xorg said:
What is the purpose of this topic?
I showed some examples of how I do not have a solid background. I'm not convinced of what I am doing. And I'm not sure how to improve it, but I really want.

Can anyone recommend books to form a solid foundation in mathematics, to feel peaceful with, for example, above questions?
 

Related to I think I have a weak formal education in mathematics

1. What is considered a weak formal education in mathematics?

A weak formal education in mathematics is typically defined as having a limited understanding and knowledge of basic mathematical concepts, such as arithmetic, algebra, geometry, and calculus. This may include struggling with problem-solving, lack of confidence in mathematical abilities, and difficulty applying math to real-life situations.

2. How can I tell if I have a weak formal education in mathematics?

There are a few signs that may indicate a weak formal education in mathematics, such as consistently struggling with math problems, feeling overwhelmed or anxious when faced with math tasks, and having a lower than average grade in math courses. Additionally, if you have not taken any math courses beyond the basic level, this may also suggest a weak formal education in mathematics.

3. Can a weak formal education in mathematics be improved?

Yes, a weak formal education in mathematics can be improved with dedication and practice. It may take some time and effort, but with the right resources and support, anyone can improve their math skills. This may include seeking extra help from a tutor, joining a study group, or utilizing online resources and practice problems.

4. Will a weak formal education in mathematics limit my career options?

While having a strong foundation in mathematics is beneficial for many careers, a weak formal education in mathematics does not necessarily limit your career options. Many careers offer training and on-the-job learning opportunities to improve math skills. Additionally, there are also careers that do not require a strong math background, such as writing, art, or social sciences.

5. How can I overcome my weak formal education in mathematics?

To overcome a weak formal education in mathematics, it is important to identify your specific areas of weakness and focus on improving them. This may involve seeking help from a tutor or mentor, practicing regularly, and using a variety of resources to better understand mathematical concepts. It is also important to have a positive attitude and not be afraid to make mistakes, as learning from them is an essential part of improving math skills.

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